{"id":3791,"date":"2025-05-04T03:48:20","date_gmt":"2025-05-04T07:48:20","guid":{"rendered":"https:\/\/calculatorcch.com\/?page_id=3791"},"modified":"2025-05-04T04:00:06","modified_gmt":"2025-05-04T08:00:06","slug":"direct-and-inverse-variation-calculator","status":"publish","type":"page","link":"https:\/\/calculatorcch.com\/en\/education-and-study-calculators\/direct-and-inverse-variation-calculator\/","title":{"rendered":"Direct and Inverse Variation Calculator"},"content":{"rendered":"<p>[et_pb_section fb_built=\u201d1\u2033 custom_padding_last_edited=\u201don|desktop\u201d _builder_version=\u201d4.27.4\u2033 _module_preset=\u201ddefault\u201d background_color=\u201drgba(214,214,214,0.2)\u201d custom_margin_tablet=\u201d\u201d custom_margin_phone=\u201d\u201d custom_margin_last_edited=\u201don|phone\u201d custom_padding=\u201d0px||0px||false|false\u201d custom_padding_tablet=\u201d22px||22px||true|false\u201d custom_padding_phone=\u201d22px||22px||true|false\u201d bottom_divider_style=\u201dwaves2\u2033 bottom_divider_color=\u201d#0970C4\u2033 bottom_divider_height=\u201d37px\u201d bottom_divider_height_tablet=\u201d37px\u201d bottom_divider_height_phone=\u201d37px\u201d bottom_divider_height_last_edited=\u201don|desktop\u201d background_last_edited=\u201don|desktop\u201d global_colors_info=\u201d{}\u201d][et_pb_row _builder_version=\u201d4.27.4\u2033 _module_preset=\u201ddefault\u201d global_colors_info=\u201d{}\u201d][et_pb_column type=\u201d4_4\u2033 _builder_version=\u201d4.27.4\u2033 _module_preset=\u201ddefault\u201d global_colors_info=\u201d{}\u201d][et_pb_text _builder_version=\u201d4.27.4\u2033 _module_preset=\u201ddefault\u201d global_colors_info=\u201d{}\u201d]<\/p>\n<h1><b>Direct and Inverse Variation Calculator \u2013 Easily Find Proportional Relationships<\/b><\/h1>\n<p>[\/et_pb_text][et_pb_code _builder_version=\u201d4.27.4\u2033 _module_preset=\u201ddefault\u201d custom_margin=\u201d||0px||false|false\u201d custom_margin_tablet=\u201d||0px||false|false\u201d custom_margin_phone=\u201d||0px||false|false\u201d custom_margin_last_edited=\u201don|desktop\u201d custom_padding=\u201d||||false|false\u201d global_colors_info=\u201d{}\u201d]<\/p>\n<div class=\"roi-calculator-container\"><!-- [et_pb_line_break_holder] -->    <\/p>\n<h2 data-translate-key=\"titulo\">Direct and Inverse Variation Calculator<\/h2>\n<div class=\"form-group\"><!-- [et_pb_line_break_holder] -->        <label for=\"tipoVariacion\" data-translate-key=\"tipoVariacionLabel\">Type of Variation<\/label><!-- [et_pb_line_break_holder] -->        <select id=\"tipoVariacion\"><!-- [et_pb_line_break_holder] --><option value=\"directa\" data-translate-key=\"directaOpcion\">Direct<\/option><!-- [et_pb_line_break_holder] --><option value=\"inversa\" data-translate-key=\"inversaOpcion\">Reverse<\/option><!-- [et_pb_line_break_holder] -->        <\/select><!-- [et_pb_line_break_holder] -->    <\/div>\n<p><!-- [et_pb_line_break_holder] -->    <\/p>\n<div class=\"form-group\"><!-- [et_pb_line_break_holder] -->        <label for=\"x1\" data-translate-key=\"x1Label\">Value of x1<\/label> <input type=\"number\" id=\"x1\" step=\"any\" placeholder=\"Ex: 2\"><!-- [et_pb_line_break_holder] -->    <\/div>\n<p><!-- [et_pb_line_break_holder] -->    <\/p>\n<div class=\"form-group\"><!-- [et_pb_line_break_holder] -->        <label for=\"y1\" data-translate-key=\"y1Label\">Value of y1<\/label> <input type=\"number\" id=\"y1\" step=\"any\" placeholder=\"Eg: 10\"><!-- [et_pb_line_break_holder] -->    <\/div>\n<p><!-- [et_pb_line_break_holder] -->    <\/p>\n<div class=\"form-group\"><!-- [et_pb_line_break_holder] -->        <label for=\"x2\" data-translate-key=\"x2Label\">Value of x2<\/label> <input type=\"number\" id=\"x2\" step=\"any\" placeholder=\"Eg: 5\"><!-- [et_pb_line_break_holder] -->    <\/div>\n<p><!-- [et_pb_line_break_holder] -->    <button type=\"button\" id=\"calcularVariacionButton\" data-translate-key=\"calcularVariacionButton\">Calculate y2<\/button> <\/p>\n<div class=\"result\" id=\"result\" style=\"margin-top: 20px;\"><\/div>\n<p><!-- [et_pb_line_break_holder] --><\/div>\n<p><!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] --><\/p>\n<style><!-- [et_pb_line_break_holder] -->    \/* INICIO BLOQUE CSS - (Sin cambios respecto a tu versi\u00f3n) *\/<!-- [et_pb_line_break_holder] -->    .roi-calculator-container { background: white; padding: 20px; border-radius: 8px; max-width: 500px; margin: 0 auto; }<!-- [et_pb_line_break_holder] -->    .roi-calculator-container h2 { font-family: Arial, sans-serif; color: #000000; text-align:center; margin-bottom:20px; } \/* Centrado *\/<!-- [et_pb_line_break_holder] -->    .roi-calculator-container .form-group { margin-bottom: 15px; }<!-- [et_pb_line_break_holder] -->    .roi-calculator-container label { display: block; margin-bottom: 5px; font-family: Arial, sans-serif; color: #000000; }<!-- [et_pb_line_break_holder] -->    .roi-calculator-container input[type=\"number\"], .roi-calculator-container select { width: 100%; padding: 8px; box-sizing: border-box; border: 1px solid #0970C4; border-radius: 4px; font-family: Arial, sans-serif; color: #000000; height: 36px;} \/* Height Added *\/<!-- [et_pb_line_break_holder] -->    .roi-calculator-container .result { font-family: Arial, sans-serif; color: #000000; padding: 15px; font-weight: bold; line-height: 1.5; } \/* Bold added *\/<!-- [et_pb_line_break_holder] -->    @media (min-width: 981px) { .roi-calculator-container label, .roi-calculator-container input[type=\"number\"], .roi-calculator-container select, .roi-calculator-container .result { font-size: 20px; } .roi-calculator-container button { font-size: 20px; text-align: center; display: block; margin: 10px auto; } .roi-calculator-container input[type=\"number\"], .roi-calculator-container select { height: 40px; } }<!-- [et_pb_line_break_holder] -->    @media (max-width: 980px) and (min-width: 768px) { .roi-calculator-container label, .roi-calculator-container input[type=\"number\"], .roi-calculator-container select, .roi-calculator-container .result { font-size: 17px; } .roi-calculator-container button { font-size: 20px; text-align: center; display: block; margin: 10px auto; } .roi-calculator-container input[type=\"number\"], .roi-calculator-container select { height: 38px; } }<!-- [et_pb_line_break_holder] -->    @media (max-width: 767px) { .roi-calculator-container label, .roi-calculator-container input[type=\"number\"], .roi-calculator-container select, .roi-calculator-container .result { font-size: 16px; } .roi-calculator-container button { font-size: 20px; text-align: center; display: block; margin: 10px auto; } .roi-calculator-container input[type=\"number\"], .roi-calculator-container select { height: 36px; } }<!-- [et_pb_line_break_holder] -->    .roi-calculator-container button { padding: 10px 20px; background-color: #C35D09; color: white; border: none; border-radius: 4px; cursor: pointer; margin-top: 10px; }<!-- [et_pb_line_break_holder] -->    .roi-calculator-container button:hover { background-color: #b35408; }<!-- [et_pb_line_break_holder] -->    \/* FIN BLOQUE CSS *\/<!-- [et_pb_line_break_holder] --><\/style>\n<p><!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] --><script><!-- [et_pb_line_break_holder] -->    const translations = {<!-- [et_pb_line_break_holder] -->        es: {<!-- [et_pb_line_break_holder] -->            titulo: 'Calculadora de Variaci\u00f3n Directa e Inversa',<!-- [et_pb_line_break_holder] -->            tipoVariacionLabel: 'Tipo de Variaci\u00f3n',<!-- [et_pb_line_break_holder] -->            directaOpcion: 'Directa (y = kx)',<!-- [et_pb_line_break_holder] -->            inversaOpcion: 'Inversa (y = k\/x)',<!-- [et_pb_line_break_holder] -->            x1Label: 'Valor conocido de x (x1)', \/\/ Texto corregido\/aclarado<!-- [et_pb_line_break_holder] -->            y1Label: 'Valor conocido de y (y1)', \/\/ Texto corregido\/aclarado<!-- [et_pb_line_break_holder] -->            x2Label: 'Nuevo valor de x (x2)',   \/\/ Texto corregido\/aclarado<!-- [et_pb_line_break_holder] -->            calcularVariacionButton: 'Calcular y2 (Valor desconocido)', \/\/ Texto bot\u00f3n aclarado<!-- [et_pb_line_break_holder] -->            resultadoY2: 'El valor desconocido de y (y2) es: ',<!-- [et_pb_line_break_holder] -->            errorValorInvalido: 'Por favor, introduce valores num\u00e9ricos v\u00e1lidos para x1, y1 y x2.',<!-- [et_pb_line_break_holder] -->            errorDivisionCero: 'Error: Divisi\u00f3n por cero. Revisa los valores de x1 (directa) o x2 (inversa).'<!-- [et_pb_line_break_holder] -->        },<!-- [et_pb_line_break_holder] -->        en: {<!-- [et_pb_line_break_holder] -->            titulo: 'Direct and Inverse Variation Calculator',<!-- [et_pb_line_break_holder] -->            tipoVariacionLabel: 'Type of Variation',<!-- [et_pb_line_break_holder] -->            directaOpcion: 'Direct (y = kx)',<!-- [et_pb_line_break_holder] -->            inversaOpcion: 'Inverse (y = k\/x)',<!-- [et_pb_line_break_holder] -->            x1Label: 'Known value of x (x1)', \/\/ Corrected text<!-- [et_pb_line_break_holder] -->            y1Label: 'Known value of y (y1)', \/\/ Corrected text<!-- [et_pb_line_break_holder] -->            x2Label: 'New value of x (x2)',   \/\/ Corrected text<!-- [et_pb_line_break_holder] -->            calcularVariacionButton: 'Calculate y2 (Unknown value)', \/\/ Clarified button text<!-- [et_pb_line_break_holder] -->            resultadoY2: 'The unknown value of y (y2) is: ',<!-- [et_pb_line_break_holder] -->            errorValorInvalido: 'Please enter valid numeric values for x1, y1, and x2.',<!-- [et_pb_line_break_holder] -->            errorDivisionCero: 'Error: Division by zero. Check x1 (direct) or x2 (inverse) values.'<!-- [et_pb_line_break_holder] -->        },<!-- [et_pb_line_break_holder] -->        fr: {<!-- [et_pb_line_break_holder] -->             titulo: 'Calculateur de Variation Directe et Inverse',<!-- [et_pb_line_break_holder] -->             tipoVariacionLabel: 'Type de Variation',<!-- [et_pb_line_break_holder] -->             directaOpcion: 'Directe (y = kx)',<!-- [et_pb_line_break_holder] -->             inversaOpcion: 'Inverse (y = k\/x)',<!-- [et_pb_line_break_holder] -->             x1Label: 'Valeur connue de x (x1)',<!-- [et_pb_line_break_holder] -->             y1Label: 'Valeur connue de y (y1)',<!-- [et_pb_line_break_holder] -->             x2Label: 'Nouvelle valeur de x (x2)',<!-- [et_pb_line_break_holder] -->             calcularVariacionButton: 'Calculer y2 (Valeur inconnue)',<!-- [et_pb_line_break_holder] -->             resultadoY2: 'La valeur inconnue de y (y2) est : ',<!-- [et_pb_line_break_holder] -->             errorValorInvalido: 'Veuillez entrer des valeurs num\u00e9riques valides pour x1, y1 et x2.',<!-- [et_pb_line_break_holder] -->             errorDivisionCero: 'Erreur : Division par z\u00e9ro. V\u00e9rifiez les valeurs de x1 (directe) ou x2 (inverse).'<!-- [et_pb_line_break_holder] -->        },<!-- [et_pb_line_break_holder] -->        pt: {<!-- [et_pb_line_break_holder] -->             titulo: 'Calculadora de Varia\u00e7\u00e3o Direta e Inversa',<!-- [et_pb_line_break_holder] -->             tipoVariacionLabel: 'Tipo de Varia\u00e7\u00e3o',<!-- [et_pb_line_break_holder] -->             directaOpcion: 'Direta (y = kx)',<!-- [et_pb_line_break_holder] -->             inversaOpcion: 'Inversa (y = k\/x)',<!-- [et_pb_line_break_holder] -->             x1Label: 'Valor conhecido de x (x1)',<!-- [et_pb_line_break_holder] -->             y1Label: 'Valor conhecido de y (y1)',<!-- [et_pb_line_break_holder] -->             x2Label: 'Novo valor de x (x2)',<!-- [et_pb_line_break_holder] -->             calcularVariacionButton: 'Calcular y2 (Valor desconhecido)',<!-- [et_pb_line_break_holder] -->             resultadoY2: 'O valor desconhecido de y (y2) \u00e9: ',<!-- [et_pb_line_break_holder] -->             errorValorInvalido: 'Por favor, insira valores num\u00e9ricos v\u00e1lidos para x1, y1 e x2.',<!-- [et_pb_line_break_holder] -->             errorDivisionCero: 'Erro: Divis\u00e3o por zero. Verifique os valores de x1 (direta) ou x2 (inversa).'<!-- [et_pb_line_break_holder] -->        }<!-- [et_pb_line_break_holder] -->    };<!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->    document.addEventListener('DOMContentLoaded', (event) => {<!-- [et_pb_line_break_holder] -->        const language = getUserLanguage();<!-- [et_pb_line_break_holder] -->        setLanguage(language);<!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->        \/\/ **CORRECCI\u00d3N: A\u00f1adir Event Listener al bot\u00f3n Calcular**<!-- [et_pb_line_break_holder] -->        const calcButton = document.getElementById('calcularVariacionButton');<!-- [et_pb_line_break_holder] -->        if (calcButton) {<!-- [et_pb_line_break_holder] -->            calcButton.addEventListener('click', calcularVariacion);<!-- [et_pb_line_break_holder] -->        }<!-- [et_pb_line_break_holder] -->         \/\/ Trigger calculation if Enter key is pressed in last input field<!-- [et_pb_line_break_holder] -->         document.getElementById('x2').addEventListener('keypress', function (e) {<!-- [et_pb_line_break_holder] -->             if (e.key === 'Enter') {<!-- [et_pb_line_break_holder] -->                 calcularVariacion();<!-- [et_pb_line_break_holder] -->             }<!-- [et_pb_line_break_holder] -->         });<!-- [et_pb_line_break_holder] -->    });<!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->    \/\/ **CORRECCI\u00d3N: Completar setLanguage**<!-- [et_pb_line_break_holder] -->    function setLanguage(language) {<!-- [et_pb_line_break_holder] -->        if (!translations[language]) language = 'en';<!-- [et_pb_line_break_holder] -->        const langTrans = translations[language];<!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->        \/\/ Translate elements using data-translate-key<!-- [et_pb_line_break_holder] -->        document.querySelectorAll('[data-translate-key]').forEach(elem => {<!-- [et_pb_line_break_holder] -->            const key = elem.getAttribute('data-translate-key');<!-- [et_pb_line_break_holder] -->            if (langTrans[key]) {<!-- [et_pb_line_break_holder] -->                 if (elem.tagName === 'OPTION') {<!-- [et_pb_line_break_holder] -->                     elem.innerText = langTrans[key];<!-- [et_pb_line_break_holder] -->                 } else if (elem.tagName === 'BUTTON') {<!-- [et_pb_line_break_holder] -->                     elem.innerText = langTrans[key];<!-- [et_pb_line_break_holder] -->                 } else if (elem.tagName === 'LABEL') {<!-- [et_pb_line_break_holder] -->                      elem.innerText = langTrans[key];<!-- [et_pb_line_break_holder] -->                 } else if (elem.tagName === 'H2') {<!-- [et_pb_line_break_holder] -->                       elem.innerText = langTrans[key];<!-- [et_pb_line_break_holder] -->                 }<!-- [et_pb_line_break_holder] -->            }<!-- [et_pb_line_break_holder] -->        });<!-- [et_pb_line_break_holder] -->        \/\/ Clear result<!-- [et_pb_line_break_holder] -->        const resultDiv = document.getElementById('result');<!-- [et_pb_line_break_holder] -->        if (resultDiv) resultDiv.innerHTML = '';<!-- [et_pb_line_break_holder] -->    }<!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->    function getUserLanguage() {<!-- [et_pb_line_break_holder] -->        const userLang = navigator.language || navigator.userLanguage;<!-- [et_pb_line_break_holder] -->        const language = userLang.split('-')[0];<!-- [et_pb_line_break_holder] -->        return translations[language] ? language : 'en'; \/\/ Ingl\u00e9s como fallback<!-- [et_pb_line_break_holder] -->    }<!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->    \/\/ **CORRECCI\u00d3N: Implementar la funci\u00f3n calcularVariacion**<!-- [et_pb_line_break_holder] -->    function calcularVariacion() {<!-- [et_pb_line_break_holder] -->        const tipoVariacion = document.getElementById('tipoVariacion').value;<!-- [et_pb_line_break_holder] -->        const x1_val = parseFloat(document.getElementById('x1').value);<!-- [et_pb_line_break_holder] -->        const y1_val = parseFloat(document.getElementById('y1').value);<!-- [et_pb_line_break_holder] -->        const x2_val = parseFloat(document.getElementById('x2').value);<!-- [et_pb_line_break_holder] -->        const resultDiv = document.getElementById('result');<!-- [et_pb_line_break_holder] -->        const language = getUserLanguage();<!-- [et_pb_line_break_holder] -->        resultDiv.innerText = ''; \/\/ Clear previous result<!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->        \/\/ Validation<!-- [et_pb_line_break_holder] -->        if (isNaN(x1_val) || isNaN(y1_val) || isNaN(x2_val)) {<!-- [et_pb_line_break_holder] -->            resultDiv.innerText = translations[language].errorValorInvalido;<!-- [et_pb_line_break_holder] -->            return;<!-- [et_pb_line_break_holder] -->        }<!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->        let y2_val;<!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->        if (tipoVariacion === 'directa') {<!-- [et_pb_line_break_holder] -->            \/\/ y = kx  => k = y\/x => y1\/x1 = y2\/x2 => y2 = (y1 * x2) \/ x1<!-- [et_pb_line_break_holder] -->            if (x1_val === 0) {<!-- [et_pb_line_break_holder] -->                resultDiv.innerText = translations[language].errorDivisionCero;<!-- [et_pb_line_break_holder] -->                return;<!-- [et_pb_line_break_holder] -->            }<!-- [et_pb_line_break_holder] -->            y2_val = (y1_val * x2_val) \/ x1_val;<!-- [et_pb_line_break_holder] -->        } else if (tipoVariacion === 'inversa') {<!-- [et_pb_line_break_holder] -->            \/\/ y = k\/x => k = y*x => y1*x1 = y2*x2 => y2 = (y1 * x1) \/ x2<!-- [et_pb_line_break_holder] -->            if (x2_val === 0) {<!-- [et_pb_line_break_holder] -->                 resultDiv.innerText = translations[language].errorDivisionCero;<!-- [et_pb_line_break_holder] -->                 return;<!-- [et_pb_line_break_holder] -->            }<!-- [et_pb_line_break_holder] -->            y2_val = (y1_val * x1_val) \/ x2_val;<!-- [et_pb_line_break_holder] -->        } else {<!-- [et_pb_line_break_holder] -->             \/\/ Should not happen with the select element<!-- [et_pb_line_break_holder] -->             console.error(\"Tipo de variaci\u00f3n desconocido:\", tipoVariacion);<!-- [et_pb_line_break_holder] -->             return;<!-- [et_pb_line_break_holder] -->        }<!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->         \/\/ Display result<!-- [et_pb_line_break_holder] -->         if (isNaN(y2_val)) {<!-- [et_pb_line_break_holder] -->             resultDiv.innerText = translations[language].errorValorInvalido; \/\/ Or a more specific calculation error<!-- [et_pb_line_break_holder] -->         } else {<!-- [et_pb_line_break_holder] -->            resultDiv.innerText = `${translations[language].resultadoY2} ${y2_val.toLocaleString(undefined, { minimumFractionDigits: 2, maximumFractionDigits: 4 })}`;<!-- [et_pb_line_break_holder] -->         }<!-- [et_pb_line_break_holder] -->    }<!-- [et_pb_line_break_holder] --><\/script>[\/et_pb_code][et_pb_text admin_label=\u201dVOTE CODE\u201d _builder_version=\u201d4.27.4\u2033 _module_preset=\u201d88b21c46-bab4-4990-9def-73fb03a32482\u2033 text_orientation=\u201dcenter\u201d custom_margin=\u201d0px||0px||true|false\u201d custom_padding=\u201d0px||0px|507px|true|false\u201d custom_padding_tablet=\u201d|||274px|true|false\u201d custom_padding_phone=\u201d|||131px|true|false\u201d custom_padding_last_edited=\u201don|desktop\u201d global_colors_info=\u201d{}\u201d]<\/p>\n<div class=\"et_social_networks et_social_autowidth et_social_slide et_social_circle et_social_top et_social_withcounts et_social_nospace et_social_mobile_on et_social_withnetworknames et_social_outer_dark\">\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t<ul class=\"et_social_icons_container\"><li class=\"et_social_like\">\n\t\t\t\t\t\t<a href=\"#\" class=\"et_social_follow\" data-social_name=\"like\" data-social_type=\"like\" data-post_id=\"0\" target=\"_blank\">\n\t\t\t\t\t\t\t<i class=\"et_social_icon et_social_icon_like\"><\/i>\n\t\t\t\t\t\t\t<div class=\"et_social_network_label\"><div class=\"et_social_networkname\">Vote<\/div><div class=\"et_social_count\">\n\t\t\t\t\t\t<span>0<\/span>\n\t\t\t\t\t\t<span class=\"et_social_count_label\">Likes<\/span>\n\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t<span class=\"et_social_overlay\"><\/span>\n\t\t\t\t\t\t<\/a>\n\t\t\t\t\t<\/li><\/ul>\n\t\t\t\t<\/div>\n<p>[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section][et_pb_section fb_built=\u201d1\u2033 custom_padding_last_edited=\u201don|phone\u201d _builder_version=\u201d4.27.4\u2033 _module_preset=\u201ddefault\u201d custom_margin_tablet=\u201d\u201d custom_margin_phone=\u201d\u201d custom_margin_last_edited=\u201don|phone\u201d custom_padding=\u201d0px||||false|false\u201d custom_padding_tablet=\u201d22px||22px||true|false\u201d custom_padding_phone=\u201d22px||22px||true|false\u201d global_colors_info=\u201d{}\u201d][et_pb_row _builder_version=\u201d4.27.4\u2033 _module_preset=\u201ddefault\u201d global_colors_info=\u201d{}\u201d][et_pb_column type=\u201d4_4\u2033 _builder_version=\u201d4.27.4\u2033 _module_preset=\u201ddefault\u201d global_colors_info=\u201d{}\u201d][et_pb_text _builder_version=\u201d4.27.4\u2033 _module_preset=\u201ddefault\u201d hover_enabled=\u201d0\u2033 global_colors_info=\u201d{}\u201d sticky_enabled=\u201d0\u2033]<\/p>\n<h2><b>Your Key Tool for Solving Proportionality Problems<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Do you need to determine how quantities vary with each other, either directly or inversely? Our Direct and Inverse Variation Calculator lets you solve these proportionality problems quickly and accurately. Simply enter the known values and discover the constant of proportionality or the unknown value.<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2705 Identify the relationship \u2013 Determine if the variables vary directly or inversely.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2705 Find the constant \u2013 Calculate the proportionality factor between the variables.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2705 Solve unknowns \u2013 Find unknown values based on the proportional relationship.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">Use our calculator now and unravel the proportional relationships between your variables.<\/span><\/p>\n<h2><b>Example of Using the Variation Calculator<\/b><\/h2>\n<h3><b>Example 1: Direct Variance (Proportional Cost)<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Imagine that the cost of apples is directly proportional to their weight. If <\/span><b>3 kilograms<\/b><span style=\"font-weight: 400;\"> (<\/span><span style=\"font-weight: 400;\">x1<\/span><span style=\"font-weight: 400;\">) cost <\/span><b>$4.50 USD<\/b><span style=\"font-weight: 400;\"> (<\/span><span style=\"font-weight: 400;\">y1<\/span><span style=\"font-weight: 400;\">), how much will it cost (<\/span><span style=\"font-weight: 400;\">y2<\/span><span style=\"font-weight: 400;\">) buy <\/span><b>7 kilograms<\/b><span style=\"font-weight: 400;\"> (<\/span><span style=\"font-weight: 400;\">x2<\/span><span style=\"font-weight: 400;\">)?<\/span><\/p>\n<p><b>Data to Enter in the Calculator:<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Type of Variation:<\/b><span style=\"font-weight: 400;\"> Select <\/span><span style=\"font-weight: 400;\">Direct (y = kx)<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Known value of x (x1):<\/b> <span style=\"font-weight: 400;\">3<\/span> <i><span style=\"font-weight: 400;\">(Initial kilograms)<\/span><\/i><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Known value of y (y1):<\/b> <span style=\"font-weight: 400;\">4.50<\/span> <i><span style=\"font-weight: 400;\">(Initial cost in USD)<\/span><\/i><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>New value of x (x2):<\/b> <span style=\"font-weight: 400;\">7<\/span> <i><span style=\"font-weight: 400;\">(Final Kilograms)<\/span><\/i><\/li>\n<\/ul>\n<p><i><span style=\"font-weight: 400;\">(The calculator will find y2, the final cost)<\/span><\/i><\/p>\n<p><b>Applying the Direct Variation Formula (y2 = y1 * x2 \/ x1):<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">y2 = (4.50 \u00d7 7) \/ 3<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">y2 = 31.50 \/ 3 = 10.50<\/span><\/li>\n<\/ul>\n<p><b>\ud83d\udcca Result:<\/b><span style=\"font-weight: 400;\"> The unknown value of y (y2) is <\/span><b>10.50<\/b><span style=\"font-weight: 400;\">.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This means that 7 kilograms of apples would cost $10.50 USD.<\/span><\/p>\n<h3><b>Example 2: Inverse Variation (Speed and Time)<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Now imagine that to travel a fixed distance, speed is inversely proportional to time. If traveling at <\/span><b>80 km\/h<\/b><span style=\"font-weight: 400;\"> (<\/span><span style=\"font-weight: 400;\">x1<\/span><span style=\"font-weight: 400;\">) you take <\/span><b>3 hours<\/b><span style=\"font-weight: 400;\"> (<\/span><span style=\"font-weight: 400;\">y1<\/span><span style=\"font-weight: 400;\">), how long (<\/span><span style=\"font-weight: 400;\">y2<\/span><span style=\"font-weight: 400;\">) it will take you if you travel to <\/span><b>60 km\/h<\/b><span style=\"font-weight: 400;\"> (<\/span><span style=\"font-weight: 400;\">x2<\/span><span style=\"font-weight: 400;\">)?<\/span><\/p>\n<p><b>Data to Enter in the Calculator:<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Type of Variation:<\/b><span style=\"font-weight: 400;\"> Select <\/span><span style=\"font-weight: 400;\">Inverse (y = k\/x)<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Known value of x (x1):<\/b> <span style=\"font-weight: 400;\">80<\/span> <i><span style=\"font-weight: 400;\">(Initial speed in km\/h)<\/span><\/i><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Known value of y (y1):<\/b> <span style=\"font-weight: 400;\">3<\/span> <i><span style=\"font-weight: 400;\">(Starting time in hours)<\/span><\/i><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>New value of x (x2):<\/b> <span style=\"font-weight: 400;\">60<\/span> <i><span style=\"font-weight: 400;\">(Final speed in km\/h)<\/span><\/i><\/li>\n<\/ul>\n<p><i><span style=\"font-weight: 400;\">(The calculator will find y2, the final time)<\/span><\/i><\/p>\n<p><b>Applying the Inverse Variation Formula (y2 = y1 * x1 \/ x2):<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">y2 = (3 \u00d7 80) \/ 60<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">y2 = 240 \/ 60 = 4<\/span><\/li>\n<\/ul>\n<p><b>\ud83d\udcca Result:<\/b><span style=\"font-weight: 400;\"> The unknown value of y (y2) is <\/span><b>4<\/b><span style=\"font-weight: 400;\">.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This means that if you travel at 60 km\/h it will take you 4 hours to cover the same distance.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\ud83d\udce2 Easily solve your direct or inverse variation problems with our calculator.<\/span><\/p>\n<h2><b>How Does Our Direct and Inverse Variation Calculator Work?<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">The process is simple:<\/span><\/p>\n<h3><b>Step 1: Selecting the Variation Type<\/b><\/h3>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u27a1\ufe0f <\/span><b>Direct Variation:<\/b><span style=\"font-weight: 400;\"> Choose this option if one variable increases when the other also increases in constant proportion.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2b05\ufe0f <\/span><b>Inverse Variation:<\/b><span style=\"font-weight: 400;\"> Choose this option if one variable decreases when the other increases in constant proportion (and vice versa).<\/span><\/li>\n<\/ul>\n<h3><b>Step 2: Entering Known Values<\/b><\/h3>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\ud83d\udd22 <\/span><b>Value 1 (x1 or y1):<\/b><span style=\"font-weight: 400;\"> Enter the first value of one of the variables. Why is this important? It&#039;s the reference point for establishing the constant of proportionality.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\ud83d\udd22 <\/span><b>Value 2 (y1 or x1):<\/b><span style=\"font-weight: 400;\"> Enter the corresponding value for the other variable. Why is this important? Together with the value 1, it allows you to calculate the constant of proportionality.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2753 <\/span><b>Value to Find (x2 or y2):<\/b><span style=\"font-weight: 400;\"> Enter the second value of one of the variables to find the corresponding value of the other. Why is this important? It&#039;s the unknown you want to solve for.<\/span><\/li>\n<\/ul>\n<h3><b>Step 3: Automatic Calculation<\/b><\/h3>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2699\ufe0f The calculator applies the corresponding formula (direct: y=kx, inverse: y=k\/x) to find the constant of proportionality (k) and then uses this constant to calculate the unknown value.<\/span><\/li>\n<\/ul>\n<h3><b>Step 4: Viewing the Result<\/b><\/h3>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2705 Obtain the unknown value based on the selected proportionality relationship and the entered values.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\ud83d\udca1 Use this result to solve problems in various areas where quantities vary proportionally.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">\ud83d\udce2 Need to adjust recipes, calculate scales, or analyze physical relationships? \ud83e\uddd0 Try our direct and inverse variation calculator.<\/span><\/p>\n<h2><b>This is only for entrepreneurs, business owners and freelancers.<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">\ud83d\ude80 If you need to launch your website, SaaS or online store, visit <a href=\"https:\/\/calculatorcch.com\/en\/nippylaunch\/\" title=\"Link to NippyLaunch.com or Nippylaunch.com\" class=\"pretty-link-keyword\"rel=\"\" target=\"_blank\">NippyLaunch.com<\/a>.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\ud83d\udcc8 If you need to do digital advertising and marketing for your company, visit <a href=\"https:\/\/calculatorcch.com\/en\/cleefcompany\/\" title=\"Link to CleefCompany.com or Cleefcompany.com\" class=\"pretty-link-keyword\"rel=\"\" target=\"_blank\">CleefCompany.com<\/a>.<\/span><\/p>\n<h2><b>What is the Direct and Inverse Variation Calculator?<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">The Direct and Inverse Variation Calculator is an online tool designed to solve problems where two variables are proportionally related. Direct variation occurs when one variable is a constant multiple of the other (y=kx). Inverse variation occurs when the product of two variables is constant (xy=koy=k\/x). The calculator allows you to determine the constant of proportionality and find unknown values based on this relationship.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This tool is useful in mathematics, physics, engineering, and other areas where proportional relationships are important for problem-solving.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\ud83d\udc49 Unravel the proportional relationships between variables and solve unknowns with our calculator.<\/span><\/p>\n<h2><b>Recommended books for further study of algebra and proportionality<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Explore these readings that will help you better understand algebra concepts and proportionality relationships.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">1\ufe0f\u20e3 <\/span><b>\u201cAlgebra for Dummies\u201d by Mary Jane Sterling:<\/b><span style=\"font-weight: 400;\"> An accessible guide to understanding the fundamentals of algebra, including proportions.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">2\ufe0f\u20e3 <\/span><b>\u201cConceptual Physics\u201d by Paul G. Hewitt:<\/b><span style=\"font-weight: 400;\"> A book that explains physical concepts using proportional relationships in an intuitive way.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">3\ufe0f\u20e3 <\/span><b>\u201cMathematics: Analysis and Applications\u201d by Paul A. Foerster:<\/b><span style=\"font-weight: 400;\"> A textbook that covers proportional relationships in various mathematical contexts.<\/span><\/p>\n<h2><b>Why Use Our Direct and Inverse Variation Calculator?<\/b><\/h2>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2705 Versatility \u2013 Solves both direct and inverse variation problems.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2705 Ease of use \u2013 Clear and simple interface for entering data.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2705 Speed \u2013 Get the solution instantly without manual calculations.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2705 Accuracy \u2013 Ensures the correct application of proportionality formulas.<\/span><\/li>\n<\/ul>\n<h2><b>Avoid These Common Mistakes When Using the Direct and Inverse Variation Calculator<\/b><\/h2>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\ud83d\udeab Incorrectly identifying the type of variation (direct or inverse) in the problem.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\ud83d\udeab Entering values in the wrong fields.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\ud83d\udeab Not understanding the meaning of the proportionality constant.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">Use our calculator to solve direct and inverse variation problems with accuracy and efficiency.<\/span><\/p>\n<h2><b>Comparison: Direct and Inverse Variation Calculator vs. Traditional Methods<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Why use our calculator instead of solving proportionality problems manually?<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2705 Speed \u2013 Get the answer immediately without performing algebraic manipulations.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2705 Accuracy \u2013 Reduces the risk of errors in calculations.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2705 Ease of use \u2013 It does not require remembering the exact formulas or performing the algebraic steps.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2705 Convenience \u2013 Available online anytime to solve your proportionality problems.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">Simplify the solution of direct and inverse variation problems with our specialized tool.<\/span><\/p>\n<h2><b>Frequently Asked Questions about the Direct and Inverse Variation Calculator<\/b><\/h2>\n<h3><b>What is direct variation?<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Direct variation occurs when one variable is a constant multiple of another. If &#039;y&#039; varies directly with &#039;x&#039;, then y=kx, where &#039;k&#039; is the constant of proportionality.<\/span><\/p>\n<h3><b>What is inverse variation?<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Inverse variation occurs when the product of two variables is constant. If &#039;y&#039; varies inversely with &#039;x&#039;, then xy=koy=k\/x, where &#039;k&#039; is the constant of proportionality.<\/span><\/p>\n<h3><b>How do I find the constant of proportionality?<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">For direct variation, k=y\/x. For inverse variation, k=xy. You can use a pair of known values to find &#039;k&#039;.<\/span><\/p>\n<h3><b>Can I use this calculator for more complex problems with multiple variables?<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">This calculator is designed for the relationship between two variables. Problems with multiple variables that vary directly or inversely with each other would require more complex analysis and possibly different formulas.<\/span><\/p>\n<h3><b>What units should I use?<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">The units must be consistent within each variable throughout the problem. The constant of proportionality will have units that relate the units of the two variables.<\/span><\/p>\n<h3><b>What happens if the proportionality constant is negative?<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">A negative constant of proportionality in direct variation indicates that when one variable increases, the other decreases, but linearly. In inverse variation, a negative constant would indicate a similar but hyperbolic relationship.<\/span><\/p>\n<h3><b>Can I use decimal numbers or fractions?<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Yes, the calculator can handle decimal numbers and fractions in the input values.<\/span><\/p>\n<h3><b>Is this tool useful for unit conversion problems?<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">If the conversion between units is a direct proportionality relationship (e.g., meters to kilometers), you can use the calculator.<\/span><\/p>\n<h2>\n<\/h2>\n<p>[\/et_pb_text][et_pb_image src=\u201d@ET-DC@eyJkeW5hbWljIjp0cnVlLCJjb250ZW50IjoicG9zdF9mZWF0dXJlZF9pbWFnZSIsInNldHRpbmdzIjp7fX0=@\u201d alt=\u201dDebt Ratio Calculator\u201d title_text=\u201dDebt Ratio Calculator\u201d align=\u201dcenter\u201d align_tablet=\u201dcenter\u201d align_phone=\u201dcenter\u201d align_last_edited=\u201don|desktop\u201d _builder_version=\u201d4.27.4\u2033 _dynamic_attributes=\u201dsrc\u201d _module_preset=\u201ddefault\u201d custom_margin_tablet=\u201d||30px||false|false\u201d custom_margin_phone=\u201d||30px||false|false\u201d custom_margin_last_edited=\u201don|phone\u201d global_colors_info=\u201d{}\u201d][\/et_pb_image][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>","protected":false},"excerpt":{"rendered":"<p>Resuelve problemas de variaci\u00f3n directa (y = kx) e inversa (y = k\/x) de forma sencilla con nuestra calculadora online. Ingresa los valores conocidos para encontrar la constante de proporcionalidad o la variable desconocida. \u00a1Entiende y calcula la proporcionalidad!<\/p>","protected":false},"author":5,"featured_media":3698,"parent":3671,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-3791","page","type-page","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/calculatorcch.com\/en\/wp-json\/wp\/v2\/pages\/3791","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/calculatorcch.com\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/calculatorcch.com\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/calculatorcch.com\/en\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/calculatorcch.com\/en\/wp-json\/wp\/v2\/comments?post=3791"}],"version-history":[{"count":3,"href":"https:\/\/calculatorcch.com\/en\/wp-json\/wp\/v2\/pages\/3791\/revisions"}],"predecessor-version":[{"id":3794,"href":"https:\/\/calculatorcch.com\/en\/wp-json\/wp\/v2\/pages\/3791\/revisions\/3794"}],"up":[{"embeddable":true,"href":"https:\/\/calculatorcch.com\/en\/wp-json\/wp\/v2\/pages\/3671"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/calculatorcch.com\/en\/wp-json\/wp\/v2\/media\/3698"}],"wp:attachment":[{"href":"https:\/\/calculatorcch.com\/en\/wp-json\/wp\/v2\/media?parent=3791"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}