An equivalent ratio is a ratio that has the same value or proportion but is expressed using different numbers. In simpler terms, two ratios are equivalent if they represent the same relationship between quantities. For instance, the ratio 1:2 is equivalent to 2:4, 3:6, and so on. This concept is fundamental in mathematics and has wide-ranging applications in various fields.
Mathematically, two ratios A:B and C:D are considered equivalent if the fraction A/B is equal to the fraction C/D. This can be expressed as:
A / B = C / D
In this calculator, we help you find a missing term in a ratio to make it equivalent to a given ratio. If you have a ratio A:B and know one part of an equivalent ratio (either C or D), we can find the missing part.
How the Calculator Works
Given two ratios, where one ratio is complete (A:B) and the other is partially complete (C:D, with one value missing), the calculator finds the missing value to ensure the ratios are equivalent.
If Denominator (D) is missing (or 0): We use the proportion A/B = C/D. To find D, we rearrange the formula to D = (C * B) / A.
If Numerator (C) is missing (or 0): We use the proportion A/B = C/D. To find C, we rearrange the formula to C = (A * D) / B.
For the calculator to work, you must provide values for A, B, and one of the values for C or D. If you enter 0 or leave the second ratio's denominator blank, it assumes you want to find the denominator (D). If you provide a value for the second ratio's denominator (D), and leave the second ratio's numerator (C) as 0 or blank, it will calculate C.
Example Use Cases
Scaling Recipes: If a recipe calls for 2 cups of flour for every 3 cups of sugar (2:3 ratio), and you want to know how much sugar you need if you use 8 cups of flour, you'd input A=2, B=3, C=8. The calculator will find D.
Map Scales: A map might have a scale where 1 cm represents 50 km (1:50,000,000). If you measure a distance on the map as 4 cm, you can find the actual distance by inputting A=1, B=50,000,000, C=4.
Currency Conversion: If the exchange rate is $1.10 USD for every €1 EUR (1.10:1 ratio), and you have €50, you can find out how many USD that is by inputting A=1.10, B=1, C=50.
Proportion Problems: In a class, the ratio of boys to girls is 5:7. If there are 35 girls, how many boys are there? Input A=5, B=7, D=35 (assuming C is the missing value, which we want to find).
The Equivalent Ratio Calculator simplifies these calculations, making it easier to work with proportions in everyday life and academic settings.
function calculateEquivalentRatio() {
var numerator1 = parseFloat(document.getElementById("numerator1").value);
var denominator1 = parseFloat(document.getElementById("denominator1").value);
var numerator2 = parseFloat(document.getElementById("numerator2").value);
var denominator2 = parseFloat(document.getElementById("denominator2").value);
var resultElement = document.getElementById("result");
resultElement.innerHTML = ""; // Clear previous results
resultElement.classList.remove("error");
// Validate inputs: Must have A, B, and at least one of C or D
if (isNaN(numerator1) || isNaN(denominator1) || denominator1 === 0) {
resultElement.innerHTML = "Please enter valid numbers for the first ratio (A and B). B cannot be zero.";
resultElement.classList.add("error");
return;
}
var findDenominator = isNaN(denominator2) || denominator2 === 0;
var findNumerator = !findDenominator && (isNaN(numerator2) || numerator2 === 0);
if (findDenominator && isNaN(numerator2)) {
resultElement.innerHTML = "Please enter a value for the second ratio's numerator (C) or denominator (D).";
resultElement.classList.add("error");
return;
}
if (!findDenominator && findNumerator && isNaN(denominator2)) {
resultElement.innerHTML = "Please enter a value for the second ratio's denominator (D).";
resultElement.classList.add("error");
return;
}
var equivalentNumerator;
var equivalentDenominator;
if (findDenominator) {
// Calculate D: A/B = C/D => D = (C * B) / A
if (isNaN(numerator2)) {
resultElement.innerHTML = "Please enter a value for the second ratio's numerator (C) to find the denominator.";
resultElement.classList.add("error");
return;
}
equivalentDenominator = (numerator2 * denominator1) / numerator1;
equivalentNumerator = numerator2;
if (isNaN(equivalentDenominator) || !isFinite(equivalentDenominator)) {
resultElement.innerHTML = "Calculation resulted in an invalid number. Check your inputs.";
resultElement.classList.add("error");
return;
}
resultElement.innerHTML = "The equivalent ratio is " + equivalentNumerator.toFixed(4) + " : " + equivalentDenominator.toFixed(4);
} else if (findNumerator) {
// Calculate C: A/B = C/D => C = (A * D) / B
if (isNaN(denominator2)) {
resultElement.innerHTML = "Please enter a value for the second ratio's denominator (D) to find the numerator.";
resultElement.classList.add("error");
return;
}
equivalentNumerator = (numerator1 * denominator2) / denominator1;
equivalentDenominator = denominator2;
if (isNaN(equivalentNumerator) || !isFinite(equivalentNumerator)) {
resultElement.innerHTML = "Calculation resulted in an invalid number. Check your inputs.";
resultElement.classList.add("error");
return;
}
resultElement.innerHTML = "The equivalent ratio is " + equivalentNumerator.toFixed(4) + " : " + equivalentDenominator.toFixed(4);
} else {
// Both C and D are provided, check for equivalence
var ratio1 = numerator1 / denominator1;
var ratio2 = numerator2 / denominator2;
// Use a small tolerance for floating point comparisons
var tolerance = 1e-9;
if (Math.abs(ratio1 – ratio2) < tolerance) {
resultElement.innerHTML = "The ratios are equivalent!";
} else {
resultElement.innerHTML = "The ratios are NOT equivalent.";
resultElement.classList.add("error");
}
}
}