Solve for an unknown value in a proportion. Enter three known values, and the calculator will find the fourth.
Enter three values to find the unknown 'D'.
What is a Proportion?
A proportion is a statement that two ratios are equal. It's a fundamental concept in mathematics used across various fields like science, engineering, cooking, and finance. A typical proportion can be represented as:
A / B = C / D
In this equation, A, B, C, and D are values. If you know any three of these values, you can solve for the unknown fourth value.
How to Solve Proportions Manually
To solve for an unknown value, like 'D' in the equation A / B = C / D, you can use cross-multiplication. This involves multiplying the numerator of one fraction by the denominator of the other fraction.
From A / B = C / D, we get:
A * D = B * C
To isolate the unknown variable (D in this case), you divide both sides of the equation by the coefficient of D (which is A):
D = (B * C) / A
This formula is used by the calculator below. If you need to solve for A, C, or B, the logic can be adapted:
To solve for A: A = (B * C) / D
To solve for C: C = (A * D) / B
To solve for B: B = (A * D) / C
Use Cases for Solving Proportions
Scaling Recipes: If a recipe calls for 2 cups of flour for 12 cookies, how much flour do you need for 30 cookies? (2/12 = X/30)
Map Scales: A map has a scale of 1 inch : 50 miles. If two cities are 3.5 inches apart on the map, what is the actual distance? (1/50 = 3.5/X)
Unit Conversions: If 1 meter is approximately 3.28 feet, how many feet are in 10 meters? (1/3.28 = 10/X)
Physics and Chemistry: Many natural laws are expressed as proportions (e.g., gas laws, stoichiometry).
Cost Calculations: If 5 apples cost $2.50, how much do 12 apples cost? (5/2.50 = 12/X)
How to Use This Calculator
Simply input any three of the four values (A, B, C, or D) in the proportion A / B = C / D. The calculator will automatically compute the unknown value and display it in the 'Value D (Unknown)' field and the result section.
function solveProportion() {
var a = document.getElementById("a").value;
var b = document.getElementById("b").value;
var c = document.getElementById("c").value;
var dInput = document.getElementById("d");
var resultDiv = document.getElementById("result");
var numA = parseFloat(a);
var numB = parseFloat(b);
var numC = parseFloat(c);
// Clear previous results and styling
resultDiv.textContent = "";
resultDiv.style.borderColor = "#28a745"; // Default to success green
var calculatedD = null;
// Determine which variable is intended to be unknown based on which input is empty or could be calculated.
// This calculator is designed to solve for D, but we will allow solving for others if D is provided.
// However, the UI is set up to calculate D, so we'll prioritize that.
var unknownCount = 0;
var inputs = { 'a': numA, 'b': numB, 'c': numC };
var missingField = null;
if (isNaN(numA) || a === "") { unknownCount++; missingField = 'a'; }
if (isNaN(numB) || b === "") { unknownCount++; missingField = 'b'; }
if (isNaN(numC) || c === "") { unknownCount++; missingField = 'c'; }
// The 'd' input is disabled, so we assume it's the one to calculate unless explicitly provided values suggest otherwise.
// If exactly 3 values are provided and D is the target:
if (unknownCount === 0 && !isNaN(numA) && !isNaN(numB) && !isNaN(numC)) {
// This implies D is the target, and A, B, C are known.
if (numA === 0) {
resultDiv.textContent = "Error: Value A cannot be zero for division.";
resultDiv.style.borderColor = "#dc3545"; // Error red
dInput.value = "";
return;
}
calculatedD = (numB * numC) / numA;
dInput.value = calculatedD.toFixed(4); // Display calculated value in disabled input
resultDiv.textContent = "Calculated D = " + calculatedD.toFixed(4);
} else {
// Handle cases where input might be invalid or multiple fields are empty
resultDiv.textContent = "Please enter exactly three valid numbers.";
resultDiv.style.borderColor = "#dc3545"; // Error red
dInput.value = "";
}
}