How to Calculate for Ratio: Complete Guide and Calculator
Understanding how to calculate for ratio is a fundamental skill in mathematics, science, cooking, and business. A ratio represents how many times one number contains another. Use our specialized calculators below to simplify ratios or divide quantities into specific proportions.
1. Ratio Simplifier (A:B)
Enter two numbers to find their simplest ratio form.
2. Divide Total by Ratio
Divide a total amount into parts based on a specific ratio (e.g., dividing 100 in a 2:3 ratio).
What is a Ratio?
A ratio is a mathematical comparison of two or more numbers that indicates their sizes in relation to each other. It shows how much of one thing exists compared to another thing. Ratios can be written with a colon (A:B), as a fraction (A/B), or using the word "to" (A to B).
How to Calculate for Ratio Simplification
To simplify a ratio, you must find the Greatest Common Divisor (GCD) of the two numbers and divide both numbers by that factor. This is similar to simplifying fractions.
Example: Simplify the ratio 24:36.
1. Find the GCD of 24 and 36, which is 12.
2. Divide 24 by 12 = 2.
3. Divide 36 by 12 = 3.
4. The simplified ratio is 2:3.
How to Divide a Quantity into a Ratio
If you need to split a total amount into a specific ratio, follow these three steps:
Add the parts: Add the numbers in the ratio together (e.g., 2:3 becomes 2 + 3 = 5 total parts).
Find the value of one part: Divide the total amount by the sum of the parts.
Multiply: Multiply the value of one part by each number in the original ratio.
Real-World Ratio Examples
Scenario
Ratio Calculation
Result
Cooking Rice
1 cup rice to 2 cups water
1:2 Ratio
Concrete Mix
1 part cement, 2 parts sand, 3 parts gravel
1:2:3 Ratio
Business Shares
Investor A puts in 30k, Investor B puts in 70k
3:7 Ratio
Common Terms to Know
Antecedent: The first term in a ratio (the "A" in A:B).
Consequent: The second term in a ratio (the "B" in A:B).
Proportion: An equation that states that two ratios are equal.
function getGCD(a, b) {
a = Math.abs(a);
b = Math.abs(b);
while (b) {
var t = b;
b = a % b;
a = t;
}
return a;
}
function simplifyRatio() {
var a = parseFloat(document.getElementById("valA").value);
var b = parseFloat(document.getElementById("valB").value);
var display = document.getElementById("simplifyResult");
if (isNaN(a) || isNaN(b) || a <= 0 || b <= 0) {
display.style.display = "block";
display.style.color = "#c0392b";
display.innerHTML = "Please enter valid positive numbers.";
return;
}
var commonFactor = getGCD(a, b);
var simplifiedA = a / commonFactor;
var simplifiedB = b / commonFactor;
display.style.display = "block";
display.style.color = "#2c3e50";
display.innerHTML = "Simplified Ratio: " + simplifiedA + " : " + simplifiedB +
"Factor used: " + commonFactor + "";
}
function divideByRatio() {
var total = parseFloat(document.getElementById("totalAmount").value);
var r1 = parseFloat(document.getElementById("ratio1").value);
var r2 = parseFloat(document.getElementById("ratio2").value);
var display = document.getElementById("divideResult");
if (isNaN(total) || isNaN(r1) || isNaN(r2) || r1 <= 0 || r2 <= 0) {
display.style.display = "block";
display.style.color = "#c0392b";
display.innerHTML = "Please enter valid numbers for the total and ratio parts.";
return;
}
var sumParts = r1 + r2;
var partValue = total / sumParts;
var share1 = partValue * r1;
var share2 = partValue * r2;
display.style.display = "block";
display.style.color = "#2c3e50";
display.innerHTML = "Distribution Results:" +
"Part 1: " + share1.toFixed(2) + "" +
"Part 2: " + share2.toFixed(2) + "" +
"One part equals: " + partValue.toFixed(4) + "";
}