Ratio Calculator
Simplify ratios to their lowest terms, solve for a missing value in a proportion, or check whether two ratios are equivalent. Results are instant and no sign-up is required.
Result
Simplified Ratio:
Enter three values; leave one field blank to solve for it.
Result
Missing Value:
Result
How to Use the Ratio Calculator
This tool has three modes. Select the mode that matches your need using the buttons at the top of the calculator.
1. Simplify Ratio
Enter values for A and B. The calculator divides both numbers by their Greatest Common Divisor (GCD) to give you the ratio in its simplest form. For example, 12 : 8 simplifies to 3 : 2.
2. Solve Missing Value
Enter three of the four values in a proportion A : B = C : D, leaving one field empty. The calculator uses cross-multiplication to find the missing number.
3. Compare Ratios
Enter two separate ratios and the calculator tells you whether they are equivalent, or which one is greater.
What Is a Ratio?
A ratio is a way of comparing two quantities by showing how many times one value contains or is contained within the other. Ratios are written as A : B, A/B, or as a fraction. They are used in everyday contexts like recipes, maps, finance, and engineering.
For example, if a recipe calls for 2 cups of flour for every 1 cup of sugar, the ratio is 2 : 1. Doubling the recipe gives 4 : 2, which is still equivalent to 2 : 1.
How to Simplify a Ratio
To simplify a ratio A : B, find the GCD of A and B, then divide both values by it.
Example: Simplify 18 : 12
GCD of 18 and 12 = 6
18 ÷ 6 = 3 | 12 ÷ 6 = 2
Result: 3 : 2
How to Solve a Proportion
A proportion states that two ratios are equal: A/B = C/D. To solve for a missing value, use cross-multiplication.
Example: Solve A/3 = 8/12
A × 12 = 3 × 8 → A = 24 ÷ 12 = 2
Common Ratio Examples
| Original Ratio | Simplified Ratio | As Fraction | As Decimal |
|---|---|---|---|
| 4 : 2 | 2 : 1 | 2/1 | 2.0 |
| 10 : 4 | 5 : 2 | 5/2 | 2.5 |
| 15 : 9 | 5 : 3 | 5/3 | 1.67 |
| 100 : 25 | 4 : 1 | 4/1 | 4.0 |
| 6 : 9 | 2 : 3 | 2/3 | 0.67 |
| 50 : 75 | 2 : 3 | 2/3 | 0.67 |
Frequently Asked Questions
What does it mean to simplify a ratio?
Simplifying a ratio means reducing it to its smallest equivalent form by dividing both values by their Greatest Common Divisor. The simplified ratio still represents the same relationship between the two quantities.
Can ratios include decimal numbers?
Yes. This calculator accepts decimal inputs. However, ratios are most commonly expressed as whole numbers. If your inputs are decimals, the result may also be shown in decimal form before simplification.
What is a proportion?
A proportion is an equation that shows two ratios are equal. For example, 1 : 2 = 3 : 6 is a proportion. Proportions are used in scaling, map reading, unit conversion, and many math problems.
How is a ratio different from a fraction?
A ratio compares two quantities (A to B), while a fraction represents a part of a whole (A out of A+B). The ratio 3 : 1 means 3 units compared to 1 unit, while the fraction 3/4 means 3 parts out of 4 total.
Is this calculator free to use?
Yes. The ToolMorph ratio calculator is completely free. No account, registration, or personal data is required. All calculations happen instantly in your browser.