Ratio Calculator
Simplify ratios, solve proportions, and divide amounts by ratios
Enter three values to solve for the missing fourth value (leave one field blank to solve for it):
How to Use the Ratio Calculator
Our free ratio calculator handles three primary types of ratio calculations:
- Simplify Ratio — Enter two integers to reduce them to their simplest form (e.g., 24:36 simplifies to 2:3).
- Solve Proportion — Solve equivalent ratios (A:B = C:D). Leave any one of the four fields blank, and the tool will calculate the missing value using cross-multiplication.
- Divide Amount by Ratio — Split a total sum of money or resources into shares based on a ratio (e.g., dividing $500 in a 2:3 ratio yields $200 and $300).
What is a Ratio and How is it Simplified?
A ratio is a mathematical comparison of two quantities, showing how many times one number contains another. Ratios are written as A:B or as fractions A/B.
To simplify a ratio:
- Find the Greatest Common Divisor (GCD) of both numbers.
- Divide both numbers in the ratio by the GCD.
- For example, to simplify 15:20, the GCD of 15 and 20 is 5. Dividing both by 5 gives the simplified ratio 3:4.
Solving Proportions (Cross-Multiplication)
A proportion states that two ratios are equal: A / B = C / D. To solve for a missing value, we use cross-multiplication:
A × D = B × C
If we want to find D, the formula is: D = (B × C) ÷ A. If we want to find A, the formula is: A = (B × C) ÷ D.
Practical Calculation Examples
Example 1: Cooking Recipe Scaling
A recipe calls for a ratio of 2 parts flour to 3 parts water. If you use 10 cups of flour, how much water is needed? Using the proportion mode: 2:3 = 10:D. Solving for D: D = (3 × 10) ÷ 2 = 30 ÷ 2 = 15. You need 15 cups of water.
Example 2: Profit Sharing
Two business partners agree to split a profit of $12,000 in a ratio of 3:5. Part A share = 3 parts, Part B share = 5 parts. Total parts = 8. Value per part = $12,000 ÷ 8 = $1,500. Partner A gets: 3 × $1,500 = $4,500. Partner B gets: 5 × $1,500 = $7,500.
Example 3: Screen Aspect Ratio
An image has dimensions of 1920 by 1080 pixels. What is its aspect ratio? Simplify 1920:1080. The GCD of 1920 and 1080 is 120. Dividing both gives 16:9 (standard widescreen format).
Frequently Asked Questions
What is the difference between a ratio and a fraction?
A ratio compares one part to another part (e.g., 2 red balls to 3 blue balls is a 2:3 ratio). A fraction compares one part to the whole total (e.g., red balls represent 2/5 of the total balls). Ratios can be converted to fractions: a ratio of A:B means the first part represents A/(A+B) of the whole.
Can a ratio have decimals?
Yes. Although ratios are conventionally written as whole numbers, you can have decimal ratios. To simplify a decimal ratio, multiply both numbers by 10, 100, or 1000 to eliminate the decimals first, then find their GCD.
How do you divide an amount in a three-part ratio?
The logic is the same: add all three parts of the ratio to get the total parts, divide the total amount by this sum to find the value of one part, and multiply this single-part value by each part of the ratio. (e.g., to divide $100 in a 1:2:2 ratio, total parts = 5, value per part = $20. Shares are $20, $40, and $40).
What does a 1:1 ratio mean?
A 1:1 ratio means the two quantities are equal. If you mix ingredients in a 1:1 ratio, you use equal parts of each ingredient.