Ratio Calculator — Step-by-Step Solutions

The Ratio Calculator simplifies ratios to their lowest terms and helps you solve proportions by finding missing values. It is useful for cooking recipes, mixing solutions, map scales, and any situation where you need to work with proportional relationships.

Enter a ratio to simplify it, or enter three values of a proportion to find the missing fourth value.

Result

—

Your calculations will appear here

How to Use the Ratio Calculator

Choose a mode: Simplify reduces a ratio to lowest terms using the greatest common divisor.
Find Missing Value solves proportions. Enter three values (a:b = c:?) and the calculator finds the fourth.
Equivalency Check tests whether two ratios are equal by cross-multiplication.
Scale Ratio multiplies both parts of a ratio by a given factor.
Multi-Term simplifies ratios with three or more parts (e.g. 12:18:24 becomes 2:3:4).
Part-to-Whole converts a ratio into percentages, fractions, and decimals for each part.

Formula and Theory

A ratio compares two or more quantities of the same kind. It shows how much of one thing there is compared to another. Ratios can be written as a:b, a/b, or 'a to b'. To simplify a ratio, divide both parts by their greatest common divisor (GCD). For example, 12:8 has GCD 4, so it simplifies to 3:2.

A proportion states that two ratios are equal: a/b = c/d. The cross-multiplication property tells us that a x d = b x c. This is the basis for finding missing values and checking equivalency. If a:b = c:d, then ad = bc.

Multi-term ratios (a:b:c) are simplified by finding the GCD of all terms. Part-to-whole conversion divides each part by the total sum. For a ratio of 3:5, the total is 8, so the parts represent 3/8 (37.5%) and 5/8 (62.5%) of the whole.

Worked Examples

Example 1: Simplifying a ratio

Problem: Simplify the ratio 48:36.

Solution: Find the GCD of 48 and 36. The factors of 48 include 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The factors of 36 include 1, 2, 3, 4, 6, 9, 12, 18, 36. The GCD is 12. Divide both parts: 48/12 = 4, 36/12 = 3.

Answer: 4:3

Example 2: Finding a missing value

Problem: If 5:8 = 20:x, find x.

Solution: Using cross-multiplication: 5 x x = 8 x 20, so 5x = 160, therefore x = 160/5 = 32.

Answer: x = 32

Example 3: Checking equivalency

Problem: Are the ratios 3:4 and 9:12 equivalent?

Solution: Cross-multiply: 3 x 12 = 36 and 4 x 9 = 36. Since both products are equal (36 = 36), the ratios are equivalent.

Answer: Yes, 3:4 = 9:12

Example 4: Scaling a ratio

Problem: Scale the ratio 2:5 by a factor of 7.

Solution: Multiply both parts by the scale factor: 2 x 7 = 14, 5 x 7 = 35.

Answer: 14:35

Example 5: Simplifying a multi-term ratio

Problem: Simplify 24:36:60.

Solution: Find the GCD of all three terms. GCD(24, 36) = 12, GCD(12, 60) = 12. Divide each term by 12: 24/12 = 2, 36/12 = 3, 60/12 = 5.

Answer: 2:3:5

Example 6: Converting ratio to percentages

Problem: Express the ratio 3:5 as percentages of the whole.

Solution: Total parts = 3 + 5 = 8. First part: 3/8 = 0.375 = 37.5%. Second part: 5/8 = 0.625 = 62.5%.

Answer: 37.5% and 62.5%

Frequently Asked Questions

What is the difference between a ratio and a fraction?

A ratio compares two separate quantities (e.g. 3 boys to 5 girls = 3:5), while a fraction represents a part of a whole (e.g. 3 out of 8 students = 3/8). A ratio of 3:5 can be converted to fractions 3/8 and 5/8 using part-to-whole conversion.

How do I check if two ratios are equivalent?

Use cross-multiplication. For ratios a:b and c:d, multiply a x d and b x c. If the products are equal, the ratios are equivalent. For example, 2:3 and 6:9 are equivalent because 2 x 9 = 18 and 3 x 6 = 18.

Can ratios have more than two terms?

Yes. Multi-term ratios like 2:3:5 compare three or more quantities. They are simplified by dividing all terms by their greatest common divisor, just like two-term ratios.

How do I convert a ratio to a percentage?

Add all parts of the ratio to find the total. Then divide each part by the total and multiply by 100. For 3:7, the total is 10. The parts are 3/10 = 30% and 7/10 = 70%.

What does it mean to scale a ratio?

Scaling a ratio means multiplying all parts by the same factor. This creates an equivalent ratio with larger or smaller values. For example, scaling 1:3 by 4 gives 4:12, which represents the same proportion.

How are ratios used in real life?

Ratios are used in cooking (scaling recipes), map reading (1:50000 means 1cm = 500m), mixing paint colours, financial analysis (debt-to-income ratio), screen dimensions (16:9 aspect ratio), and probability calculations.