Ratio Simplifier

Simplify ratios to their lowest terms and convert between ratio notation (a:b) and fraction notation (a/b). This calculator shows the simplification steps and explains the relationship between ratios and fractions.

Enter Your Ratio

First Value

Second Value

What This Calculator Does

A ratio expresses the relationship between two quantities. Simplifying a ratio means finding an equivalent ratio with the smallest possible whole numbers while maintaining the same proportional relationship.

Like fractions, ratios are simplified by finding the greatest common divisor of both values and dividing each by that number. The calculator also shows the equivalent fraction notation, as ratios and fractions represent similar mathematical relationships.

When You'd Use This

Scale Drawings: Architects and engineers use simplified ratios to represent large structures on paper (1:100 instead of 12:1200)
Mixing Ratios: Recipes, paints, concrete, and chemical solutions often specify ingredient ratios that need simplification for practical use
Gear Ratios: Mechanical systems use simplified ratios to describe the relationship between rotating components
Financial Ratios: Business and accounting use simplified ratios for analysis, such as debt-to-equity or current ratios

Ratios vs Fractions

While ratios and fractions use similar mathematical operations, they represent slightly different concepts:

Fractions represent a part of a whole (3/4 means 3 parts out of 4 total parts)
Ratios compare two separate quantities (3:4 means for every 3 of one thing, there are 4 of another)

Despite this conceptual difference, the mathematical simplification process is identical. For more on the relationship between ratios and fractions, see Britannica's article on ratios.

Step-by-Step Method

Find the Greatest Common Divisor

Determine the largest number that divides evenly into both values of the ratio. This can be done by listing factors or using the Euclidean algorithm.

Example: For 15:25, the GCD is 5

Divide Both Values by the GCD

Divide each number in the ratio by the GCD to get the simplified ratio.

Example: 15 ÷ 5 = 3 and 25 ÷ 5 = 5, giving us 3:5

Verify the Result

Check that the two values share no common factors other than 1. If they do, repeat the process.

Example: 3 and 5 share only the factor 1, so 3:5 is fully simplified

Frequently Asked Questions

Can ratios have more than two values?

Yes, ratios can compare three or more quantities (like 2:3:5). This calculator handles two-value ratios, but the same simplification method applies to ratios with more values by finding the GCD of all values involved.

What if the ratio values are already simplified?

If the two values share no common factors other than 1, the ratio is already in simplest form. The calculator will return the same ratio.

Can I use this for recipes?

Yes, though note that simplified ratios may not always be practical for cooking. A ratio of 12:8 simplifies to 3:2, but you might prefer working with the original values if they correspond to convenient measuring units.

How do I convert a ratio to a percentage?

For a ratio a:b, you can express it as a percentage by calculating (a / (a + b)) × 100 for the first value's percentage. For example, 3:2 means 3/(3+2) = 60% and 2/(3+2) = 40%.