Calculators

Ratio Calculator

Calculate, simplify, and solve ratios quickly. Find simplified ratios, equivalent ratios, and missing values in proportions.

Ratio Calculator Tool

Simplified Ratio

Enter two values to simplify the ratio.

What Is a Ratio?

A ratio compares two or more quantities and describes their relative relationship. Written as "2 : 3", it means that for every 2 units of one quantity, there are 3 units of another. Ratios don't say how big the quantities actually are — only how they relate to each other.

How to Simplify a Ratio

Both parts of a ratio can be divided by their greatest common divisor (GCD) — the largest number that divides both values evenly — without changing what the ratio represents.

Example

12 : 18
GCD = 6
12 ÷ 6 = 2
18 ÷ 6 = 3
Therefore, 12 : 18 = 2 : 3

What Are Equivalent Ratios?

Equivalent ratios represent the same relationship even though the numbers themselves are different — each one is the same ratio scaled up or down by a constant multiplier.

2 : 3
4 : 6
6 : 9
8 : 12
All four represent the same ratio.

How to Solve a Proportion

A proportion sets two ratios equal to each other. If one value is missing, cross-multiplying turns the proportion into a simple equation you can solve.

Formula

A ÷ B = C ÷ D, so D = (B × C) ÷ A

Example

2 : 3 = 8 : X
2 ÷ 3 = 8 ÷ X
Cross multiply: 2X = 24
X = 12
Therefore, 2 : 3 = 8 : 12

Ratio Examples

A quick-reference table of common ratios and their simplified form.
Original Ratio Simplified Ratio
10 : 152 : 3
12 : 182 : 3
20 : 302 : 3
25 : 1001 : 4
100 : 2502 : 5

Ratio vs. Proportion

These two words are related but not interchangeable:

Ratio

Compares two (or more) quantities — for example, 2 : 3.

Proportion

States that two ratios are equal — for example, 2 : 3 = 4 : 6. A proportion is always built from two ratios; a single ratio on its own isn't a proportion.

Real-World Uses of Ratios

Ratios show up anywhere two quantities need to stay in balance: scaling a recipe up or down, reading a map's scale, mixing ingredients (like paint, concrete, or fuel) in the correct proportion, comparing business figures such as cost to revenue, keeping a design's proportions consistent, following construction and material mix ratios, comparing units like price per item, and working out proportional splits in a budget.

Frequently Asked Questions

What is a ratio?

A ratio compares two (or more) quantities and describes their relative size. "2 : 3" means that for every 2 units of one quantity, there are 3 units of another.

How do I simplify a ratio?

Find the greatest common divisor (GCD) of both values, then divide both sides by it. For 12 : 18, the GCD is 6, so 12 ÷ 6 = 2 and 18 ÷ 6 = 3, giving the simplified ratio 2 : 3.

How do you find the greatest common divisor of a ratio?

The GCD is the largest number that divides both values with no remainder. This calculator finds it automatically using the Euclidean algorithm, so you don't need to work it out by hand.

What are equivalent ratios?

Equivalent ratios represent the same relationship using different numbers — 2 : 3, 4 : 6, 6 : 9, and 8 : 12 are all equivalent, since each is the original ratio scaled up by the same amount.

How do I solve a ratio with a missing value?

Write the two ratios as a proportion (A : B = C : D) and cross-multiply: A × D = B × C. Solve for whichever value is missing by dividing. For 2 : 3 = 8 : X, that's X = (3 × 8) ÷ 2 = 12.

What is the difference between a ratio and a proportion?

A ratio compares two quantities (like 2 : 3). A proportion is a statement that two ratios are equal (like 2 : 3 = 4 : 6). Every proportion is built from two ratios; a single ratio on its own isn't a proportion.

Can ratios contain decimals?

Yes. This calculator accepts decimal values in the Simplify Ratio mode and converts them precisely (not by rounding) before simplifying — for example, 1.5 : 2.5 simplifies to 3 : 5.

Can ratios contain fractions?

Ratios can be written using fractions, but this calculator works with decimal numbers rather than fraction notation. Convert a fraction to its decimal form first (e.g. use Brekzy's Percentage Calculator or a quick division) and enter that instead.

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