Calculate, simplify, and solve ratios quickly. Find simplified ratios, equivalent ratios, and missing values in proportions.
Enter two values to simplify the ratio.
Enter a ratio and a multiplier to scale it up.
Fill in the three known values to solve for the missing one.
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.
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.
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.
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.
| Original Ratio | Simplified Ratio |
|---|---|
| 10 : 15 | 2 : 3 |
| 12 : 18 | 2 : 3 |
| 20 : 30 | 2 : 3 |
| 25 : 100 | 1 : 4 |
| 100 : 250 | 2 : 5 |
These two words are related but not interchangeable:
Compares two (or more) quantities — for example, 2 : 3.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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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