Ratio Calculator

How the ratio calculator works

A ratio compares quantities of the same kind, and this tool does the two jobs people reach for most: solving a proportion for a missing value, and simplifying a ratio to its lowest terms. Pick a mode with the pills at the top, type your numbers, and the result updates as you go. It handles whole numbers and decimals, and it guards against dividing by zero so you never see a broken result.

What a ratio and a proportion are

A ratio puts two or more numbers side by side to show their relative size, written with a colon: 8 : 12, or 1 : 2 : 3 for three parts. It describes proportion, not totals, so 8 : 12 and 2 : 3 are the same ratio expressed at different scales.

A proportion is a statement that two ratios are equal:

• A : B = C : D

When one of those four values is unknown, you can always find it from the other three. That is the everyday task behind scaling a recipe up, resizing an image without distortion, or converting between units.

Solving for the unknown by cross multiplication

Because the two ratios are equal, their cross products are equal:

• A × D = B × C

Rearrange for whichever term is blank:

• A = (B × C) ÷ D
• B = (A × D) ÷ C
• C = (A × D) ÷ B
• D = (B × C) ÷ A

Worked example, 1 : 2 = 3 : ?. Here A = 1, B = 2, C = 3, and D is unknown. So D = (B × C) ÷ A = (2 × 3) ÷ 1 = 6, and the completed proportion is 1 : 2 = 3 : 6. In the calculator’s solve mode you enter 1, 2, and 3, leave the last box empty, and 6 appears. Leave exactly one box blank; if you clear two, the tool asks you to fill one back in, and it will not divide by a zero denominator.

Simplifying by dividing both sides by the GCD

To reduce a ratio, divide every term by the greatest common divisor (GCD) of all the terms, exactly as you would reduce a fraction.

Worked example, 8 : 12. The GCD of 8 and 12 is 4, so:

• 8 ÷ 4 : 12 ÷ 4 = 2 : 3

2 : 3 cannot be reduced further because 2 and 3 share no common factor above 1. For decimal inputs, the calculator first scales every term up to a whole number by the smallest power of ten that clears the decimals, then reduces. So 1.5 : 2 becomes 15 : 20, which reduces to 3 : 4. It also shows the decimal form A ÷ B, so 2 : 3 reads as about 0.6667, another handy way to compare the two quantities.

Real uses: recipes, maps, mixing, and aspect ratios

Ratios show up constantly once you look for them:

• Recipes. A vinaigrette at 1 : 3 vinegar to oil scales cleanly. To use 12 tbsp of oil, solve 1 : 3 = ? : 12 to get 4 tbsp of vinegar.
• Maps and models. A scale of 1 : 25,000 means 1 cm on the map is 25,000 cm (250 m) on the ground.
• Mixing and dilution. Concrete, fertilizer, and cleaning solutions are given as part ratios like 1 : 2 : 3 (cement : sand : gravel); simplifying keeps the mix consistent at any batch size.
• Aspect ratios. A 1920 by 1080 screen simplifies to 16 : 9, which is why that shorthand is used for widescreen video.

These results are for planning and quick math. For engineering mixes, dosing, or anything safety-critical, follow the manufacturer’s or a professional’s exact specification.