Ratio Calculator
Simplify and scale ratios
Ratio Calculator tool
Results
Simplified Ratio
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Step-by-step:
- 1.Find GCD of 12, 18, 24: 6
- 2.Divide each by GCD:
- 3.12 / 6 = 0
- 4.18 / 6 = 0
- 5.24 / 6 = 0
- 6.Simplified ratio:
Ratio Calculator: key facts
- What it does
- Simplify and scale ratios
- Category
- Math Calculators
- Cost
- Free, with no account, sign-up, or install.
- Your data
- Runs entirely in your browser — the files and text you enter are never uploaded to a server.
- Last reviewed
- . Report an incorrect result.
What the Ratio Calculator does
Ratios express how quantities relate — 3:2, 16:9, 1:4 — and working with them means simplifying, scaling, or solving for a missing part. This calculator simplifies a ratio to its lowest terms, scales it by any factor, and even handles three-part ratios.
Cooks scale recipes, designers reason about aspect ratios, and students simplify ratios for homework. Builders and hobbyists use it for mixing ratios like paint or concrete. Because it accepts an optional third value and a scale factor, it goes beyond simple two-part reduction to the practical cases people actually meet.
Using the Ratio Calculator, step by step
- Enter the ratio values in fields A and B (and C for a three-part ratio).
- Read the simplified ratio, reduced to its lowest whole-number terms.
- Enter a scale factor to multiply the ratio up or down.
- Check the scaled ratio and, for two-part ratios, the fraction form, plus the step-by-step working.
Simplifying and scaling
A ratio is simplified by dividing every term by the greatest common divisor of all of them, computed with the Euclidean algorithm. For three-part ratios the divisor is found by taking the greatest common divisor of the first pair and then of that result with the third term.
Simplification does not change what a ratio means, only how compactly it is written. 12:18:24 and 2:3:4 describe identical proportions, and the reduced form is easier to hold in mind and to scale.
The scale factor multiplies every term equally, which is the operation behind most practical ratio work: scaling a recipe up, resizing an image without distortion, or mixing a larger batch of something in the same proportions. Multiplying only some terms changes the relationship rather than the quantity.
- The defaults — 12:18:24 — share a greatest common divisor of 6, simplifying to 2:3:4.
- Scaling 2:3:4 by the default factor of 2 gives 4:6:8, the same proportions at twice the size.
- A 16:9 aspect ratio scaled by 120 gives 1920:1080, which is how that familiar resolution arises.
What makes this one worth using
- It supports three-part ratios (A:B:C), not just two terms, covering mixes and proportions other tools cannot.
- It both simplifies and scales — reducing to lowest terms and multiplying by a factor — in one place.
- It shows the greatest-common-divisor steps behind the simplification, so the reduction is transparent.
- It runs entirely client-side with no account.
Ratios, proportions, and the part-to-whole trap
The most frequent mistake with ratios is reading a part-to-part relationship as part-to-whole. A 2:3 mix is two parts of one thing to three of another, which means five parts in total — so the first ingredient is two-fifths of the mixture, not two-thirds. Concrete, paint, and cocktail recipes all go wrong in exactly this way.
Ratios are unitless when both terms share units, and that is what makes them portable: the same 16:9 works in pixels, centimetres, or feet. Where the units differ the result is a rate rather than a ratio — kilometres per hour, price per kilogram — and it carries units accordingly.
Equating two ratios gives a proportion, and cross-multiplication solves it for any missing term. That single technique covers scale drawings, map distances, currency conversion, and unit conversion, which is why proportional reasoning is worth more than the specific formulas built on it.
Frequently Asked Questions
How do you simplify a ratio?
You divide every term by their greatest common divisor, the same way you reduce a fraction. For 12:8, the GCD is 4, so it simplifies to 3:2. The calculator finds the GCD across all terms and shows the division.
How do I scale a ratio up or down?
Multiply each term by the same factor. To double 3:2 you get 6:4; to triple it you get 9:6. Enter a scale factor and the calculator applies it to every part of the simplified ratio.
What is the difference between a ratio and a fraction?
A ratio compares quantities (3:2 means three parts to two), while a fraction expresses a part of a whole (3/5). They are related — the calculator shows a two-part ratio as a fraction — but a ratio can have more than two terms, which a single fraction cannot.
How do I keep a ratio the same when changing one quantity?
Multiply or divide every term by the same number so the proportion holds. If a 2:3 paint mix needs 6 units of the first color, scale by 3 to get 6:9. Enter your ratio and a scale factor and the calculator works out the matching amounts.
