Precision Utility
Ratio
Calculator
Three essential ratio tools in one place. Simplify any ratio to its lowest terms, scale a ratio to find a missing value, or divide an amount into parts by ratio. Results update instantly as you type.
Simplify a Ratio
Reduce to lowest terms using GCD
Simplified Ratio
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Scale a Ratio
A : B = C : ? — find the missing value
Missing Value
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Divide Amount by Ratio
Split a total into proportional parts
Split Amounts
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How the ratio calculator works
This tool covers the three most common ratio calculations. Each mode works independently — just enter your numbers and the result appears instantly.
"Simplify a Ratio" finds the greatest common divisor (GCD) of both values using the Euclidean algorithm and divides each part by it. For example, 12:8 becomes 3:2 because the GCD of 12 and 8 is 4.
"Scale a Ratio" solves the proportion A:B = C:? using cross-multiplication. If you know three of the four values, the calculator finds the missing one. This is the same technique taught in GCSE maths for equivalent ratios.
"Divide Amount by Ratio" splits a total into proportional parts. It adds the ratio components together, divides the total by that sum, then multiplies by each part. For example, dividing 100 in the ratio 3:2 gives 60 and 40.
What you need to know about ratios
A ratio is a way of comparing two or more quantities. The ratio 3:1 means "three of one thing for every one of another." Ratios are used throughout everyday life — from cooking recipes and map scales to mixing paint and splitting bills.
Key concepts:
- Ratios can be simplified just like fractions — divide both sides by their greatest common divisor
- Equivalent ratios have the same relationship between parts (e.g. 2:3, 4:6 and 10:15 are all equivalent)
- To scale a ratio up, multiply both parts by the same number; to scale down, divide
- Ratios with decimals can be converted to whole numbers by multiplying both sides by a power of 10
- When dividing an amount, the ratio tells you the relative size of each share, not the actual values
Ratios appear in GCSE and A-level maths, financial analysis, science experiments and construction. Understanding how to simplify, scale and apply ratios is a fundamental numeracy skill.
Frequently asked questions
How do I simplify a ratio?
Find the greatest common divisor (GCD) of both numbers and divide each part by it. For example, 12:8 — the GCD is 4, so the simplified ratio is 3:2.
What is a ratio?
A ratio compares two quantities by showing how many times one value contains or is contained within the other. It is written as A:B, for example 3:1 means three of A for every one of B.
How do I scale a ratio?
To scale a ratio, multiply or divide both parts by the same number. If A:B = C:?, then ? = (B x C) / A. For example, 2:5 = 6:? gives ? = (5 x 6) / 2 = 15.
How do I divide an amount by a ratio?
Add the ratio parts together to get the total number of shares. Divide the amount by the total shares, then multiply by each part. For example, divide 100 in the ratio 3:2 — total shares = 5, so the parts are 60 and 40.
Can ratios have decimals?
Yes, ratios can include decimals. This calculator handles decimal inputs and simplifies the result to whole numbers where possible by multiplying both sides to remove the decimal places first.
What is the difference between a ratio and a fraction?
A ratio compares two separate quantities (A:B), while a fraction represents a part of a whole (A/B). The ratio 3:2 means 3 parts to 2 parts; as fractions of the whole, that is 3/5 and 2/5.