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.
How ratios are used across the UK
Ratios are woven into everyday life in the United Kingdom, from the kitchen to the betting shop to the building site. British recipes frequently mix imperial and metric measurements — a classic Victoria sponge, for instance, uses a 1:1:1 ratio of butter, sugar and flour by weight (typically 225 g of each). Understanding ratios makes it simple to scale recipes up or down without losing the correct proportions.
In UK betting, fractional odds are expressed as ratios. Odds of 5/1 (read "five to one") mean you win £5 for every £1 staked, plus your stake back. Converting between fractional, decimal and percentage odds all relies on ratio arithmetic — a skill that millions of British punters use every weekend during the football season and at events like the Grand National and Royal Ascot.
On UK building sites, mixing ratios are critical. A standard general-purpose concrete mix follows a 1:2:3 ratio (one part cement, two parts sharp sand, three parts gravel) as recommended by British Standards. For mortar, a common ratio is 1:4 or 1:5 (cement to building sand), depending on exposure conditions specified in BS 5628. Getting these ratios wrong can compromise structural integrity — so accuracy matters.
Ratios are a major topic in the GCSE Mathematics syllabus across AQA, Edexcel and OCR exam boards. Students must be able to simplify ratios, share amounts in a given ratio, and solve proportion problems — all skills tested in both foundation and higher tier papers.
Worked examples for UK life
Example 1: Splitting a restaurant bill
Three friends eat out in London. Their meals cost £18, £24 and £30. They want to split the £72 total in proportion to what each person ordered (ratio 18:24:30).
Solution: Simplify 18:24:30 by dividing each by 6 → 3:4:5. Total parts = 12. Each part = £72 ÷ 12 = £6. So they pay £18, £24 and £30 respectively — confirming each pays for their own meal. If a 12.5% service charge is added (£9), divide £9 in the ratio 3:4:5: £2.25, £3.00 and £3.75.
Example 2: Mixing concrete for a garden path
You need to lay a small garden path and require 180 kg of concrete mix. The ratio is 1:2:3 (cement : sand : gravel).
Solution: Total parts = 1 + 2 + 3 = 6. Each part = 180 ÷ 6 = 30 kg. You need 30 kg cement, 60 kg sharp sand and 90 kg gravel. A standard 25 kg bag of cement from a UK builders' merchant means you would need two bags (with 20 kg spare for wastage).
Example 3: Betting odds conversion
A horse at Cheltenham has fractional odds of 7/2. What is the implied probability, and how much would you win on a £10 bet?
Solution: Fractional odds of 7/2 mean the ratio of profit to stake is 7:2. Implied probability = 2 ÷ (7 + 2) = 2/9 ≈ 22.2%. A £10 bet returns £10 × (7/2) = £35 profit, plus your £10 stake back = £45 total.
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.