Ratio Calculator
Simplify a ratio, solve for a missing value, scale it up or down, or share an amount out — with the working shown.
Separate the parts with a colon, a comma or a space. Decimals are fine.
Fill in any three boxes and leave one empty — the empty one is worked out.
Use a number below 1 to make the ratio smaller — 0.5 halves every part.
Money, grams, litres — the units are yours; the calculator only splits the number.
12 : 18 : 24 simplifies to 2 : 3 : 4, dividing every part by 6. The parts are 22.22%, 33.33%, 44.44% of the whole.
Breakdown
- Highest common factor
- 6
- Total number of parts
- 9
- As 1 : n
- 1 : 1.5 : 2
- As n : 1
- 0.5 : 0.75 : 1
- First part as a fraction of the whole
- 2/9
- First part as a decimal of the whole
- 0.222222
Show your working
The same ratio, written four ways
| Form | Ratio |
|---|---|
| As entered | 12 : 18 : 24 |
| Lowest terms | 2 : 3 : 4 |
| 1 : n | 1 : 1.5 : 2 |
| n : 1 | 0.5 : 0.75 : 1 |
All four describe exactly the same proportion.
Share of the whole
Part to part is the ratio; part to whole is the percentage.
Assumptions
- Every part of a ratio must be greater than zero; ratios compare quantities of the same kind.
- Decimal parts are multiplied by a power of ten before the highest common factor is taken, so the lowest terms are exact whole numbers.
- The 1 : n and n : 1 forms are rounded for display to six decimal places.
- Shares are not rounded to whole units — a real split of money may need a penny adjusting somewhere.
Ratio facts
- How do you simplify a ratio?
- Divide every part by their highest common factor. For 12 : 18 : 24 the highest common factor is 6, so it simplifies to 2 : 3 : 4.
- How do you find a missing value?
- Cross-multiply: if A : B = C : D then A × D = B × C. With 3 : 5 = 12 : D, that gives 3 × D = 60, so D = 20.
- How do you share an amount in a ratio?
- Add the parts, divide the amount by that total, then multiply by each part. Sharing 120 in the ratio 3 : 5 gives 8 parts of 15 each, so the shares are 45 and 75.
- Can a ratio contain decimals?
- Yes. Every part is multiplied by a power of ten until they are whole numbers, then simplified — 2.5 : 4 becomes 25 : 40, which is 5 : 8.
Understanding ratios
What a ratio actually says
A ratio compares quantities of the same kind. 3 : 5 says that for every 3 of the first thing there are 5 of the second — it fixes the proportion, not the amounts.
That is why 3 : 5, 6 : 10 and 30 : 50 are the same ratio. Simplifying finds the smallest whole numbers that say it.
Part-to-part and part-to-whole
3 : 5 is part to part. The whole is 3 + 5 = 8 parts, so the first quantity is 3/8 of the total, or 37.5% — not 3/5.
Mixing the two up is the most common mistake in ratio questions. This calculator prints both so the difference is visible.
1 : n and n : 1 forms
Dividing every part by the first gives the 1 : n form, which is how map scales, odds and gear ratios are usually quoted. Dividing by the last gives n : 1.
These forms usually involve decimals, and that is expected — they trade whole numbers for a fixed reference point.
Ratios with more than two parts
Three-part ratios such as 2 : 3 : 4 work exactly the same way: the highest common factor is taken across all the parts at once, and the whole is the sum of all of them.
Every mode here accepts as many parts as you enter, so recipes and three-way splits need no extra steps.
Related calculations
Ratios and percentages are the same arithmetic asked two ways — the percentage calculator handles the percentage form, and the percentage formulas guide sets out the working. For part-of-a-whole in fraction form, use the fractions calculator.
Worked example
A concrete mix is specified as 12 : 18 : 24 — cement, sand and aggregate. Every part divides by 6, so in lowest terms the mix is 2 : 3 : 4.
That is 9 parts in total, so cement is 2/9 of the mix (22.22%), sand 3/9 (33.33%) and aggregate 4/9 (44.44%). To make 90 kg, one part is 10 kg, giving 20 kg, 30 kg and 40 kg.
Evidence & Methodology
How This Page Is Grounded
Method
Lowest terms are found by first multiplying every part by the smallest power of ten that makes them whole numbers, then dividing by their highest common factor found with the Euclidean algorithm. Taking a highest common factor of floating-point values directly is what produces results such as 1 : 1.6000000000000001, so the integer step comes first. Missing values are found by cross-multiplication, and an amount is shared by dividing it by the total number of parts and multiplying by each part.
Important limitation: Every part must be greater than zero, and a ratio compares quantities of the same kind. Decimal inputs are integerised to at most six decimal places. Shares are not rounded to whole units, so splitting money exactly may leave a penny to allocate by hand. The 1 : n and n : 1 forms are displayed to six decimal places.
Primary Sources
- National curriculum in England: mathematics programmes of study — ratio, proportion and rates of change Department for Education
- Ratio and proportion: guidance for teaching National Centre for Excellence in the Teaching of Mathematics
Quality Checks
Simplification, cross-multiplication and amount-sharing checked against worked examples for two-part and three-part ratios, including decimal inputs and ratios already in lowest terms.
See how sources are selected and corrections are handled in our Editorial & Calculation Methodology, and which automated checks this page has to pass in How We Test.
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