OneTaskBy Tim King · Updated
Ratio Calculator
Simplify 12:18 and Split an Amount in a Ratio, With Working
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How the Ratio Calculator works
Type a ratio such as 12:18 and this ratio calculator simplifies it to 2:3 straight away, with the 1:n form and each part as a percentage of the whole. Use it as a sharing ratio calculator to split a total, such as 100 in the ratio 2:3 into 40 and 60, or scale the ratio so one term matches a number you already know. Ratios with three or more parts, like 2:3:5, work the same way.
A ratio compares sizes rather than amounts: 2:3 and 40:60 describe the same mix. Simplifying divides every part by their greatest common factor, and decimal ratios are first scaled up to whole numbers. Splitting a total works by adding the parts to find how many shares there are, then giving each part its number of shares.
How the ratio calculator works
The formula for splitting a total T in the ratio a:b is a share of T × a / (a + b) and T × b / (a + b). For more parts, divide by the sum of all of them. Scaling to a first term multiplies every part by the new first term divided by the old one. Shares of the whole are each part over the sum, also given as a percentage.
First example. Share 100 in the ratio 2:3. There are 5 shares, each worth 20, so the split is 40 : 60, or 40% and 60%.
Second example. 16:9 scaled to a first term of 1920 gives 1920 : 1080, the size of a full HD screen.
How many parts are in a ratio? Add the simplified terms. 2:3:5 has 10 parts, so the shares are 20%, 30% and 50%.
Common ratios as shares and decimals
| Ratio | First share | Second share | First ÷ second |
|---|---|---|---|
| 1 : 1 | 50% | 50% | 1 |
| 1 : 2 | 33.33% | 66.67% | 0.5 |
| 1 : 3 | 25% | 75% | 0.333333 |
| 1 : 4 | 20% | 80% | 0.25 |
| 2 : 3 | 40% | 60% | 0.666667 |
| 3 : 4 | 42.86% | 57.14% | 0.75 |
| 3 : 2 | 60% | 40% | 1.5 |
| 4 : 3 | 57.14% | 42.86% | 1.333333 |
| 5 : 4 | 55.56% | 44.44% | 1.25 |
| 16 : 9 | 64% | 36% | 1.777778 |
| 16 : 10 | 61.54% | 38.46% | 1.6 |
| 21 : 9 | 70% | 30% | 2.333333 |
| 3 : 5 | 37.5% | 62.5% | 0.6 |
| 5 : 8 | 38.46% | 61.54% | 0.625 |
| 1 : 5 | 16.67% | 83.33% | 0.2 |
| 1 : 10 | 9.09% | 90.91% | 0.1 |
| 7 : 3 | 70% | 30% | 2.333333 |
| 9 : 16 | 36% | 64% | 0.5625 |
| 2 : 1 | 66.67% | 33.33% | 2 |
| 3 : 1 | 75% | 25% | 3 |
| 1.618 : 1 | 61.8% | 38.2% | 1.618 |
| 4 : 1 | 80% | 20% | 4 |
| 5 : 3 | 62.5% | 37.5% | 1.666667 |
| 2 : 5 | 28.57% | 71.43% | 0.4 |
| 3 : 8 | 27.27% | 72.73% | 0.375 |
Ratio to percentage
To turn a ratio into percentages, divide each part by the sum of the parts and multiply by 100. For 3:5 there are 8 parts, so the first is 3 ÷ 8 × 100 = 37.5% and the second is 62.5%. The two percentages always add up to 100%. Do not divide one part by the other: 3 ÷ 5 = 60% compares the parts with each other, not with the whole.
Ratio to fraction
Each part of a ratio is a fraction of the whole with the sum of the parts as the denominator. In 2:3 the first part is 2/5 and the second is 3/5. The ratio itself can also be written as the fraction first ÷ second, so 2:3 is 2/3 and 16:9 is 16/9, or about 1.78. The calculator shows both: the shares of the whole as fractions and the 1 : n and n : 1 forms.
Tips and pitfalls
- Order matters. 2:3 boys to girls is not 3:2; keep the terms in the order of the question.
- Shares are not the ratio. In 2:3, the first part is 2/5 of the total, not 2/3.
- Use the same units. Convert 50 cm : 2 m to 50 : 200 before simplifying, which gives 1 : 4.
- Rounding a split. When a split does not divide evenly, round each part and check they still add up to the total.
Sources: Ratio.
Checked against: 2:3 split of 100 = 40 and 60
FAQ
How do you simplify a ratio?
Divide every part by the greatest common factor of all the parts. For 12:18 the GCF is 6, so the ratio simplifies to 2:3. If the ratio has decimals, multiply all parts by 10 or 100 first so they are whole numbers, then simplify.
How do you split an amount in a ratio?
Add the parts to find the total number of shares, divide the amount by that, then multiply by each part. To split 250 in 3:2, there are 5 shares of 50, so the amounts are 150 and 100. The calculator does this for any number of parts.
How do you turn a ratio into a percentage?
Divide each part by the sum of all the parts and multiply by 100. A ratio of 1:3 has 4 parts, so the first is 25% and the second is 75%. The calculator lists these shares under the simplified ratio for every ratio you enter.
What does a ratio of 1:n mean?
It rescales the ratio so the first part is 1, which makes comparisons easy. A ratio of 4:10 is 1 : 2.5, meaning there are 2.5 of the second for every one of the first. Map scales such as 1:25,000 are written this way.
Can a ratio have more than two parts?
Yes. A concrete mix of 1:2:3 cement, sand and gravel is a three-part ratio. Enter it with colons and the calculator simplifies it, gives each part's share of the whole and splits a total across all three parts.
How do I find a missing number in a ratio?
Scale the ratio so its first term matches the number you know. For 3:5 = 12:?, scale 3:5 to a first term of 12 and the ratio becomes 12:20, so the missing number is 20. If you know the second number instead, enter the ratio the other way round, as 5:3, and scale that.
See also: all Arithmetic tools, Number Theory, Algebra and Geometry, Statistics, Trigonometry and Calculus.
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