How to use the ratio calculator
- Choose what you want to do: simplify a ratio, find a missing value in a proportion, scale a ratio, or split a total in a ratio.
- Enter the two parts of the ratio, A and B. Decimals are fine, such as 1.5 : 2.25.
- To solve a proportion, fill in three of A, B, C and D and leave the unknown one empty.
- To scale, enter the factor to multiply by. To split, enter the total amount.
- Read the answer with the working, plus the ratio as a fraction, in 1 : n form and as percentages of the whole.
How ratios are calculated
A ratio compares two amounts by division, so multiplying or dividing both parts by the same number gives an equivalent ratio. To simplify, divide both parts by their greatest common divisor g. If the parts have decimals, first multiply both by 10, 100 or 1,000 to make them whole numbers. A proportion says two ratios are equal. Cross-multiplying turns it into an ordinary equation you can solve for the missing value. To split a total, add the parts to find how many equal shares there are.
Worked example
The calculator starts with 12 : 16:
- The greatest common divisor of 12 and 16 is 4.
- Divide both parts by 4: 12 ÷ 4 = 3 and 16 ÷ 4 = 4, so the ratio is 3 : 4.
- As a fraction, A ÷ B = 3/4 = 0.75. Out of the whole, A is 3/7 = 42.86% and B is 4/7 = 57.14%.
The other modes use the same numbers. To solve 12 : 16 = 15 : ?, cross-multiply: 12 × D = 16 × 15 = 240, so D = 240 ÷ 12 = 20. Scaling 12 : 16 by 2.5 gives 30 : 40, which still simplifies to 3 : 4. Splitting 700 in the ratio 12 : 16 means 3 + 4 = 7 parts of 100 each, so the shares are 300 and 400.
Ratios in everyday life
| Situation | Ratio | What it means |
|---|---|---|
| Concrete mix | 1 : 2 : 3 | 1 part cement, 2 sand, 3 gravel |
| Screen shape | 16 : 9 | 16 units wide for every 9 tall |
| Recipe scaling | 2 : 3 flour to water | 400 g flour needs 600 g water |
| Map scale | 1 : 50,000 | 1 cm on the map is 500 m on the ground |
| Class size | 24 : 1 | 24 students per teacher |
Ratios, fractions and percentages
A ratio of parts and a fraction of the whole are different things, and mixing them up is a common mistake. In a class with a boys-to-girls ratio of 3 : 4, boys are not 3/4 of the class. They are 3 of every 7 students, or 3/7 ≈ 42.9%. The fraction A/B = 3/4 compares the two groups with each other, which is the same information as the ratio.
Frequently asked questions
How do I simplify a ratio with decimals?
Multiply both parts by the same power of 10 to remove the decimals, then divide by the greatest common divisor. For 1.5 : 2.25, multiply by 100 to get 150 : 225. The GCD is 75, so the simplest form is 2 : 3.
How do I find the missing number in a ratio?
Write the two ratios as fractions, set them equal, and cross-multiply. For 3 : 5 = x : 40, you get 5 × x = 3 × 40 = 120, so x = 24. The calculator does this for whichever of the four boxes you leave empty.
How do I divide money in a ratio?
Add the parts of the ratio to find the number of shares, divide the total by that number, then give each person their number of shares. Splitting $600 in the ratio 2 : 3 gives 5 shares of $120, so the amounts are $240 and $360.
What is the 1 : n form of a ratio?
It rescales the ratio so the first part is 1, which makes ratios easy to compare. 4 : 10 becomes 1 : 2.5, and 3 : 8 becomes 1 : 2.667, so the second has relatively more of B. Map scales and gear ratios are often written this way.
Related calculators
- Fraction Calculator — Add, subtract, multiply and divide fractions and mixed numbers, simplify fractions and turn decimals into fractions.
- Percentage Calculator — Percent of a number, what percent one number is of another, percentage change and difference.
- Average Calculator — The mean of a list of numbers with the working shown, plus a weighted average for grades and scores.
- GCF Calculator — Greatest common factor of two or more whole numbers, with Euclid's algorithm and a prime factorization check.
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