Ratio and Proportion Calculator
History
Your results will appear here. Tap Use on any of them to carry it into the next calculation, in this calculator or another one. History is kept while this tab is open.
This ratio calculator doubles as a proportion calculator and a ratio solver: it finds the missing value in A : B = C : D by cross-multiplication. 6 : 8 = 15 : x gives x = 15 × 8 ÷ 6 = 20, and with only A and B it simplifies: 6 : 8 = 3 : 4.
Simplify a Ratio
To simplify a ratio, divide both terms by their greatest common divisor. 6 : 8 becomes 3 : 4, and the ratio of 4 to 8 becomes 1 : 2. Decimals turn into whole numbers first: 1.5 : 2.5 = 3 : 5.
A fraction is already a ratio, so 1/2 as a ratio is 1 : 2. Order matters. A 2:1 ratio is not a 1:2 ratio. Use sends a simplified ratio to the fraction calculator as a single fraction: 3 : 4 arrives as 3/4.
Fill in only A and B and press Calculate. If the ratio can't be reduced, like 2 : 5, the display says Already in simplest form.
How It's Calculated
To calculate a ratio a : b, divide: its value is a ÷ b. A proportion says two ratios are equal, and in a true proportion the cross products match:
A × D = B × C
So any one term follows from the other three:
D = C × B ÷ A
C = D × A ÷ B
B = A × D ÷ C
A = B × C ÷ D
The formula line on the display shows this step with your numbers, for example D = 15 × 8 ÷ 6 = 20. Results are rounded to 12 significant digits: 3 : 7 = 5 : x gives 11.6666666667. Simplifying divides by the greatest common divisor, as in Simplify a Ratio.
Leave one field empty, fill in the other three and press Calculate.
Examples
This ratio calculator scales grams in a recipe or lengths on a drawing with one proportion. Each row is one calculation.
| You enter | Result | Also shown | Formula |
|---|---|---|---|
| 6 : 8 = 15 : x | D = 20 | 6 : 8 = 15 : 20 · 6 : 8 = 3 : 4 | D = 15 × 8 ÷ 6 = 20 |
| x : 8 = 15 : 20 | A = 6 | 6 : 8 = 15 : 20 · 6 : 8 = 3 : 4 | A = 8 × 15 ÷ 20 = 6 |
| 2 : 5 = 4 : x | D = 10 | 2 : 5 = 4 : 10 | D = 4 × 5 ÷ 2 = 10 |
| 6 : 8 (A and B only) | 3 : 4 | — | — |
| 1.5 : 2.5 (A and B only) | 3 : 5 | — | — |
| Recipe: 250 g : 150 g = 400 g : x | D = 240 | 250 : 150 = 400 : 240 · 250 : 150 = 5 : 3 | D = 400 × 150 ÷ 250 = 240 |
| Drawing: 1 : 50 = 3.5 : x | D = 175 | 1 : 50 = 3.5 : 175 | D = 3.5 × 50 ÷ 1 = 175 |
| 3 : 7 = 5 : x | D = 11.6666666667 | 3 : 7 = 5 : 11.6666666667 | D = 5 × 7 ÷ 3 = 11.6666666667 |
FAQ
What is a ratio in math?
A ratio compares two quantities by division and is written a : b or a/b. The order of the terms matters: 1 : 2 and 2 : 1 are different ratios.
How do I calculate the ratio between two numbers?
To find the ratio, write the two numbers as a : b and divide both by their greatest common divisor: 6 and 8 give 6 : 8, which is 3 : 4. In the calculator above, enter 6 in A and 8 in B and press Calculate.
What is the ratio of 2 to 5?
It's 2 : 5, or the fraction 2/5 = 0.4, and it's already in simplest form. Scaled up, 2 : 5 = 4 : 10.
How do I do ratios on a calculator?
On an ordinary calculator, divide a by b to get the value of the ratio: 2 ÷ 5 = 0.4. For the missing term of a proportion, multiply and then divide (C × B ÷ A): 6 : 8 = 15 : x gives 15 × 8 ÷ 6 = 20. On this page, fill in three fields and press Calculate.
What does a 1:2 ratio mean?
For every 1 part of the first quantity there are 2 parts of the second. The first is half the second and a third of the whole: 1 ÷ 3 = 33.33%. To turn parts into percentages, use the percentage calculator. A 2:1 ratio means the reverse.