Ratio Calculator
Enter a ratio such as 1920:1080, 3/4 or 12 to 8 and get its simplest form, the same ratio as 1 : n and as a decimal, each term's share of the whole and a table of equivalent ratios. Two more tabs solve a proportion with one missing term and scale a ratio from one known value or split a total. Decimals are allowed. Everything runs in your browser.
| Multiply by | Equivalent ratio |
|---|---|
| 1 | 16 : 9 |
| 2 | 32 : 18 |
| 3 | 48 : 27 |
| 4 | 64 : 36 |
| 5 | 80 : 45 |
| 6 | 96 : 54 |
| 7 | 112 : 63 |
| 8 | 128 : 72 |
A ratio compares quantities, and it keeps its meaning when every term is multiplied or divided by the same number. To simplify, the tool divides every term by their greatest common divisor, and decimals are scaled out first, so 2.5 : 10 becomes 25 : 100 and then 1 : 4. In a proportion A : B = C : D, the cross products are equal, so a missing term is the product of the two opposite terms divided by the remaining one. To split a total, each part is its term divided by the sum of the terms, times the total. Everything is worked out in your browser and nothing is uploaded.
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Student ToolsAbout the Ratio Calculator
A ratio compares quantities, and it keeps its meaning when every term is multiplied or divided by the same number. To simplify one, the tool divides every term by their greatest common divisor, found exactly with whole-number arithmetic, so 1920:1080 becomes 16:9 after dividing by 120. Decimals are scaled out first by multiplying every term by the same power of ten, so 2.5 : 10 becomes 25 : 100 and then 1 : 4. A ratio can have from two to five terms, and a zero is allowed as long as one term is not zero. The 1 : n form divides the second term by the first, and the shares are each term over the total, in percent. The proportion tab solves A : B = C : D when exactly one of the four is empty, using cross multiplication: the product of the two opposite terms divided by the remaining one. The scale tab takes a known value for one term, such as 450 of the first term in a 3 : 2 recipe, and gives the other terms, and it can split a total, such as 1,000 in the ratio 2 : 3 : 5, into 200, 300 and 500. Nothing is uploaded.
How do I simplify a ratio?▾
Divide every term by the greatest common divisor. For 12 : 8 the divisor is 4, so the ratio is 3 : 2. If one of the terms is a decimal, multiply all the terms by a power of ten first. The tool does both steps.
How do I solve a proportion?▾
In A : B = C : D, the cross products are equal: A x D = B x C. So the missing term is the product of the two terms on the opposite corners divided by the remaining one. For 3 : 4 = 9 : x, x is 4 x 9 / 3, which is 12.
How do I split an amount in a ratio?▾
Add the terms of the ratio, divide the amount by that sum, and multiply by each term. Splitting 1,000 in the ratio 2 : 3 : 5 gives 200, 300 and 500, because the terms add up to 10 and each part is 100 times its term.
What is the ratio 16:9?▾
It is the shape of most widescreen displays: the width is 16 units for every 9 of height. 1920 x 1080 simplifies to exactly 16:9, which is also 1 : 0.5625 or a width that is 1.7778 times the height.
Can a ratio have more than two terms?▾
Yes, up to five in this tool, such as 2 : 3 : 5. It simplifies them all together and gives each term's share of the whole. Your numbers are not uploaded.