Ratio Calculator

How to Use the Ratio Calculator

This ratio calculator does five jobs: it simplifies a ratio (a ratio simplifier for two or three terms), solves a proportion such as A:B = C:?, scales a ratio up or down, splits an amount in a ratio, and works out aspect ratios for screens, photos and video. Every answer comes with the working, so you can follow each step and check it against your own.

Ratio Formulas

Worked Examples

Simplify 24:36. The GCD of 24 and 36 is 12, so 24 ÷ 12 : 36 ÷ 12 = 2:3. That is the fraction 2/3 (0.6667), a split of 40% : 60%, and the form 1 : 1.5.

Simplify 1.5:2.5. Multiply both terms by 10 to get 15:25. The GCD is 5, so the ratio is 3:5, a split of 37.5% : 62.5%.

Solve 3:4 = x:20. Cross-multiplying gives 3 × 20 = 60, so x = 60 ÷ 4 = 15. The check works: 4 × 15 = 60, and the right side is 5 times the left.

Split $500 in the ratio 2:3. There are 2 + 3 = 5 parts, so one part is $500 ÷ 5 = $100. The shares are $200 and $300.

Aspect ratio of 1920 × 1080. The GCD is 120, so the ratio is 16:9. Scaled to a width of 1280, the height is 1280 × 1080 ÷ 1920 = 720.

Ratios, Fractions and Percentages

A ratio such as 3:5 can be read three ways. As A ÷ B it is the fraction 3/5, or 0.6. As a share of the whole it is 3 out of 8, or 37.5%, with the other part at 62.5%. And in the 1:n form it is 1 : 1.667, which is handy for saying “for every 1 of A there are 1.667 of B”. The calculator shows all of these so you can pick the one your question needs.

Frequently Asked Questions

How do I simplify a ratio?

Divide every term by their greatest common divisor (GCD). For 24:36 the GCD is 12, so the ratio simplifies to 2:3. If the terms are decimals, multiply them all by 10, 100 or 1,000 first to make whole numbers: 1.5:2.5 becomes 15:25, and dividing by 5 gives 3:5.

How do I calculate a ratio?

Write the two quantities in the order they are named, separated by a colon, then simplify. If a class has 12 boys and 18 girls, the ratio of boys to girls is 12:18, which simplifies to 2:3. Always keep the units the same on both sides, so convert 30 minutes and 2 hours to 30 and 120 minutes before comparing them.

How do I solve a proportion like 3:4 = x:20?

Cross-multiply: A × D = B × C, so for 3:4 = x:20 you get 3 × 20 = 4 × x, which gives x = 60 ÷ 4 = 15. Leave one box blank on the Proportion tab and the proportion calculator works out the missing value and checks that both cross-products match. The same method solves recipe scaling, map scales and currency or unit-rate problems.

How do I convert a ratio to a percentage?

Add the parts to get the total, then divide each part by the total and multiply by 100. For 3:5 the total is 8, so the shares are 3 ÷ 8 = 37.5% and 5 ÷ 8 = 62.5%. The percentages always add up to 100%, and the Simplify tab shows them alongside the fraction and decimal forms.

How do I split an amount by a ratio or divide money in a ratio?

Add the parts of the ratio, divide the amount by that total to get the value of one part, then multiply by each part. To divide $500 in the ratio 2:3, one part is $500 ÷ 5 = $100, so the shares are $200 and $300. The Split an amount tab does this for two to six parts and can round to whole cents.

What happens when an amount doesn't split evenly into cents?

Some splits don't come out in whole cents: $100 shared in the ratio 1:1:1 is $33.33 each with a cent left over. With rounding on, the calculator rounds each share down and gives the leftover cents to the parts with the largest fractional remainders, so $100 becomes $33.34, $33.33 and $33.33 and the parts add up to the total exactly. If the split matters, such as a legal or tax arrangement, agree the rounding rule in advance.

How do I find the ratio of three numbers?

Enter all three terms and the ratio is simplified the same way, using the GCD of all three numbers. For example 20:30:50 simplifies to 2:3:5. The shares of the total are then 20%, 30% and 50%, and the 1:n form reads 1 : 1.5 : 2.5. A ratio can have up to six terms in this calculator.

How do I calculate an aspect ratio?

Divide the width and height by their GCD. A 1920 × 1080 screen has a GCD of 120, so its aspect ratio is 16:9. To resize while keeping the shape, multiply a new width by height ÷ width: at a width of 1280 the height is 1280 × 1080 ÷ 1920 = 720 pixels. If the answer is not a whole number, such as 562.5 for a width of 1000, round to the nearest pixel.

What is the difference between a ratio and a fraction?

A ratio compares parts to each other, while a fraction compares a part to the whole. The ratio 3:5 compares one part with another, so A ÷ B is 3/5. As a fraction of the whole, though, the first part is 3 out of 8, or 3/8 (37.5%). Mixing the two up is the most common mistake when turning ratios into percentages.