Ratio calculator, solve, simplify and split.

A ratio calculator keeps two or more amounts in the same proportion while their size changes. This one does five jobs: it finds the missing number in A:B = C:?, simplifies a ratio, splits a total in a ratio, scales a ratio up or down, and checks whether two ratios are equal. Numbers are kept as exact fractions, so a ratio with decimals such as 0.1:0.3 reduces to 1:3 with no rounding error. Every answer comes with its steps written out, so you can follow the working or copy it into homework.

How to use the calculator

1. Pick the job in Work out.
2. For Solve A:B = C:?, choose two or three in Terms in each ratio. Type what you know into First ratio and Second ratio and leave the box you want to find empty. You need at least one full pair, a number and the one under it.
3. For Simplify a ratio, type the ratio in Ratio as 12:18, 12 to 18 or 1.5:4.5. Three or more parts work too.
4. For Split a total in a ratio, type the Total to share and the Ratio. Add Names if you like, and pick a rounding in Round shares to if you want tidy amounts.
5. For Scale a ratio up or down, choose a factor, or choose Until one term has a size I choose and type the term number and its New size.
6. For Compare two ratios, fill every box.
7. Copy result copies the answer as a sentence. Copy link to these numbers gives a link that opens with your inputs.

Solving A:B = C:?

Two ratios are equal when one is the other multiplied by the same number. Find that number from the pair you know, then use it on the box you do not. For 3:4 = 9:?, the pair is 3 and 9, so the scale factor is 9 ÷ 3 = 3, and the missing number is 4 × 3 = 12. Check by cross multiplying: 3 × 12 = 36 and 4 × 9 = 36.

A recipe is a good test. If the flour to water ratio is 2:3 and you use 500 g of flour, the factor is 500 ÷ 2 = 250, and the water is 3 × 250 = 750 g. The unknown can sit in either ratio. For 3:4 = ?:12, the factor is 12 ÷ 4 = 3, and the missing number is 3 × 3 = 9. With three terms, one known pair is still enough to find the other terms.

Simplifying a ratio, even with decimals

To simplify, first make every term a whole number, then divide all of them by their greatest common divisor. For 12:18 the divisor is 6, so the answer is 2:3. For 0.1:0.3, multiply both terms by 10 to get 1:3, which cannot be reduced further. For 1/2:3/4, multiply by 4 to get 2:3. The page shows the multiplier it used, because a decimal or fraction ratio is where hand work usually goes wrong.

A ratio in simplest form is also the easiest to read. A screen of 1920 by 1080 pixels reduces to 16:9, since both numbers divide by 120. The aspect ratio calculator is built for sizes of screens, pictures and videos, with new sizes that keep the shape.

Splitting a total in a ratio

Add the parts, divide the total by that sum to get the size of one part, then multiply each term by it. To share 250 in the ratio 3:2, the parts add to 5, one part is 50, and the shares are 150 and 100. For 2:3:5 of 1,000, the parts add to 10, one part is 100, and the shares are 200, 300 and 500.

Some totals do not divide evenly. Splitting 100 in 1:2 gives 33.333333 and 66.666667 exactly. Choose 2 decimal places to get 33.33 and 66.67, which still add to 100. When rounded shares do not add back to the total, the page tells you so. That is only rounding.

Scaling a ratio

Scaling multiplies or divides every term by the same factor and leaves the ratio unchanged. 3:2 times 2.5 is 7.5:5, which is still 3:2 in simplest form. If you know the size one term must have, choose the second option instead. For 2:3 with the first term set to 500, the factor is 250, and the result is 500:750. The table of equal ratios shows the simplest form times 1 to 10, handy for picking whole-number sizes.

Comparing two ratios

Two ratios are equal when their simplest forms match. 3:4 and 6:8 both reduce to 3:4, so they are equal. To see which of two unequal ratios is bigger, cross multiply. For 3:4 against 5:7, 3 × 7 = 21 and 4 × 5 = 20, so 3:4 is the bigger ratio, because 3 ÷ 4 = 0.75 is more than 5 ÷ 7 = 0.714286.

Common mistakes

• Adding instead of multiplying. 3:4 grown by adding 6 to each term gives 9:10, which is a different ratio. Multiplying by 3 gives 9:12.
• Mixing up the order. 3:2 and 2:3 are different ratios, so keep the terms in the same order in both ratios.
• Forgetting what the parts mean. In a 3:2 split the first person gets 3 of 5 parts, which is 60%, not 3 of 2.
• Rounding too early. Keep the exact figure and round at the end, as the page does.

To turn a ratio into a percent, or to work out a share of a number, the percentage calculator shows every step. For ratios written as fractions, the fraction calculator adds, divides and simplifies them.