Simplify a ratio to lowest terms, solve a proportion a:b = c:x, or split a total in a ratio. Exact, with steps.
Type 2 or 3 numbers separated by colons, such as 12:18 or 2:3:5. Decimals are allowed (1.5:4.5), negative numbers are not. The page multiplies every term by a power of 10 until they are whole numbers, then divides all of them by their greatest common divisor: 12:18 has gcd 6 and becomes 2:3, and 1.5:4.5 becomes 15:45 and then 1:3. It also gives the ratio as 1 : n (divide every term by the first, so 2:3 is 1 : 1.5) and, for two terms, as n : 1 (0.6666666667 : 1). A first term of 0 has no 1 : n form. At least one term must be above 0.
A proportion a : b = c : x says two ratios are equal, which means a × x = b × c. Fill three of the four boxes and leave one empty; the empty one is solved by cross-multiplying. For 3 : 4 = 9 : x, x = 4 × 9 ÷ 3 = 12. The empty box can be any of the four: x : 4 = 9 : 12 gives 3. If solving needs a division by zero, such as 0 : 5 = 3 : x, the page says so instead of showing a number. If the answer does not end, as 3 : 7 = 1 : x giving 2.3333333333, it is rounded to 10 decimal places and a note says so.
To share 120 in the ratio 2:3, add the terms (2 + 3 = 5), then each part is total × term ÷ sum: 120 × 2 ÷ 5 = 48 and 120 × 3 ÷ 5 = 72. Up to 3 terms are supported, and the table lists each part with its reduced share of the total (2/5 and 3/5) and its amount. When the parts do not divide evenly, such as 100 in 1:2:3, they are rounded to 10 decimal places and the page warns that they may not add up to the total exactly.
Numbers are read as exact decimals and all arithmetic uses BigInt fractions, so there are no floating-point errors: 0.1:0.3 is exactly 1:3. A term can have up to 30 characters. Nothing you type is stored or sent anywhere. A browser without BigInt gets a message instead of an approximate answer.
Divide every term by the greatest common divisor. For 12:18 the gcd is 6, so the simplest form is 2:3. If the terms are decimals, multiply them all by 10, 100 and so on first, as in 1.5:4.5 becoming 15:45, and then reduce to 1:3.
Add the terms to get 5, then multiply the total by each term over 5. For 120 that gives 48 and 72. Choose Split a total, type 2:3 and 120, and the table shows each part and its share.
Choose Solve, fill three boxes and leave one empty. The page cross-multiplies: for 3 : 4 = 9 : x it computes 4 × 9 ÷ 3 = 12. Leaving a, b or c empty also works.
It is the ratio rewritten so the first term is 1. Divide every term by the first one: 2:3 becomes 1 : 1.5. The n : 1 form divides by the last term instead and is shown only for ratios with two terms.
Resizing a width and height while keeping their shape is a different job, handled by the tool linked under related tools. This page works on any ratio of numbers, such as recipe or mixing proportions.
A term can be 0 (0:5 simplifies to 0:1) as long as another term is above 0. Negative numbers are not accepted, and 0:0 shows a message.