About this tool
This ratio calculator covers the four jobs ratios turn up in: reducing a ratio such as 12:18 or 4:6:8 to its simplest whole-number form, solving a proportion a:b = c:d when one of the four terms is unknown, dividing a sum of money or a quantity between people in a given ratio, and reading or resizing screen and photo aspect ratios such as 16:9 and 4:3. It also converts a ratio into a fraction, a decimal, and percentages, and turns a percentage or fraction back into a part-to-rest ratio. It is written for students checking homework, cooks scaling recipes, anyone splitting a bill or a prize by shares, and designers who need the height that keeps an image in proportion. Every result shows the arithmetic used to reach it and can be copied or shared by link.
How it works
A ratio is simplified by dividing every term by the greatest common divisor of all the terms, found with Euclid's algorithm; decimal terms are first multiplied by a power of ten so the arithmetic stays exact (1.5:2.5 becomes 15:25, then 3:5). A proportion a:b = c:d is solved by cross-multiplying, a x d = b x c, and isolating the missing term, so 3:4 = x:12 gives x = 3 x 12 / 4 = 9. Splitting a total by a ratio gives each part total x part / (sum of parts); the whole-units option floors every share and hands the leftover units to the shares with the largest remainders so they still add up exactly. An aspect ratio is the simplified width:height pair; the nearest common ratio is the standard screen or photo ratio whose width / height differs least, in relative terms, from yours.
Frequently asked questions
How do you simplify a ratio?
Find the greatest common divisor (GCD) of all the terms and divide each term by it. For 12:18 the GCD of 12 and 18 is 6, so 12:18 = 2:3. For three or more terms use the GCD of the whole list: 4:6:8 has GCD 2 and simplifies to 2:3:4. If any term is a decimal, multiply every term by 10, 100, or 1,000 first so they are all whole numbers, then simplify. 1.5:2.5 becomes 15:25, which reduces to 3:5.
What is the difference between a ratio and a fraction?
A ratio compares two or more quantities to each other (2 parts sand to 3 parts cement, 2:3), while a fraction compares one part with the whole. The ratio 2:3 corresponds to the fractions 2/5 and 3/5 of the total, not to 2/3, although 2/3 is the value of the first term divided by the second. The calculator shows both readings: the ratio as a fraction a/b and each term's share of the whole.
How do I split money in a ratio?
Add the ratio terms to get the number of shares, divide the total by that number to get the value of one share, then multiply by each term. To split $500 in the ratio 3:2 there are 5 shares of $100, so the parts are $300 and $200. When the total does not divide evenly and you need whole dollars or whole items, round each share down and give the leftover units to the shares with the largest fractional parts so the pieces still add up to the total.
What aspect ratio is 1920 x 1080?
1920 x 1080 simplifies to 16:9 (both numbers divide by 120), the standard ratio for HD and 4K television and most laptop screens. Dividing width by height gives 1.78, which is how film and camera ratios are often written (1.78:1). Ultrawide monitors such as 2560 x 1080 are marketed as 21:9 but are exactly 64:27 (2.37:1); the calculator reports both the exact ratio and the nearest common name.