Ratio Calculator
Fill in three of the four numbers in a:b = c:d, leave one empty and read off the missing value. The guide covers simplifying and combining ratios, odds and screen aspect ratios.
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Created by the Reeliy Editorial Team. Last updated: Oct 19, 2026
What is a ratio?
A ratio compares two quantities by division. Written as a:b, it says that for every a units of the first thing there are b units of the second. A fruit punch mixed at 2:3 uses two parts juice for every three parts water; a map drawn at 1:25,000 shows one unit of distance for every 25,000 units on the ground.
Ratios have no units of their own, provided both quantities are measured in the same unit. They can be written with a colon (2:3), as a fraction (2/3) or in words (2 to 3). Multiplying or dividing both terms by the same non-zero number produces an equivalent ratio, so 2:3, 4:6 and 20:30 all describe the same relationship.
Ratios with more than two terms
A ratio can compare three or more quantities, such as 2:3:5. To split a total in that ratio, add the parts and divide the total by the sum. A prize of 20 shared 2:3:5 has 2 + 3 + 5 = 10 parts, each worth 2, so the shares are 4, 6 and 10.
How to use the calculator
The form holds two equal ratios, written a : b = c : d. Type any three numbers and leave the fourth box empty. The calculator reports which term is missing and what it should be. Leaving it as it opens, 2 : 3 = 400 : ?, gives 600 for the second denominator.
Exactly one box must be empty. A box that contains 0 counts as empty, so the calculator cannot use zero as a term. Results show up to four decimal places, with thousands separators for large values.
How to solve for a missing term
Two ratios are equal when their cross products match, so a:b = c:d means a × d = b × c. Rearranged for each unknown:
a = b × c ÷ d b = a × d ÷ c c = a × d ÷ b d = b × c ÷ a
Example: a gardener mixes plant food at 5:8 plant food to water. If the water is 56 litres, how much food is needed? Set 5:8 = x:56, so x = 5 × 56 ÷ 8 = 35.
Example: coffee brewed at 1:16 coffee to water, with 480 ml of water, needs 480 ÷ 16 = 30 g of coffee. The coffee ratio calculator does this for common brewing methods.
The same idea is the basis of the proportion calculator, which writes the two ratios as fractions.
Simplifying, scaling and combining ratios
Simplify a ratio by dividing both terms by their greatest common divisor. For 48:36 the divisor is 12, so the ratio reduces to 4:3. The GCD calculator finds the divisor and the simplify fractions calculator handles it for the fraction form.
Scale a ratio by multiplying both terms by the same factor: 2:3 scaled by 4 is 8:12.
Combine two ratios that share a term by making the shared terms equal. If A:B = 2:3 and B:C = 4:5, scale the first by 4 and the second by 3 so that B is 12 in both. Then A:B:C = 8:12:15.
Convert to a fraction or percentage by dividing one part by the total. In a 3:2 mix of 20 litres there are 5 parts of 4 litres each, so the first component is 12 litres, which is 60% of the whole. See the fractions calculator for more on working with the fraction form.
Odds as ratios
Odds are a ratio of favourable to unfavourable outcomes, while probability is favourable outcomes over all outcomes. Odds of 3:1 in favour mean three chances of success to one of failure, so the probability is 3 ÷ (3 + 1) = 75%.
probability = a ÷ (a + b) odds = p ÷ (1 − p)For odds a:b in favour and a probability p.
Going the other way, a probability of 0.2 gives odds of 0.2 ÷ 0.8 = 0.25, which is 1:4. Our odds calculator converts between the two forms, and the odds ratio calculator compares odds between two groups.
Aspect ratio calculations
An aspect ratio is the ratio of width to height of a screen, photo or video. Resizing an image without distortion means keeping that ratio fixed, which is exactly the equal-ratio problem the calculator solves.
A 16:9 video that is 1920 pixels wide must be 1920 × 9 ÷ 16 = 1080 pixels high. A 4:3 image 800 pixels wide needs a height of 800 × 3 ÷ 4 = 600, and a 16:10 display 1440 pixels wide is 1440 × 10 ÷ 16 = 900 high. To find the width from a height, put the unknown in the width position instead.
| Aspect ratio | Width | Height |
|---|---|---|
| 16:9 | 1920 | 1080 |
| 4:3 | 800 | 600 |
| 16:10 | 1440 | 900 |
| 1:1 | 1000 | 1000 |
Ratios in geometry and graphs
Similar shapes have the same angles and proportional sides, so the ratio of any pair of matching sides is constant. If a 6 cm side on a small triangle matches a 15 cm side on a larger one, the scale ratio is 6:15, which simplifies to 2:5, and every other side of the large triangle is 2.5 times its partner.
On a graph, quantities that stay in a fixed ratio plot as a straight line through the origin, and the slope of that line is the ratio. Checking whether points lie on one line is a quick way to test whether a relationship is truly proportional.
Make sure both quantities in a ratio use the same unit before you calculate. A ratio of 30 minutes to 2 hours is 30:120, which simplifies to 1:4, not 30:2.
Frequently asked questions
How do you find a missing number in a ratio?
Use cross multiplication. For a:b = c:d, multiply the two numbers on the diagonal that does not contain the unknown, then divide by the number opposite the unknown.
How do you simplify a ratio?
Divide both terms by their greatest common divisor. For example, 48:36 simplifies to 4:3 because both numbers divide by 12.
Can I use decimals or negative numbers?
Yes, decimals and negatives are accepted. A zero in any box is treated as an empty box, so the calculator needs exactly three non-zero numbers.
How do I keep an image's aspect ratio when resizing?
Write the original width and height as the first ratio, put your new width in the second ratio's first box, and leave the new height empty. The result is the height that keeps the proportions.
Cite this calculator and page
If you use this page in your work, you can cite it as:
Reeliy Editorial Team. (2026). Ratio Calculator. Reeliy. https://reeliy.com/calculators/ratio-calculator“Ratio Calculator.” Reeliy, 2026, https://reeliy.com/calculators/ratio-calculator.