Ratio Calculator

How to Use the Ratio Calculator

A ratio compares two or more quantities to each other rather than to a whole, which is the single distinction that makes it different from a fraction and the one people most often lose track of. This calculator handles the three things anyone actually needs a ratio for.

1. Simplify reduces a ratio to its lowest terms and shows it as a decimal, a fraction and a share of the total. Enter the two terms and read the answer.
2. Solve for a term handles a proportion with one unknown: if a is to b as c is to what. Enter the three you know and the calculator cross-multiplies.
3. Share a total divides an amount in a given ratio — the mode you want for splitting a bill, mixing a batch or allocating a budget. A third part is optional; leave it at zero for a two-way split.
4. Use whichever notation you like. The terms do not have to be whole numbers. A ratio of 1.5 : 2.25 simplifies just as readily as 24 : 36.
5. Check the share percentage. It is the number that catches the classic error — in a 2 : 3 ratio the first part is 40% of the total, not 66.7% and not 2%.

The order of the terms matters and is not recoverable from the simplified form alone. A ratio of 3 : 5 is not the same statement as 5 : 3, even though both simplify to themselves.

Ratio Formulas

Three operations, one of which is the identity that underpins the whole subject.

The distinction between a ratio and a fraction is worth stating precisely. In 2 : 3, the ratio of the first part to the second is 2/3, and the fraction of the whole represented by the first part is 2/5. Both fractions are correct answers to different questions, and using one where the other belongs is the commonest ratio mistake there is.

Example

Simplifying 24 : 36

1. Find the greatest common divisor of 24 and 36: it is 12.
2. Divide both: 24 ÷ 12 = 2, and 36 ÷ 12 = 3. The ratio is 2 : 3.
3. As a decimal: 24 ÷ 36 = 0.666667.
4. Total parts: 2 + 3 = 5.
5. The first term is 2 ÷ 5 = 40% of the whole, and the second is 60%.
6. As a fraction of each other: 2/3. As a fraction of the whole: 2/5.

Solving a proportion

If 3 : 5 = 12 : what? Cross-multiply: the missing term is 5 × 12 ÷ 3 = 20. Check it by comparing the cross products — 3 × 20 = 60 and 5 × 12 = 60, which match, so the proportion holds. That single check catches almost every arithmetic slip in this kind of problem.

Sharing 750 in the ratio 2 : 3

Add the parts: 2 + 3 = 5. One part is 750 ÷ 5 = 150. The first share is 2 × 150 = 300 and the second is 3 × 150 = 450. They add back to 750, which is the check worth doing every time. The same method extends to any number of parts: a 3 : 5 : 1 mix of 4.5 kg gives 1.5 kg, 2.5 kg and 0.5 kg.

Ratios, Proportions and Odds

The same simplified ratio scaled up.

Every one of those rows describes the identical relationship. That is what makes ratios useful for scaling: a recipe written as 2 : 3 works for two people or two hundred, and the only thing that changes is what one part is worth.

Where ratios get misread is in the difference between a ratio and a proportion of the whole. “Two parts water to three parts concentrate” means the mixture is 40% water. “The mixture is two parts in three water” means 66.7%. Both sentences use similar words and describe very different liquids, which is why anyone mixing chemicals, concrete or feed writes the total parts down explicitly.

The other frequent confusion is odds against probability. Odds of 3 : 1 against mean three losing outcomes for every winning one, so the probability of winning is 1/4, not 1/3. Betting markets, medical statistics and risk reporting all use odds, and converting them to a probability requires dividing by the total rather than by the other term — the probability calculator works in probabilities throughout for exactly that reason.

Four Places Getting the Ratio Right Matters

Four practical uses where getting the ratio right matters more than usual.

Mixing to a specification. Concrete, fertiliser, fuel mixes and cleaning solutions are all specified as ratios, and the difference between “1 : 10” and “1 in 10” is the difference between one part in eleven and one part in ten. On a safety-critical dilution that is not a rounding difference — the concrete calculator sets out one common case in detail.

Scaling a recipe. Ingredients scale linearly and cooking times do not. Doubling a cake mixture doubles every ingredient and adds perhaps a quarter to the baking time, because heat has to reach the middle of something thicker.

Aspect ratios. A 16 : 9 image scaled to a 1,920-pixel width needs a height of 9 × 1,920 ÷ 16 = 1,080. That is a proportion problem with the same cross-multiplication, and it is worth knowing that 16 : 9 simplifies from 1,920 : 1,080 by a common factor of 120.

Financial ratios. Debt to equity, current ratio and price to earnings are all ratios rather than percentages, which means a value of 1.5 needs interpreting rather than reading. Whether higher is better depends entirely on which ratio it is.

A note on notation. Ratios are written with a colon, proportions with an equals sign between two ratios, and rates with a slash or the word "per". They are close relatives and the distinctions matter in writing: 60 miles per hour is a rate because the two quantities have different units, while 2 : 3 is a ratio because they share one. Dividing quantities with different units gives you a new unit; dividing quantities with the same unit gives you a bare number.

Two related tools: the fraction calculator for the exact arithmetic once a ratio has been turned into a fraction, and the percentage calculator for converting the resulting shares into percentages of a whole.