How to calculate a ratio
A ratio is just a way to compare quantities. Here is how to write one, simplify it, scale it, split an amount in a ratio, and turn it into a percentage, each with a worked example.
Simplify a ratio and solve a proportion in one place.
Ratios turn up everywhere once you notice them: two parts of this to one part of that in a recipe, a map scale, an aspect ratio, the mix for concrete, the odds in a bet. A ratio is simply a way to compare two or more quantities and show their relative sizes. The good news is that calculating with ratios comes down to a handful of moves: write it, simplify it, scale it, and sometimes split an amount by it. Here is each one with a worked example, plus how to turn a ratio into a fraction or a percentage. A free ratio calculator does the arithmetic for you, but the method is worth understanding.
What is a ratio?
A ratio compares quantities of the same kind and is written with a colon, like 3:2, read "three to two". It says that for every 3 of the first thing there are 2 of the second. Order matters: 3:2 is not the same as 2:3, so always keep the quantities in the order you named them. A ratio can have more than two terms too, such as 2:3:5 for three ingredients.
One distinction clears up most confusion. A part-to-part ratio compares the parts to each other (3 parts juice to 2 parts water). A part-to-whole ratio compares one part to the total (3 parts juice out of 5 parts drink). You get the whole by adding the parts: 3 + 2 = 5. Knowing which one you are dealing with is half the battle.
How to find the ratio of two numbers
If you are given two actual amounts and asked for the ratio, write them in order and then simplify. Say a class has 12 boys and 18 girls. The ratio of boys to girls is 12:18, and the greatest common factor of 12 and 18 is 6, so it simplifies to 2:3. The same works for three numbers: 12:18:30 all share a factor of 6, giving 2:3:5. Always convert to the same unit first, so a ratio of 1 hour to 30 minutes is 60:30 = 2:1, not 1:30.
How to simplify a ratio
Simplifying a ratio means writing it in its smallest whole numbers, exactly like simplifying a fraction. You divide every term by their greatest common factor (the largest number that divides all of them).
Say you have 20:50. The greatest common factor of 20 and 50 is 10, so divide both by 10: 20:50 = 2:5. The ratio is unchanged, just written more simply. If you are not sure of the common factor, our GCF calculator finds it, or you can keep dividing by any shared factor until nothing divides both: 20:50 → 10:25 (divided by 2) → 2:5 (divided by 5). Same answer.
Two more cases. If the numbers share no common factor, like 4:9, the ratio is already simplest. And if a term is a decimal or fraction, first multiply every term by the same number to clear it: 1.5:2 becomes 3:4 (multiply both by 2), and ½:¼ becomes 2:1 (multiply both by 4).
How to scale a ratio up or down
Scaling keeps the ratio the same while changing the actual amounts. You multiply or divide every term by the same number. This is how a recipe for 2 scales to 6, or a model keeps its proportions.
A worked example: a paint mix is 3:1, base to tint, and you have 12 litres of base. The tint is 12 ÷ 3 = 4 litres, so the mix is 12:4, which simplifies back to 3:1. Or to triple a 3:1 mix, multiply both terms by 3 to get 9:3. A related move is the missing value: if x:12 has to equal 2:3, then 12 is the "3" part, so one part is 12 ÷ 3 = 4, and x is the "2" part, so x = 2 × 4 = 8. For turning a ratio into real quantities from a total, use the splitting method next, which is the one people need most.
How to split an amount in a given ratio
This is the most useful ratio skill and the one exam questions love. You are told a total and a ratio, and asked how much each share is. The method is three steps:
- Add the parts to get the total number of parts.
- Divide the amount by the total parts to get the value of one part.
- Multiply each ratio term by the value of one part.
Worked example: split 200 in the ratio 3:2. Add the parts: 3 + 2 = 5. One part is 200 ÷ 5 = 40. So the shares are 3 × 40 = 120 and 2 × 40 = 80. Check it: 120 + 80 = 200, and 120:80 simplifies back to 3:2. A three-term example works the same way: split 1,000 in 2:3:5. Parts total 10, one part is 100, so the shares are 200, 300 and 500.
The check at the end matters: your shares should add back to the original total, and their ratio should simplify to the one you started with. If they do not, you divided by the wrong number of parts.
Ratio to fraction and percentage
A ratio and a fraction are close cousins. For a part-to-part ratio of 3:2, the first quantity is 3 out of every 5, so it is the fraction 3/5, and the second is 2/5. Turn those into percentages by dividing and multiplying by 100: 3 ÷ 5 = 0.6 = 60 percent, and 2/5 = 40 percent. So a 3:2 ratio is a 60/40 split. If you often go the other way too, our guide on how to work out a percentage covers the reverse.
Comparing two ratios uses the same idea. To see whether 3:4 and 6:8 are equivalent, simplify both: 6:8 divides by 2 to give 3:4, so yes, they are equal. Turning each into a fraction (3/4 = 0.75, 6/8 = 0.75) is another way to check.
Real-life ratio examples
Recipes are the everyday one: a classic vinaigrette is 3:1 oil to vinegar, so for 200 ml of dressing you need 150 ml oil and 50 ml vinegar (3:1 means 3 out of 4 parts is oil, and 3/4 of 200 is 150). Maps use ratios as scale: 1:50,000 means 1 cm on the map is 50,000 cm, or 500 m, on the ground. Screens use aspect ratios like 16:9. Mixing concrete, fuel for a two-stroke engine, currency conversion and sharing a bill or a prize all reduce to the same splitting method above.
Odds are a ratio too, though read carefully: odds of 2:1 against mean 2 losing outcomes to 1 winning one, so a 1 in 3 chance, not 1 in 2. The ratio is honest; the trap is reading it as a fraction of the whole when it is part-to-part.
Common ratio mistakes
- Swapping the order. 3:2 and 2:3 are different ratios. Keep the terms in the order you named the quantities.
- Mixing units. A ratio compares like with like, so convert first: a ratio of 1 hour to 30 minutes is 60:30 = 2:1, not 1:30.
- Dividing by the wrong total when splitting. Divide the amount by the sum of the parts (5 for 3:2), not by the number of terms (2).
- Treating a part-to-part ratio as part-to-whole. In 3:2, the first share is 3/5 of the total, not 3/2.
Get the order right, simplify by the greatest common factor, and remember that splitting an amount is just "add the parts, find one part, multiply back", and ratios stop being intimidating. When you want the arithmetic done instantly, including simplifying, scaling and splitting, the free ratio calculator handles it, and the fraction calculator helps when a ratio has fractions in it.