How to Calculate Ratios (With Worked Examples)
A ratio is just a comparison between two numbers, written with a colon: 3:2, read as three to two. It tells you how the parts relate to each other — not how big they are in total, and not what units they are in. Once you see that, most ratio problems become the same three steps: write the numbers in order, simplify if you can, and scale up or down to the amount you actually need.
I use ratios more than I expected to: splitting a bill fairly, scaling a recipe, checking why a video looks stretched on a new screen, reading a map. The maths is school-level, but the mistakes are adult ones — usually writing the numbers in the wrong order, or mixing units. This guide works through five real examples, slowly, so you can check each step against your own problem.
What a ratio is, in plain language
Take 3 red pens and 2 blue pens. The ratio of red to blue is 3:2. That does not mean there are only 5 pens in the world — it means that for every 3 red pens, there are 2 blue ones. A box with 30 red and 20 blue pens has the same ratio, because 30:20 simplifies to 3:2.
Two rules matter from the start. First, order matters. Red to blue is 3:2. Blue to red is 2:3. They describe the same pens, but they are not the same ratio. Always write the numbers in the order the question asks for them. Second, a ratio has no units of its own. 3 cups to 2 cups is 3:2, and so is 3 litres to 2 litres. But 3 metres to 2 centimetres is NOT 3:2 — you must convert to the same unit first, as I explain in my guide to converting units accurately.
Ratio vs fraction vs percentage
These three describe the same relationship in different clothes. For a ratio of 3:2, the total parts are 3 + 2 = 5. The first part as a fraction is 3 out of 5, or 3/5. As a percentage it is 3 divided by 5 = 0.6 = 60%. The second part is 2/5 = 40%.
So if someone says the ratio is 3:2, you can also say 60% of the total is the first part. Use whichever form the question wants. If it asks for a ratio, answer with a ratio — do not hand back a percentage and call it done. Our Percentage Calculator converts between these forms instantly, which is handy when a question switches form halfway through.
5 worked examples, step by step
Example 1: Scaling a recipe
Problem: a rice recipe uses rice and water in the ratio 1:2. You want to cook 3 cups of rice. How much water do you need? Step 1 — write the ratio in order: rice : water = 1 : 2. Step 2 — find the scale factor: you have 3 cups of rice, and the recipe's rice part is 1, so the scale factor is 3 divided by 1 = 3. Step 3 — scale the other part by the same factor: water = 2 times 3 = 6 cups. Answer: 6 cups of water. The check is simple: 3:6 simplifies back to 1:2, so the proportion is unchanged. The golden rule of scaling a ratio is that you multiply (or divide) both parts by the same number — never just one.
Example 2: Splitting money fairly
Problem: two friends split $120 in the ratio 3:2. How much does each get? Step 1 — add the parts: 3 + 2 = 5 total parts. Step 2 — find the value of one part: $120 divided by 5 = $24 per part. Step 3 — multiply back: first friend 3 times $24 = $72, second friend 2 times $24 = $48. Answer: $72 and $48. Check: $72 + $48 = $120, and 72:48 simplifies to 3:2. This total-parts method is the one to reach for whenever a question gives you a total amount and a ratio.
Example 3: Screen size and aspect ratio
Problem: a video is 16:9. If the width is 1,920 pixels, what is the height? Step 1 — write the ratio in order: width : height = 16 : 9. Step 2 — find the scale factor: width part is 16, actual width is 1,920, so the scale factor is 1,920 divided by 16 = 120. Step 3 — scale the height: height = 9 times 120 = 1,080 pixels. Answer: 1,920 by 1,080 — the standard Full HD size. This is also why a 16:9 video looks stretched or letterboxed on a 4:3 screen: the ratio of the video and the ratio of the screen do not match, so something has to give.
Example 4: Reading a map scale
Problem: a map has a scale of 1:50,000. Two towns are 4 cm apart on the map. How far apart are they in real life? Step 1 — read the scale as a ratio: map distance : real distance = 1 : 50,000, in the same unit. Step 2 — scale up: real distance = 4 cm times 50,000 = 200,000 cm. Step 3 — convert to a useful unit: 200,000 cm = 2,000 m = 2 km. Answer: 2 km. Map scales are ratios in disguise, and the usual slip is stopping at 200,000 cm and calling that the answer. Always convert to kilometres or miles at the end, or the number means nothing to a reader.
Example 5: A class ratio, simplified
Problem: a class has 18 boys and 12 girls. What is the ratio of boys to girls, in simplest form? Step 1 — write it in order: boys : girls = 18 : 12. Step 2 — find the greatest common divisor: the largest number dividing both 18 and 12 is 6. Step 3 — divide both parts by it: 18 divided by 6 = 3, 12 divided by 6 = 2. Answer: 3:2. The ratio 18:12 is correct but unsimplified; 3:2 is the same relationship in its cleanest form, and it is the form markers and readers expect.
How to simplify a ratio
Find the greatest common divisor (GCD) of the two numbers — the largest whole number that divides both. Divide both parts by it. If the GCD is 1, the ratio is already in simplest form. Examples: 24:36, divide by 12, gives 2:3. 10:15, divide by 5, gives 2:3. 7:4 has a GCD of 1, so it is already simplest. Note that 24:36 and 10:15 simplify to the same ratio, 2:3 — different numbers, same relationship.
If a ratio has three parts (say 2:3:5), the same method applies: divide all three by their GCD. And if the numbers are awkward — large totals, three-part ratios, or a proportion to solve — check yourself with our Percentage Calculator, which solves proportions and simplifies ratios in your browser.
Two common mistakes
Mistake 1: flipping the order. Boys to girls is not the same as girls to boys. Before you write anything, underline which quantity the question names first, and put that number first. Half of all ratio errors are just this.
Mistake 2: mixing units. 1 metre to 50 centimetres is not 1:50. Convert first: 1 metre = 100 centimetres, so the ratio is 100:50, which simplifies to 2:1. Whenever the two numbers carry different units — metres and centimetres, hours and minutes, dollars and cents — convert to one unit before you do anything else. I gave unit conversions the same slow treatment in my guide to converting units accurately, including the temperature trap that once cost NASA a spacecraft.
Quick answers to common questions
What is a ratio in simple words?
A ratio compares two quantities by division, written as a:b. It shows how many times bigger one quantity is relative to the other, without stating the total.
How do you calculate a ratio from two numbers?
Write them in the order asked, in the same unit, then divide both by their greatest common divisor to simplify. For example, 18:12 becomes 3:2.
What is the difference between a ratio and a fraction?
A ratio compares part to part (3:2); a fraction usually compares part to whole (3/5). For 3:2, the total is 5 parts, so the first part is 3/5 of the whole.
How do you split an amount by a ratio?
Add the parts to get the total parts, divide the amount by that total to get one part's value, then multiply by each part. For $120 in the ratio 3:2: 5 parts, $24 each, giving $72 and $48.