What this calculator does
This tool reduces a ratio to its lowest terms, which means the smallest whole numbers that still describe the same relationship. Enter something like 24 : 36 and it returns 2 : 3. It also shows how it got there, so you can check your homework, double-check a recipe, or learn the method yourself.
How to use it
- Type your numbers into the boxes. You need at least two. The third and fourth are optional.
- Decimals are fine, for example 0.75 : 1.5.
- Press Simplify. You can also press Try an example to see a finished one.
- Read the answer, then scroll down for the step-by-step explanation and the same working in math form.
How the calculator simplifies a ratio
It follows the same three steps you would use on paper:
- Clear any decimals. If a number has decimals, every number is multiplied by 10, 100 or 1000 until they are all whole.
- Find the greatest common divisor (GCD). This is the largest number that divides every part with no remainder. The calculator uses Euclid's method, which is quick even for big numbers.
- Divide every part by the GCD. The result is the simplest form.
If the GCD turns out to be 1, the ratio is already as simple as it gets, and the calculator tells you so.
Examples you can try
| You enter | Simplest form | Why |
|---|---|---|
| 24 : 36 | 2 : 3 | GCD is 12 |
| 12 : 18 : 30 | 2 : 3 : 5 | GCD is 6 |
| 0.75 : 1.5 | 1 : 2 | Becomes 75 : 150, then GCD is 75 |
| 8 : 20 | 2 : 5 | GCD is 4 |
| 100 : 25 | 4 : 1 | GCD is 25 |
| 1920 : 1080 | 16 : 9 | The familiar screen shape; GCD is 120 |
Where people use it
- Recipes: a mix of 1.5 cups flour to 0.5 cups sugar is 15 : 5, which simplifies to 3 : 1.
- Screens and video: 1920 × 1080 simplifies to 16 : 9. Our aspect ratio guide covers the common shapes.
- Schools: 540 students to 27 teachers is a 20 : 1 student-teacher ratio.
- Mixing and building: paint, concrete or fuel mixes are usually quoted in their simplest ratio so they are easy to measure.
Tips for reliable answers
- Use the same unit on every number. Convert feet to inches, or cups to ounces, before you simplify. A ratio of 3 ft to 18 in is really 36 in to 18 in, which is 2 : 1.
- Keep the order. 24 : 36 simplifies to 2 : 3, while 36 : 24 simplifies to 3 : 2.
- Zero is allowed in one position (for example 0 : 5 becomes 0 : 1), but at least one number must be greater than zero.
- Results are shown to up to six decimal places when a decimal is needed.
Read our short guide with worked examples you can follow on paper.
Frequently asked questions
How do you simplify a ratio?
Find the greatest common divisor of all the numbers and divide each number by it. For 24 : 36 the GCD is 12, so the simplified ratio is 2 : 3.
Can I simplify a ratio that has decimals?
Yes. Multiply every number by 10, 100 or 1000 until they are all whole, then simplify as usual. The calculator does this automatically and tells you what it did.
What if the ratio is already in its simplest form?
Then the greatest common divisor is 1 and the numbers cannot be reduced. For example, 7 : 5 stays 7 : 5.
Does the order of the numbers matter?
Yes. A ratio of 24 : 36 is not the same as 36 : 24. The first simplifies to 2 : 3 and the second to 3 : 2.
Can I simplify a ratio with three or four numbers?
Yes. Enter up to four numbers. The calculator finds the GCD of all of them and divides each one, so 12 : 18 : 30 becomes 2 : 3 : 5.