What this calculator does
A ratio simplifier reduces numbers like 12:18 down to their lowest terms, 2:3, without changing what the ratio actually represents. The two ratios describe exactly the same relationship, one is just written with smaller numbers. This is the same idea as reducing a fraction, applied to two or more quantities being compared at once rather than one number over another.
The method is to find the greatest common divisor, the largest number that divides every term in the ratio evenly, and divide each term by it. Enter the terms separated by a colon or comma, in any order, including three or more terms if you are simplifying a ratio that splits something three or more ways.
The formula
Every term of the ratio is divided by the greatest common divisor (GCD) of all the terms together. If the terms are not whole numbers, they are first scaled up by a power of ten so the GCD can be found on integers, then simplified the same way.
| Term | Meaning |
|---|---|
| Ratio | A comparison of two or more quantities, written with a colon between the terms, such as 3:4. |
| Greatest common divisor (GCD) | The largest whole number that divides every term of the ratio with no remainder. |
| Lowest terms | A ratio written using the smallest whole numbers that still represent the same proportion. |
The inputs explained
| Field | What to enter |
|---|---|
| Ratio terms (comma or colon separated) | Enter the ratio terms separated by a colon, comma, or space, for example 12:18 or 4, 8, 20. |
When to use it
Simplifying a recipe or mixing ratio
A recipe or mix might specify quantities like 200:300 for two ingredients. Simplifying to 2:3 makes the underlying proportion obvious and easier to scale to any batch size.
Reducing a scale or aspect ratio
A map scale or image dimension written as an awkward pair of numbers, such as 1920:1080, simplifies to a smaller, more recognisable ratio, in this case 16:9.
Comparing two ratios quickly
Reducing two different-looking ratios to their simplest form is the fastest way to check whether they actually represent the same proportion.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What do common ratios simplify to?
A handful of ratios reduced to their simplest whole-number form.
| Ratio entered | Simplified ratio | Greatest common divisor used |
|---|---|---|
| 12:18 | 2 : 3 | 6 |
| 4:8 | 1 : 2 | 4 |
| 15:25 | 3 : 5 | 5 |
| 9:81 | 1 : 9 | 9 |
| 100:250 | 2 : 5 | 50 |
| 1920:1080 | 16 : 9 | 120 |
Questions
Can I simplify a ratio with more than two terms?
Yes. Enter as many terms as the ratio has, separated by colons or commas, such as 6:9:12. The calculator finds the greatest common divisor across all of them and divides every term by it.
What if the ratio includes decimals?
The terms are scaled up to whole numbers first (using the number of decimal places entered), simplified using their greatest common divisor, then shown in whole-number form.
Is this the same as the GCD and LCM calculator?
It uses the same greatest common divisor arithmetic, but this calculator is framed specifically around reducing a ratio to its simplest form. For the GCD and LCM of a set of numbers on their own, see the GCD & LCM calculator.
Why might two terms already be in their simplest form?
If the only common divisor the terms share is 1, they are already fully reduced, and the simplified ratio will match what you entered.
For the greatest common divisor and lowest common multiple of a set of numbers on their own, see the GCD & LCM calculator.