Transparent method
The formula
Worked example
Example inputs
How to interpret the result
A ratio and its simplified form describe the exact same proportion, just written with smaller numbers: 8-to-12 and 2-to-3 mean identically the same relationship, the way 4/8 and 1/2 are the same fraction. The simplification changes nothing about what's being described; it only makes the relationship easier to see and compare at a glance.
Before you rely on it
What to check
Confirm two ratios are actually comparable by reducing both to lowest terms first. Ratios that look different on the surface, like 6:9 and 4:6, can be identical once simplified.
The common error
Where people go wrong with ratio simplifier calculator
Treating an unsimplified ratio as somehow less accurate than a reduced one. 8:12 isn't wrong; it's the same proportion as 2:3 written with larger numbers, and reducing it is a clarity step, not a correction.
Sensitivity evidence
How first value changes the simplified first value
| First value | Simplified first value | Simplified second value |
|---|---|---|
| 6 | 1 | 2 |
| 7 | 7 | 12 |
| 8worked example | 2 | 3 |
| 9 | 3 | 4 |
| 10 | 5 | 6 |
Every input, tested
Which input moves the simplified first value most
| Input | Tested from | To | Simplified first value at each end | Swing |
|---|---|---|---|---|
| First value | 7 | 9 | 7 to 3 | 4 (200%) |
| Second value | 11 | 13 | 8 to 8 | none |
Two variables at once
Simplified first value by first value and second value
| First value \ Second value | 10 | 12 | 14 |
|---|---|---|---|
| 6 | 3 | 1 | 3 |
| 7 | 7 | 7 | 1 |
| 8 | 4 | 2 | 4 |
| 9 | 9 | 3 | 9 |
| 10 | 1 | 5 | 5 |
Step by step
The worked example, input by input
| Input | Value used |
|---|---|
| First value | 8 |
| Second value | 12 |
| Simplified first value | 2 |
| Simplified second value | 3 |
Where the inputs come from
Enter the two values of the ratio as whole numbers, such as 8 to 12. The calculator divides both by their greatest common factor to give the simplest whole-number ratio. If your values are decimals, multiply both by the same power of ten to make them whole first, for example 1.5 to 2.5 becomes 15 to 25. Both terms should be in the same units, so convert before simplifying.
When the result stops applying
Reordering a ratio changes its meaning, so 2 to 3 differs from 3 to 2. Three-part ratios need the greatest common factor of all three numbers. Ratios with zero are not meaningful.
What to compare it with
Solve for an unknown quantity on the proportion calculator, find common factors on the GCF and LCM page, and reduce fractions on the fraction simplifier. The percentage and percent difference calculators express comparisons differently. The golden ratio page covers one famous ratio.
People also ask
Frequently asked questions
How do I simplify a ratio?
Divide both terms by their greatest common factor. The ratio 8 to 12 divides by 4 to give 2 to 3.
What is the difference between a ratio and a fraction?
A ratio compares two quantities, while a fraction describes a part of one whole. A 2 to 3 ratio corresponds to fractions two fifths and three fifths of the total.
Can I simplify a ratio with decimals?
Yes. Multiply both terms by the same power of ten to make them whole numbers, then divide by their greatest common factor.