Ratio & proportion tools
Simplify Ratio
Reduce any ratio to its simplest whole-number form — including decimals, fractions and three-part ratios.
Two or more parts, including decimals (1.5:2.5) and fractions (1/2 : 3/4).
Exact result
2 : 3
12:18 simplified
Working
- Every part is already a whole number.
- Greatest common divisor (GCD) = 6.
- 12 ÷ 6 = 2
- 18 ÷ 6 = 3
Whole numbers: divide by the greatest common divisor
12:18
- The divisors of 12 are 1, 2, 3, 4, 6, 12; of 18 they are 1, 2, 3, 6, 9, 18.
- The greatest divisor they share is 6.
- 12 ÷ 6 = 2 and 18 ÷ 6 = 3, so 12:18 = 2:3.
- 2 and 3 share no divisor above 1, so 2:3 is final.
Decimals: become exact integers first
A decimal ratio is simplified by turning it into an exact integer relationship before any division happens. SnapRatios reads each decimal as a rational number, so 1.5 is held as 3/2 and 2.25 as 9/4 — there is no floating-point step and no rounding at any point.
1.5 : 2.25
Scale both parts by 100 to clear the decimal places: 150 : 225.
The greatest common divisor of 150 and 225 is 75.
150 ÷ 75 = 2 and 225 ÷ 75 = 3, so 1.5 : 2.25 = 2:3.
Check: 2 × 0.75 = 1.5 and 3 × 0.75 = 2.25 — one part is 0.75.
Multiplying every part by the same factor is what makes this safe. 1.5 : 2.25 and 150 : 225 describe the same relationship because both parts grew by ×100 together; only the units of “one part” changed.
Fractions: clear the denominators
3/4 : 1/2
Put both parts over the common denominator 4: 3/4 : 2/4.
Multiply both parts by 4 — the same non-zero factor — giving 3 : 2.
The greatest common divisor of 3 and 2 is 1, so 3:2 is already simplest.
Check: 3 × 0.25 = 0.75 and 2 × 0.25 = 0.5 — the original quantities return.
The transformation preserves the ratio for the same reason the decimal one does. A ratio fixes the quotient between the parts, and multiplying both a and b by k leaves (k·a)/(k·b) = a/b unchanged for any non-zero k. Simplification is just that rule run in the dividing direction.
What each input form reduces to
| Input | Exact integer form | Simplest ratio |
|---|---|---|
| 12:18 | 12 : 18 | 2:3 |
| 1.5 : 2.25 | 150 : 225 | 2:3 |
| 3/4 : 1/2 | 3 : 2 | 3:2 |
| 0.2 : 0.05 | 20 : 5 | 4:1 |
| 4:6:10 | 4 : 6 : 10 | 2:3:5 |
Three-part ratios use the same rule: one greatest common divisor taken across all parts at once.