Ratio Calculator
Free ratio calculator. Simplify any ratio (6:8 → 3:4) and solve missing values when scaling ratios. Instant, no signup.
Simplifying and scaling ratios
A ratio calculator reduces a pair of numbers to their lowest terms and solves the missing term when one side of a ratio is scaled. Enter 6 and 8 and it returns the simplified ratio 3 : 4; switch to scale mode, give a new first value, and it returns the matching second value that keeps the proportion identical.
How the simplification works
Simplification divides both parts by their greatest common divisor. The tool finds the GCD with the Euclidean algorithm — repeatedly replacing the larger number with the remainder of dividing the pair until the remainder is zero. It then reports four things: the simplified ratio, the decimal value of the first number divided by the second, that decimal as a percentage, and the GCD itself.
Note that the GCD step rounds each part to the nearest whole number before dividing, so decimal ratios are reduced only when their rounded parts share a factor. The output keeps up to four decimal places.
How the scale mode works
Scale mode solves the proportion a : b = c : ?. It multiplies the second term by the same factor the first term grew by:
missing value = c × (b ÷ a)
The tool shows the missing value and restates the verified ratio. It asks for a new value for the first term, not the second, so read the prompt before typing.
Worked example with the default values
The form loads a = 6 and b = 8 in simplify mode. The Euclidean algorithm runs 8 mod 6 = 2, then 6 mod 2 = 0, so the GCD is 2. Dividing both parts by 2 gives 3 : 4.
| Output | Working | Value |
|---|---|---|
| Simplest form | 6 ÷ 2 and 8 ÷ 2 | 3 : 4 |
| Decimal (a/b) | 6 ÷ 8 | 0.75 |
| a as % of b | 0.75 × 100 | 75% |
| GCD | Euclidean algorithm | 2 |
Switching to scale mode with the default c = 12 gives a missing value of 12 × (8 ÷ 6) = 12 × 1.3333 = 16. The verified ratio becomes 12 : 16, which reduces back to 3 : 4, so the proportion is unchanged.
Reference: common ratios and their equivalents
| Ratio | Simplified | First as % of second |
|---|---|---|
| 6 : 8 | 3 : 4 | 75% |
| 10 : 15 | 2 : 3 | 66.7% |
| 9 : 3 | 3 : 1 | 300% |
| 1 : 4 | 1 : 4 | 25% |
| 12 : 18 | 2 : 3 | 66.7% |
| 20 : 8 | 5 : 2 | 250% |
A 2 : 3 mix scaled to a first value of 30 requires 45 of the second part, because 30 × (3 ÷ 2) = 45. Mixing problems, paint tints, and recipe batches all follow this single rule.
Common mistakes
- Reversing the order. 3 : 4 and 4 : 3 are different ratios. Keep the first and second parts on the sides you intended.
- Scaling only one side. Changing the first term without changing the second by the same factor breaks the proportion.
- Rounding during mixing. Round only the final quantity, or repeated small batches drift away from the intended ratio.
- Entering zero. A ratio needs both parts non-zero; the tool will not produce a result if either is 0.
- Expecting decimal ratios to simplify. Because the GCD is computed from rounded values, 1.5 : 2.5 simplifies as 2 : 3 rather than reducing the decimals directly.
What does a ratio decimal mean?
The decimal is simply the first number divided by the second. A decimal of 0.75 means the first part is three quarters of the second, which is the same statement as the percentage 75%. It is a convenience for comparing ratios against each other at a glance.
How do I solve a proportion with three known values?
Write it as a : b = c : ?. Multiply b by the factor c ÷ a, which is exactly what scale mode does. For 5 : 2 = 20 : ?, the factor is 20 ÷ 5 = 4, so the missing term is 2 × 4 = 8.
Are 6 : 8 and 24 : 32 the same ratio?
Yes. Both reduce to 3 : 4, because 24 and 32 share a factor of 8. Equivalent ratios are the same relationship written at different scales, which is why simplification is the quickest way to compare them.
Can I use decimal or fractional inputs?
Yes. The decimal and percentage readouts handle non-integer parts directly, and the simplified form divides the supplied values by the GCD of their rounded integers. Whole numbers give the cleanest simplified ratios.
The percentage calculator expresses the same proportional relationship on a 0 to 100 scale, and the unit converter handles the measurement conversions that ratios are often built on.