A ratio compares two or more quantities by division, written as a:b (read "a to b"). A ratio of 4:6 means for every 4 units of the first quantity, there are 6 of the second. This calculator handles two common ratio tasks: simplifying a ratio to its lowest terms, and scaling a ratio to hit a target total or a target value for one of its parts.
Simplifying a Ratio
Simplifying a ratio works exactly like simplifying a fraction: find the GCF of all the numbers in the ratio, then divide each by it. For 4:6, the GCF of 4 and 6 is 2, so dividing both by 2 gives 2:3 — the simplest form, since 2 and 3 share no common factor besides 1. For a three-part ratio like 12:18:24, the GCF of all three numbers (6) simplifies it to 2:3:4.
Worked example one: simplify the ratio 15:25. GCF(15,25) = 5, so 15÷5 : 25÷5 = 3:5. Worked example two: scale the ratio 2:3 so the two parts add up to 40 total. The ratio 2:3 represents 2+3=5 "parts" total; scaling factor = 40 ÷ 5 = 8; so the actual quantities are 2×8=16 and 3×8=24 (and 16+24=40, confirming the scale-up).
Splitting a Shared Total
A common real-world use is splitting a shared total according to a ratio — dividing a $600 bonus between two people in a 2:3 ratio, for instance. The method is the same as the scaling example above: the ratio's parts sum to 5, the scaling factor is 600 ÷ 5 = 120, so the split is 2×120 = $240 and 3×120 = $360 (which does sum to $600).
A common mistake is treating a ratio like a fraction of the total directly — reading "2:3" as meaning the first quantity is 2/3 of the total, when it's actually 2/5 of the total (since the ratio's two parts sum to 5, not 3). This mix-up is easy to make because a ratio and a fraction look superficially similar but represent different relationships: a fraction compares a part to a whole, while a ratio compares parts to each other.
A three-part ratio scales the same way as a two-part one, just with an extra part to account for in the total. Worked example: a paint mix uses red:yellow:blue in a 3:2:1 ratio, and you need 12 liters total. The parts sum to 3+2+1=6; scaling factor = 12÷6 = 2; so the mix is 3×2=6L red, 2×2=4L yellow, 1×2=2L blue (6+4+2=12L, confirming the total). Ratios also appear as "for every" statements in real contexts — a recipe ratio of flour to sugar of 3:1 scales identically whether you're doubling a recipe or making a tenth of it, as long as both ingredients scale by the same factor.
Ratios, Rates, and Proportions
Ratios also connect to rates and unit conversion — a ratio like "60 miles : 2 hours" simplifies to "30 miles : 1 hour," which is exactly how a rate like "30 mph" gets derived. Proportions — statements that two ratios are equal, like 2:3 = 8:12 — are how ratios get used to solve for an unknown quantity directly, a method often called "cross-multiplying": if 2:3 = x:18, then 2×18 = 3×x, so x = 36÷3 = 12. This is exactly the same underlying relationship as scaling a ratio, just solved algebraically instead of by finding a scaling factor first, and both methods always agree. Ratios written with different units on each side (like the miles-per-hour example above) are technically called rates rather than pure ratios, but they're calculated and simplified with the identical GCF-based method described here.
For the underlying method with more worked examples across two-part and three-part ratios, see How to Calculate a Ratio.