Ratio calculator 3 numbers
A three-part ratio simplifies the same way a fraction does: divide all three numbers by whatever divides into every one of them. The boxes above handle the arithmetic; below is the method and the check.
12 × 12 = 144
Adding 12 to itself 12 times gives the same answer.
Simplifying a:b:c
Find the largest number that divides into all three, then divide each term by it. For 12:18:30, the number is 6, and the ratio becomes 2:3:5. If nothing but 1 divides into all three, the ratio is already in its simplest form.
Work it in stages if the common divisor is not obvious. Halve 12:18:30 to 6:9:15, then divide by 3. Two easy steps beat one hard one, and the destination is the same.
Sharing a total in a ratio
- Add the three terms together to get the number of parts. For 2:3:5 that is 10.
- Divide the total by the number of parts to find what one part is worth.
- Multiply that by each term in turn.
Splitting 450 in 2:3:5 gives one part = 45, so the shares are 90, 135 and 225. The three shares must add back to 450 — that addition is the whole check.
When it will not simplify
- Decimals. Multiply all three by 10, or 100, until they are whole numbers, then simplify. 1.5:2:3.5 becomes 3:4:7.
- Fractions. Put all three over the same denominator, then keep only the numerators.
- Pairwise reducing. Simplifying a:b on its own and then b:c breaks the link between the ends. Divide all three by the same number, always.
- Different units. 1 hour : 30 minutes : 15 minutes is 4:2:1 only after everything is in minutes.
For two-term work, and for filling in a missing number, use the equivalent ratio calculator. A ratio used in practice is on the coffee-to-water ratio calculator, and the rest are under calculators.