Equivalent ratio calculator
Two ratios are equivalent when one is the other multiplied or divided throughout by the same number. The boxes above scale a ratio up or down; the missing-term method is below.
12 × 12 = 144
Adding 12 to itself 12 times gives the same answer.
What makes two ratios equivalent
Multiply both terms by the same number, or divide both by the same number, and the ratio is unchanged. 3:4 is the same relationship as 6:8, 9:12 and 30:40. The test is division: 3 ÷ 4 and 30 ÷ 40 both give 0.75, so they describe the same thing.
Adding does not work. Adding 2 to each side of 3:4 gives 5:6, and 5 ÷ 6 is 0.833. That is a different ratio wearing a similar coat, and it is the single most common slip here.
Finding a missing term
Write it as two fractions and cross-multiply. For 3:4 = 15:x, multiply 4 by 15 to get 60, then divide by 3, so x = 20. The rule holds wherever the gap is: multiply the two numbers diagonally opposite the gap, then divide by the number diagonally opposite it.
Down to simplest form
- Find the largest number that divides into both terms.
- Divide each term by it.
- Check that nothing but 1 divides into both of the results.
18:24 divides by 6 to give 3:4. Doing it in two steps — by 2, then by 3 — lands in the same place.
When the answer looks wrong
- Units first. 2 m : 50 cm is 4:1, not 2:50. Convert before you simplify.
- Order matters. 3:4 and 4:3 are not the same ratio; keep the terms in the order the question uses.
- Decimals in the answer. Scale both terms up until they are whole numbers rather than rounding one of them.
For three-term work, use the ratio calculator for 3 numbers; for the cross-multiplication step on its own, see fraction solve for x. The rest are on the calculators page.