Ratio & proportion tools
Proportion Calculator
Leave one value empty in a : b = c : d and get the exact answer with full cross-multiplication working.
Write x (or leave empty) in the position you want to solve.
4 : 7 = x : 21
Exact result
x = 12
Solved by cross-multiplication
Working
- Cross-multiply: c = (a × d) ÷ b
- 4 × 21 = 84
- 84 ÷ 7 = 12
Solving for x
A proportion states that two ratios are equal. If a : b = c : d then a × d = b × c, and rearranging that single equation isolates whichever of the four values you left blank.
The four rearrangements
- a is unknown → a = (b × c) ÷ d
- b is unknown → b = (a × d) ÷ c
- c is unknown → c = (a × d) ÷ b
- d is unknown → d = (b × c) ÷ a
Worked example: reading a map scale
1:25,000 map, 3.4 cm measured
Known: 1 cm on the map : 25,000 cm on the ground = 3.4 cm measured : x cm on the ground.
Equation: 1 : 25,000 = 3.4 : x
Cross-multiply: 1 × x = 25,000 × 3.4
Solve: x = 85,000 cm = 850 m
Verify: 85,000 ÷ 25,000 = 3.4, which is the measurement you started from.
The same shape fits any fixed-rate relationship: a recipe scaled from 4 to 7 portions, a unit price applied to a different quantity, or a drawing scaled to build size. What makes it proportional is that the ratio between the two columns stays constant — if it does not, cross-multiplication is the wrong tool.
Zero, negatives and unsolvable inputs
Negative values are accepted and solved normally; the sign carries through the multiplication and division. Zero is also accepted as a known value, but only where it does not become the divisor: solving for d in a : b = c : d requires dividing by a, so a = 0 has no solution and the calculator says so rather than returning a number.
Leaving two or more values empty is rejected as well. Three knowns is the minimum that pins the fourth value down, so the calculator refuses to guess instead of inventing an answer.