Proportion Calculator
Solves a : b = c : d for whichever term you leave blank, by cross-multiplication.
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Leave exactly one of the four blank.
Result
- D
- 20.00000000
- Completed proportion
- 3.0000 : 4.0000 = 15.0000 : 20.0000
- Check — A × D
- 60.000000
- Check — B × C
- 60.000000
The value that balances the proportion
The two cross products must match
Solving for D…
A ÷ B = C ÷ D ⟹ A × D = B × C
3.0000 × 20.0000 = 4.0000 × 15.0000
Rearranged to isolate D
D = 20.00000000
Formula — written step by step
Solving 3 : 4 = 15 : D…
A ÷ B = C ÷ D ⟹ A × D = B × C
Cross-multiply: 3 × D = 4 × 15
3D = 60
D = 60 ÷ 3
D = 20
A proportion says two ratios are equal. Cross-multiplying turns the equation into a single multiplication, which can then be rearranged for whichever term is unknown.
A worked example
Scaling a recipe
- Original
- 250 g flour for 4 people
- Needed
- enough for 7 people
- Set up: 250 ÷ 4 = x ÷ 7
- Cross-multiply: 250 × 7 = 4 × x
- 1750 = 4x
- x = 1750 ÷ 4
437.5 g of flour
The order matters when setting up the proportion: flour must sit opposite flour and people opposite people. Writing 250 ÷ 4 = 7 ÷ x instead gives 0.112, which is nonsense — the units are a check on whether the arrangement is right.
How to use this calculator
- Enter three of the four values and leave the fourth blank — that is the one the calculator solves for.
- Keep the arrangement consistent: if A and C are the same kind of quantity, B and D must be too.
- Fill in all four instead to test whether an existing proportion is true.
- Use the two check rows to confirm the answer: the cross products must match exactly.
What a proportion states
A proportion asserts that two ratios are equal: A is to B as C is to D. It is the mathematical form of "the same rate", and it underlies scaling recipes, converting units, reading maps, mixing solutions and interpreting any similar-triangle problem.
The key property is that a true proportion has equal cross products. If A ÷ B = C ÷ D, then multiplying both sides by B and by D gives A × D = B × C. That single step turns an equation with two divisions into one with none, which is why it is the standard method.
Setting it up correctly
Almost every wrong answer in proportion work comes from setting the ratio up inconsistently rather than from arithmetic. If the left-hand ratio is kilometres per litre, the right-hand one must be too — not litres per kilometre.
A reliable check is to write the units alongside the numbers. When the same unit appears in the same position on both sides, the arrangement is right. When kilometres sit on top on one side and underneath on the other, the answer will be the reciprocal of what you wanted, and it will look plausible enough to miss.
Direct and inverse proportion
This calculator handles direct proportion, where one quantity rising means the other rises too: twice the flour for twice the servings. Cross-multiplication applies exactly here.
Inverse proportion behaves differently — as one quantity rises the other falls, and their product rather than their ratio stays constant. Four workers taking six hours means eight workers take three, because 4 × 6 = 8 × 3 = 24. Applying the direct method to an inverse relationship gives twelve hours, which is wrong in the most obvious possible direction. Ask which quantity stays fixed before choosing the method.
Ways of writing the same proportion
| Form | Written | Reads as |
|---|---|---|
| Colon | A : B = C : D | A is to B as C is to D |
| Fraction | A/B = C/D | Two equal fractions |
| Cross product | A × D = B × C | The rearranged equation |
| Scale factor | C = kA and D = kB | Both terms scaled equally |
All four say the same thing. The cross-product form is the useful one for solving, because it removes the division and leaves a straightforward equation.
Frequently asked questions
What does cross-multiplication actually do?
It clears the fractions. Multiplying both sides of A/B = C/D by B and by D leaves A × D = B × C, an equation with no division that can be rearranged for any unknown term.
Can I leave more than one value blank?
No. Three knowns are needed to determine the fourth. With two blanks there are infinitely many solutions, so the calculator asks you to fill one in.
How do I know if my proportion is set up correctly?
Write the units next to each number. The same unit should occupy the same position on both sides. If it does not, the ratio is inverted.
What is a mean proportional?
It is the value x in A : x = x : B, so x is the geometric mean, √(A × B). This calculator solves for a single missing term rather than a repeated one.