How to use the Proportion Calculator
- Enter the three values you know as A, B and C.
- The calculator solves A/B = C/D for D.
- Rearrange your problem so the unknown sits in the D position.
- Sanity-check the direction: if C is larger than A, D should be larger than B.
How the calculation works
A proportion states that two ratios are equal. Cross multiplication turns that statement into a single equation — A·D = B·C — which rearranges to D = (B·C) ÷ A. The method works because multiplying both sides of an equation by the same quantity preserves equality; the cross-product form just does two such multiplications at once.
The critical discipline is keeping units consistent on each side. Miles per hour compared with miles per hour is valid; miles per hour compared with kilometres per minute is not, and the arithmetic will happily produce a confidently wrong number. Write the units next to each term before solving and cancel them as you go — if the surviving units on both sides do not match, the setup is wrong, not the arithmetic.
Direct proportion is what this solves. Inverse proportion — where one quantity rises as the other falls, such as workers and time to finish a job — uses A·B = C·D instead, so swap two terms before entering.
If A/B = C/D then D = (B × C) / ASource: Standard proportional reasoning and cross-multiplication identities.
Worked example
A 400 g pack costs £3.20. What should an 850 g pack cost at the same unit price?
- Set A = 400 g, B = £3.20, C = 850 g.
- D = (3.20 × 850) ÷ 400.
- D = 2,720 ÷ 400.
£6.80 for the larger pack at identical unit pricing — anything above that is a worse deal per gram.
Frequently asked questions
What if the relationship is inverse?+
Use A × B = C × D instead. More workers means less time, so the product stays constant rather than the ratio.
Does the order of the terms matter?+
Yes. Keep like units in matching positions — quantity with quantity, price with price.
Can I use this for scale drawings?+
Yes. A 1:50 drawing means one drawn unit equals fifty real units; set the proportion accordingly.
Why does my answer look far too large?+
Almost always a units mismatch, such as grams on one side and kilograms on the other.
Last reviewed September 1, 2026. We review this page whenever the underlying formula, tax year, published rate or standard changes.