Proportion Calculator
Solve A/B = C/D for any missing term by cross-multiplication (every step substituted and shown).
Details
Your proportion
Missing value (D)
20
2/5 = 8/D
This solves a proportion: two ratios set equal to each other with one value missing. Enter the three you know and it finds the fourth.
It shows the cross-multiplication step, so you can follow how the answer was reached rather than just copying it.
What a proportion is
A proportion says two ratios are equal. Written 3/4 = x/20, it means 3 relates to 4 in the same way that x relates to 20.
It is the tool for every 'if this, then how much of that' question. Scaling a recipe, converting a map distance, working out a better-value pack size, mixing paint or fuel.
Given any three of the four values, the fourth is fixed. Finding it takes one multiplication and one division.
Multiply diagonally: 3 × 20 = 60. Then divide by the remaining value: 60 ÷ 4 = 15. So x is 15.
What to enter
- Which value is missing?
- Choose the position of the unknown: A, B, C or D. The calculator adjusts which boxes it needs.
- The three known values
- Fill in the rest. Keep the units consistent on each side, since the arrangement is what makes a proportion work.
What this assumes
The relationship is directly proportional: double one side and the other doubles too.
Units are consistent within each ratio. Comparing miles to minutes on one side and kilometres to hours on the other will not work.
How to calculate a missing value in a proportion
Cross-multiply, then divide. It is the same two steps whichever position the unknown sits in.
- A × D
- One diagonal
- B × C
- The other diagonal. They are always equal
Set it up carefully. Keep the same kind of thing in the same position on both sides. Cups on top and servings underneath, on both sides.
Multiply diagonally. Take the two values that are diagonally opposite and known, and multiply them.
Divide by the remaining one. That gives the missing value.
Sanity check it. If one side got five times bigger, the other should have too. If your answer breaks that, the setup was wrong.
See a worked example: a recipe for 4 that you want to make for 20
- Recipe
- 3 cups of flour serves 4
- You want
- enough for 20
Write it as a proportion: 3/4 = x/20. Cups on top, servings underneath, on both sides.
Cross-multiply the known diagonal: 3 × 20 = 60.
Divide by the remaining value: 60 ÷ 4 = 15.
Check it: 20 servings is five times 4, and 15 cups is five times 3. Consistent.
15 cups of flour
Frequently asked questions
A ratio compares two quantities: 3 : 4. A proportion is a statement that two ratios are equal: 3/4 = 15/20.
So a ratio is a relationship, and a proportion is an equation built from two of them. The ratio calculator handles simplifying and scaling a single ratio.
It clears the fractions. Multiplying both sides of 3/4 = x/20 by both denominators leaves 3 × 20 = 4 × x, which is far easier to solve.
It is a shortcut for that algebra, not a separate rule, which is why it always works on a proportion and never on a plain sum of fractions.
Cross-multiply and see whether the two products match. For 3/4 and 15/20: 3 × 20 = 60 and 4 × 15 = 60, so they are proportional.
You can also simplify both and compare. 15/20 reduces to 3/4, which is the same conclusion by a different route.
When one value going up makes the other go down. Four workers taking six hours means eight workers take three, not twelve.
Cross-multiplication does not apply there. Instead the product stays constant: 4 × 6 = 24, so 8 × 3 = 24. This calculator handles direct proportion, which is the far more common case.
A scale of 1:50,000 means one unit on the map is 50,000 in reality. Set it up as 1/50,000 = measured/actual.
Measuring 7 cm gives 7 × 50,000 = 350,000 cm, which is 3.5 km. Converting the units at the end is where this usually goes wrong.
Problems people actually run into
Setting up the proportion inconsistently
Writing cups over servings on one side and servings over cups on the other gives an answer that is confidently upside down.
Label the positions before filling anything in. If cups are on top on the left, cups go on top on the right, without exception.
Using direct proportion where the relationship is inverse
Not everything scales the same way. More workers means less time, not more, so treating it as a direct proportion gives an answer that is wrong in the opposite direction.
The check is simple: ask whether increasing one side should genuinely increase the other. If it should decrease it, the relationship is inverse and needs the constant-product method instead.
Results are estimates for general information only and are not professional financial, medical, or legal advice. Read our full disclaimer.
Last updated: September 4, 2026