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Proportion Calculator
Sign up to favourite this calculatorFind the missing value in A/B = C/D: enter three of the four terms, leave one blank, and get the answer with the full cross-multiplication working.
Missing term C
Completed proportion
7/12 = 56/96Cross products
672 and 672Ratio as a decimal
0.5833Scale factor
×8- Write the proportion
- 7/12 = x/96
- Cross-multiply
- 7 × 96 = 12 × x
- Multiply out
- 12x = 672
- Divide both sides by 12
- x = 672 ÷ 12 = 56
- Check
- 7/12 = 56/96
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Keep this calculation as a scenario, change any input above, and the Now column shows how the result moves. Keep up to three, A to C; Open puts one back in the calculator.
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Assumptions and limits
- An estimate from the numbers you entered, for guidance only. It is not financial, tax or medical advice.
- Calculator version 1, last updated 25 October 2026.
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How to use this calculator
- Enter the first fraction as A over B — the two values you already know.
- Enter whichever part of the second fraction you know, and leave the unknown one blank. Any of the four terms can be the blank.
- Read the missing value above the supporting figures, then open the working panel for the cross-multiplication line by line.
The cross products are worth a glance whenever an answer looks wrong. When the proportion is correct, the two products match exactly — if they do not, one of the three entries is not what you meant.
What do I enter to solve a proportion?
- A — first numerator and B — first denominator — the top and bottom of the first fraction. B cannot be zero.
- C — second numerator and D — second denominator — the top and bottom of the second fraction. D cannot be zero.
Fill in exactly three terms and leave one blank; the blank is the term that gets solved. Each term is a number up to 1,000,000,000,000 in size, and decimals and negatives are accepted.
What do the results show?
- Missing term — the main figure: the value of whichever of A, B, C or D you left blank.
- Completed proportion — A/B = C/D with the answer filled in.
- Cross products — A × D and B × C, which match when the proportion holds.
- Ratio as a decimal and scale factor — A ÷ B, and the factor C ÷ A that scales the first fraction's top to the second's.
- Working — the cross-multiplication line by line, ending in a check.
How to solve a proportion
A proportion says two fractions are equal. Multiplying each numerator by the opposite denominator turns that statement into a straightforward equation.
A/B = C/D means A × D = B × C
- A, B — the first fraction, e.g. 7 and 12
- C, D — the second fraction, e.g. x and 96
- x — whichever term was left blank
| Step | Working |
|---|---|
| Write the proportion | 7/12 = x/96 |
| Cross-multiply | 7 × 96 = 12 × x |
| Multiply out | 12x = 672 |
| Divide both sides by 12 | x = 672 ÷ 12 = 56 |
| Check | 7/12 = 56/96 |
The same four lines solve any proportion, wherever the blank sits. Only the division at the end changes: divide by whichever number ended up multiplied by x.
Where proportions are used
- Scaling recipes — 7 people out of a 12-person recipe, applied to 96 grams of an ingredient.
- Map and model scales — 1 cm on a 1:25,000 map covers 25,000 cm on the ground.
- Unit pricing — if 12 items cost £7, a proportion gives the price of 96.
- Medicine and mixtures — a dose per kilogram, applied to a body weight.
- Similar triangles — corresponding sides of similar shapes are always in proportion, which is how heights are measured from shadows.
All five are the same sum. Whatever the units, if two quantities rise and fall together at a fixed rate, three known values give the fourth.
Prefer colon notation? The Ratio Calculator solves the same cross-multiplication written as A : B = C : D.
Frequently asked questions
How do I solve a proportion?
Cross-multiply, then divide. For 7/12 = x/96, multiply 7 by 96 to get 672, then divide by 12 to get x = 56. The calculator shows each of those lines in the working panel.
Why does cross-multiplication work?
Because multiplying both sides of an equation by the same thing keeps it true. Multiplying 7/12 = x/96 by 12 and by 96 clears both denominators in one move and leaves 7 × 96 = 12 × x, which is an ordinary equation with one unknown.
What is the difference between a proportion and a ratio?
A ratio compares two quantities, such as 7 : 12. A proportion is the statement that two ratios are equal, such as 7/12 = 56/96. The ratio calculator handles the same maths in colon notation if that is how your problem is written.
Can a proportion have no answer?
Only when solving would mean dividing by zero. In 7/12 = x/0 there is no value of x that works, because nothing can be divided by zero. The calculator says so rather than showing a number.
What is the scale factor?
It is how many times bigger the second ratio is than the first: 56/7 gives a factor of 8, and 96/12 gives the same 8. Equal scale factors on both sides are the whole reason a proportion holds.
What is the difference between direct and inverse proportion?
In direct proportion, doubling one quantity doubles the other, and the ratio between them stays fixed — that is what this calculator solves. In inverse proportion, doubling one halves the other, so it is the product that stays fixed rather than the ratio.
Last updated 25 October 2026.