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Proportion Calculator
A proportion calculator solves the equation a/b = c/d when one of the four values is missing. Enter any three numbers, leave the unknown box empty, and it finds the missing value with the working shown — or switch to direct or inverse proportion mode to scale a known pair up or down, with the scale factor shown. Handy for scaling recipes, converting units, and solving ratio problems in homework and everyday life.
Enter three values and leave the unknown one blank.
A known pair (x₁, y₁) and a new x₂ — the calculator finds the matching y₂.
| Cross product (a × d) | |
| Cross product (b × c) | |
| Scale factor (x₂ ÷ x₁) | — |
| Completed proportion |
How it works
A proportion says that two ratios are equal. The ratio a/b compares a to b, and the ratio c/d compares c to d, and the proportion a/b = c/d claims those two comparisons come out the same. If three of the four numbers are known, the fourth is forced: there is only one value that keeps the two sides equal, and finding it is the whole job of this calculator.
The key move is cross-multiplication. Starting from a/b = c/d, multiply both sides by b × d and the denominators cancel, leaving a × d = b × c. The two cross products are always equal in a true proportion, which gives you a plain multiplication equation with one unknown. Divide both sides by the number multiplying the unknown and you have the answer. For example, in 3/4 = x/12, cross-multiplication gives 4x = 36, so x = 36 ÷ 4 = 9.
If a is missing: a = (b × c) ÷ d • if b is missing: b = (a × d) ÷ c
If c is missing: c = (a × d) ÷ b • if d is missing: d = (b × c) ÷ a
Which box you leave blank decides which formula runs, but the idea is identical every time: cross-multiply, then divide. A missing numerator is solved by multiplying the two known numbers on the opposite diagonal and dividing by the remaining denominator, while a missing denominator works the same way with the roles swapped. The calculator shows both cross products so you can check that they match once the answer is filled in — if they do, the proportion is correct.
There are two rules to keep in mind. First, a denominator can never be zero, because division by zero has no meaning; the calculator will flag a zero in b or d. Second, proportions only work when the relationship really is proportional — doubling one side must double the other. That is true for a recipe scaled up, a map distance, or a currency conversion at a fixed rate, but not for things like taxi fares with a flat pickup fee, where a fixed charge breaks the pure ratio.
Direct and inverse proportions are the two ways quantities can be linked. In a direct proportion, the two quantities grow together in step: y = k × x, where k is a constant, so the ratio y ÷ x never changes. Scale a recipe from 4 servings to 12 and every ingredient triples — the scale factor is 12 ÷ 4 = 3. In an inverse proportion, one quantity grows while the other shrinks: y = k ÷ x, so the product x × y never changes. If 4 workers take 6 days to finish a job, 8 workers take 3 days, because 4 × 6 = 8 × 3 = 24 worker-days. Pick the mode above, enter the known pair and the new x, and the calculator gives the matching y, the scale factor, and the constant k.
Proportions show up constantly outside math class. A cook scaling a recipe from 4 servings to 12 multiplies every ingredient by 3. A driver who covers 180 miles on 6 gallons expects about 30 miles per gallon, and can work out the fuel for a 450-mile trip the same way. A photographer resizing an image keeps its width-to-height ratio so the picture does not stretch. In each case, the known ratio and the new total are three of the four numbers, and the proportion fills in the fourth.
Worked example
Maria is baking for a school bake sale in Chicago. Her muffin recipe makes 4 muffins with 3 cups of flour, and she needs 12 muffins. How much flour should she use? The ratio of flour to muffins stays the same, so this is a proportion: 3/4 = x/12, where x is the flour for 12 muffins.
Step 1 — cross-multiply: 4 × x = 3 × 12, so 4x = 36. Step 2 — divide both sides by 4: x = 36 ÷ 4 = 9. Maria needs 9 cups of flour for 12 muffins. Check it by comparing the ratios: 3 ÷ 4 = 0.75 cups per muffin, and 9 ÷ 12 = 0.75 cups per muffin, so the two sides agree.
Try it yourself: enter a = 3, b = 4, d = 12, leave c blank, and the calculator gives x = 9, with cross products of 36 on both sides.
FAQ
What is the difference between direct and inverse proportion?
In a direct proportion, both quantities grow together: doubling one doubles the other, so y = k times x and the ratio y/x stays constant. In an inverse proportion, one grows while the other shrinks: doubling one halves the other, so y = k divided by x and the product x times y stays constant. Recipe scaling is direct; more workers finishing a job in less time is inverse.
What is a proportion?
A proportion is an equation that says two ratios are equal, written as a/b = c/d. It states that the relationship between a and b is the same as the relationship between c and d. Proportions are used to scale recipes up or down, convert between units, and find unknown amounts that keep the same ratio.
How do you solve a proportion for x?
Use cross-multiplication: multiply the numerator of one side by the denominator of the other side, so a/b = c/d becomes a x d = b x c. Then divide to isolate the unknown. For example, 3/4 = x/12 gives 4x = 36, so x = 9.
What if the missing value is in the denominator?
The same cross-multiplication works. If the unknown is a denominator, cross-multiplying puts it in a multiplication on one side, and you divide to solve for it. For example, 5/x = 10/30 cross-multiplies to 10x = 150, so x = 15. Just leave the unknown box empty and the calculator works out which step applies.
Can a proportion have a zero in it?
A numerator can be zero, which makes that ratio equal to zero, but a denominator cannot be zero because division by zero is undefined. If you enter zero as b or d, the calculator will ask you to change it. A zero in the numerator of the solved side simply gives an answer of zero.