Proportion Calculator
This proportion calculator solves for the missing value with the unknown in any of the four places, and shows the shortcut as well as the long way.
Type 3/4 = x/12 as written, exactly as it is printed in front of you. One box, not four.
What a Proportion Actually Says
Solving proportions starts with knowing what one is. Two ratios, set equal. a/b = c/d, or a:b = c:d, or in the older form still used across Indian textbooks, a : b :: c : d — "a is to b as c is to d". This page reads all three.
Ratio proportion questions are taught as one topic for a reason: a proportion is nothing more than two ratios placed side by side. The statement is not that the numbers are alike. It is that the relationship is the same. 3 to 4 and 9 to 12 look nothing like each other, yet both come to 0.75.
The Shortcut Everybody Uses and No Calculator Shows
Look at 3/4 = x/12 for a second before reaching for a method.
The 4 became 12. That is three times. So the 3 becomes 9, and you are done — no algebra, no diagonal arrows, about two seconds. That is how the question was built and how it is meant to be read.
Every proportion calculator I could find skips straight to cross multiplication. It always works, which is why it gets taught, but it is the slow route on most classroom questions and a teacher would rather see the multiplier spotted. This page shows both, and tells you which one was on offer.
When there is no tidy multiple — 4/10 = x/15, where the multiplier is 1.5 — it says so, and that is exactly when cross multiplication earns its keep.
Cross Multiplication, and Why It Works
Multiply diagonally across the equals sign. In a/b = c/d, that gives a × d and b × c, and those two are equal for every true proportion.
It is not a trick. Multiply both sides of a/b = c/d by b and by d, and the b cancels on the left, the d on the right, leaving ad = bc. That is all it is — the same move done twice, written down as a rule.
| Proportion | Cross multiply | Answer |
|---|---|---|
| 3/4 = x/12 | 3 × 12 = 4x | x = 9 |
| 3/x = 6/8 | 3 × 8 = 6x | x = 4 |
| x/45 = 1/15 | 15x = 45 | x = 3 |
| 4/10 = x/15 | 4 × 15 = 10x | x = 6 |
The Unknown Can Sit Anywhere
x on the top left, the bottom left, the top right, the bottom right — it makes no difference to the method.
One well-known calculator disagrees. Its own instructions say that if your unknown is in a different position you should rearrange the equation so the missing value ends up in the bottom-right corner. Read that again: the tool is asking you to do the fiddly part yourself before it will help.
Type it here however it appears in your book.
Where the Marks Really Go
Not in the multiplying. In the setting up.
Take: two cups of flour serve four people, how much for ten? The proportion is 2/4 = x/10, and the answer is 5 cups. But write it as 2/4 = 10/x and you get 20 — a number, confidently produced, and completely wrong.
The rule that prevents it is short. Whatever is on top of the first ratio must be the same kind of thing as what is on top of the second. Cups above cups, people below people.
Get the corners right and the arithmetic looks after itself.
Proportions Turn Up Everywhere
They are the piece of school algebra you keep using after school.
A map scale of one inch to fifty miles, with two towns three and a half inches apart: 1/50 = 3.5/d gives 175 miles. A currency rate of one dollar to 0.85 euros, converting 250 dollars: 1/0.85 = 250/x gives 212.50. Doubling a recipe, resizing a photograph without stretching it, working out a dose by body weight, reading a scale drawing — all the same shape of question.
Similar triangles are proportions too. Corresponding sides keep the same ratio, which is why a stick of known height and its shadow will tell you how tall a building is.
Equivalent Ratios: Checking Whether Two Match
Leave the unknown out entirely and type 6/9 = 8/12. The page will tell you whether that is true.
Equivalent ratios are two that reduce to the same thing, and any two of them form a true proportion. Both of these reduce to 2/3, so it holds. And when two ratios do not match, the page says which of them is bigger and by how much — because “not a proportion” on its own tells you nothing about where the setup slipped. Cross multiplying agrees: 6 × 12 = 72 and 9 × 8 = 72. Two different tests, one answer, which is the whole point of doing both when you are marking your own work.
Two Missing Numbers Is Not a Question
Three known values pin down the fourth. Two known values pin down nothing: 2/3 = c/d is satisfied by 4 and 6, by 6 and 9, by 20 and 30, and by endlessly many other pairs.
So it is worth knowing what two well-known calculators do here. One states in its own documentation that if you give it only A and B, it multiplies both by two to produce C and D. The other describes the same behaviour in almost the same words. They are not solving anything — they are inventing an answer that looks like one, and a student who trusted it would have no way to tell.
This page refuses, and says why.
Answers That Are Not Whole Numbers
1/0.85 = 250/x comes to 212.5, and 4/6 = x/9 comes to 6. Both are ordinary.
Where an answer is a fraction this page keeps it as one and puts the decimal underneath, because rounding early is how a small error grows into a wrong final line. It also gives the ratio as a percentage, which is often what the question was really asking for.
How to Use This Proportion Calculator
Type the proportion with x in place of the missing number: 3/4 = x/12. Colons work just as well — 3:4 = x:12 — and so does 3:4::x:12. Decimals are fine, and so are negatives.
Any letter can stand in for the unknown, not only x; tap My keyboard for one the pad does not carry. If your line has an unknown on the bottom of a fraction alongside other terms it is a rational equation rather than a proportion, and if it is a straightforward equation with one unknown, the linear equation calculator is the page for it.
Proportion Calculator FAQ
What is a proportion?
How do you solve a proportion?
Does it matter where the unknown is?
What does cross multiplying actually do?
How do I know two ratios form a proportion?
What does a : b :: c : d mean?
Why is my answer wrong when the arithmetic is right?
Can a proportion have two unknowns?
Check the multiplier before you cross multiply, keep the same quantity on top of both ratios, and put the answer back in to see the two sides agree.
