Proportion Calculator
Proportion calculator — enter three values of a proportion (a : b = c : x) and it solves for the missing fourth term by cross-multiplication. Perfect for scaling recipes, maps, mixtures and homework. Runs in your browser.
Proportion Calculator
a : b = c : x
How to Use the Proportion Calculator
Enter the known ratio
Type a and b — the ratio you already know.
Enter the third term
Type c, the value matching a.
Read x
The missing fourth term is solved instantly.
Apply it
Use it to scale recipes, maps or mixtures.
The Rule of Three, Automated
A proportion is the simple, powerful statement that two ratios are equal — a : b = c : x — and the everyday task it solves is finding a missing fourth value when you already know the other three. This is the calculation behind scaling a recipe, reading a map, mixing a solution, converting units and a hundred other practical problems, and it has a name as old as commerce itself: the rule of three. This calculator automates it. Enter a, b and c, and it returns x, the value that makes the two ratios equal, along with the completed proportion so you can see the relationship.
The method is cross-multiplication. Because a/b equals c/x, multiplying diagonally gives a·x = b·c, and rearranging gives the missing term as x = b·c ÷ a. In the proportion 2 : 3 = 10 : x, that is (3 × 10) ÷ 2 = 15. The only requirement is that the first term, a, is not zero, since the formula divides by it. The calculator accepts decimals as readily as whole numbers, so it works for measurements, money and any non-whole quantities, and the cross-multiplication is exact in every case.
Setting the problem up correctly is the whole skill, and it is worth a moment’s care: put matching quantities in corresponding positions. To scale a recipe that uses 200 grams of flour for 4 servings up to 6 servings, write 4 : 200 = 6 : x, which solves to 300 grams. To read a 1:50,000 map where two points are 3 centimetres apart, write 1 : 50,000 = 3 : x for 150,000 centimetres, or 1.5 kilometres, on the ground. The same shape handles similar triangles in geometry, medication dosing by body weight, currency conversion and unit changes. One caveat: this tool solves direct proportion, where the two quantities rise and fall together; inverse proportion, where one rises as the other falls, is a different relationship. For the vast majority of scaling problems, though, the rule of three is exactly what you need — and as with every RECATOOLS tool, the calculation runs entirely in your browser.
Know three of the four, find the fourth: cross-multiply, and x = b × c ÷ a. The oldest trick in practical arithmetic.
10 Facts About Proportions
A proportion states that two ratios are equal.
Solve it by cross-multiplication: a·x = b·c.
So the missing term x = b × c ÷ a.
Proportions scale recipes up or down.
Map scales are proportions: 1 cm : 50,000 cm.
Direct proportion: as one grows, the other grows.
Unit conversions are proportions in disguise.
Similar triangles have proportional sides.
The “rule of three” is just solving a proportion.
This calculator runs in your browser — nothing is uploaded.
Frequently Asked Questions
- A proportion is a statement that two ratios are equal, written a : b = c : x or a/b = c/x. If you know three of the four values, you can always find the fourth. This calculator takes a, b and c and solves for the missing term x, which is one of the most common tasks in everyday and school mathematics.
- By cross-multiplication. If a/b = c/x then a·x = b·c, so x = b·c ÷ a. For example, in 2 : 3 = 10 : x, the missing term is (3 × 10) ÷ 2 = 15. The calculator performs this cross-multiplication automatically and shows the completed proportion.
- The rule of three is the traditional name for solving a proportion with one unknown — given three values, find the fourth. It is one of the oldest and most practical pieces of arithmetic, used for centuries in trade and cooking, and it is exactly what this calculator automates.
- Set up the known ratio and the new quantity. If a recipe uses 200 g of flour for 4 servings and you want 6 servings, solve 4 : 200 = 6 : x to get 300 g. Put the matching quantities in corresponding positions and the calculator returns the scaled amount.
- Yes. Map scales, model scales and unit conversions are all proportions. A 1:50,000 map where 3 cm separates two points represents 1 : 50,000 = 3 : x, giving 150,000 cm (1.5 km) on the ground. Any “if this, then that” scaling problem fits the same a : b = c : x form.
- In direct proportion, the two quantities rise and fall together, which is what this calculator solves: double one and the other doubles. In inverse proportion, one rises as the other falls (their product is constant), such as speed and travel time. This tool handles direct proportion; for inverse problems you would multiply rather than cross-divide.
- Because the formula divides by a (x = b·c ÷ a), and division by zero is undefined. If the first term of your known ratio is zero, the proportion cannot be solved for x. Rearrange the proportion so a non-zero value is in the first position if possible.
- Yes. The calculator accepts decimal inputs and returns a precise decimal result, so it works for measurements, currency and any non-whole quantities. Cross-multiplication is exact regardless of whether the inputs are whole numbers or decimals.
- Everywhere quantities scale together: recipes, mixing ratios, map and model scales, currency and unit conversion, similar triangles in geometry, medication dosing by weight, and countless trade calculations. Mastering the single skill of solving a proportion unlocks all of them.
- Completely free, with no account or limit. It works offline once the page has loaded and collects no data.
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