Proportion Calculator
Solves proportions (rule of three) with up to 4 terms: A is to B as C is to X. Computes the unknown.
A is to B as C is to X
What is a proportion?
A proportion is simply two equal ratios: A/B = C/X. With three terms in hand, we find the fourth using X = (B × C) / A.
It is the familiar "rule of three" that shows up every day when you scale a recipe, convert currency or work out a dose.
The computation runs 100% locally.
What a proportion is and how to solve it
A proportion is an equality between two ratios — written as a:b :: c:d or a/b = c/d and read "a is to b as c is to d". The values a and d are called extremes, while b and c are the means. The fundamental property of proportions states that the product of the extremes equals the product of the means: a·d = b·c. From it, isolating any unknown term is straightforward — given a, b, c, the missing x = (b·c)/a.
Example: if 2 kg of flour costs $4 and you want to know the price of 5 kg, write 2/4 = 5/x, apply the cross product to get 2x = 20, and solve x = 10. The same logic underpins percentage problems, currency conversion and unit conversion — they are all proportions in disguise.
Where proportions show up in practice
Map scales (1:50,000 means 1 cm on paper equals 50,000 cm in reality), architectural blueprints, scaling recipes from 4 to 6 servings, currency conversion at the day's exchange rate, weight-based medication dosing (mg per kg of body weight), screen aspect ratios (16:9, 4:3), photographic prints and the famous golden ratio 1:1.618, used in design and architecture since antiquity.
FAQ
What is the difference between ratio and proportion? A ratio compares two quantities (a:b). A proportion is the equality between two ratios (a:b = c:d).
Can any of the four terms be zero? Denominators b and d cannot be zero (division by zero is undefined). The numerators a and c can be zero, but the proportion becomes trivial.
What does "directly proportional" mean? Two quantities are directly proportional when their ratio stays constant — doubling one doubles the other. In inverse proportionality, the product stays constant — doubling one halves the other.
Is the golden ratio really a proportion? Yes — it is the irrational number φ ≈ 1.618 that satisfies (a+b)/a = a/b, present in shells, leaves, the Parthenon and Renaissance paintings.
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Rule of three and proportions
The rule of three is perhaps the most useful calculation in all of school maths: "if A is to B, then C is to X". This calculator solves those proportions in seconds, finding the missing term from the other three.
It comes in handy in countless everyday situations, whether you're adjusting a recipe's quantities, calculating the proportional price of a quantity, converting scales or estimating time and consumption. You fill in the three known values and the tool finds the fourth, laying the relationship out clearly.
The calculation happens in the browser. A simple tool for solving proportions without having to set up the cross-multiplication by hand every time.