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.
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.
Frequently asked questions
What is the difference between ratio and proportion?
Can any of the four terms be zero?
What does "directly proportional" mean?
Is the golden ratio really a proportion?
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Gear Base Pitch
Calculate the base pitch of an involute gear, p_b = π·m·cos(φ), from the module m (mm) and the pressure angle φ (degrees). The base pitch is the distance between two homologous flanks of consecutive teeth, measured along the base circle (or, equivalently, along the line of action) — different from the circular pitch (π·m), measured on the pitch circle. The base pitch is a FUNDAMENTAL property of involute meshing for an elegant reason: for two meshes to transmit motion correctly, they must have the SAME base pitch — it is the conjugacy condition of involute profiles. Moreover, the base pitch appears directly in the CONTACT RATIO (the average number of teeth in simultaneous contact, found by dividing the line-of-action length by the base pitch): a contact ratio above 1 (ideally above 1.4) ensures there is always at least one tooth pair meshed, transmitting motion continuously and smoothly, without impacts. The base pitch is also the basis of checking gears 'over two pins' or by span measurement (W over teeth), classic dimensional-control methods. It is an essential parameter in gear geometry and metrology. Enter the module and the pressure angle.
Agresti-Coull Interval (Proportion)
Computes the Agresti-Coull confidence interval for a proportion, an elegant middle ground between the simplicity of the Wald interval and the accuracy of Wilson's. The almost folkloric idea is to add a few fictitious successes and failures to the sample before applying the Wald formula — which fixes Wald's terrible behavior in small samples or extreme proportions. For 95% confidence, it's like adding two successes and two failures. Enter the successes, the total and the confidence level.
Stripping Ratio (SR)
Compute the stripping ratio (SR) of an open-pit mine by dividing the amount of waste (worthless rock that must be removed) by the ore extracted. It is the central economic indicator of open-pit mining: the higher the SR, the more useless material is moved per tonne of ore, and the higher the cost. It defines the pit limit and the viability of the operation. Enter the waste and ore quantities.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.