Skip to content
Allin
Sign up · Sign in

Rule of three

Solve a proportion: if A gives B, what does C give?

Related tools

All Percentages & ratios tools →
Cramer's Rule CalculatorSolves a 2×2 or 3×3 system with exact fractions, shows every determinant expanded term by term, and when D = 0 separates the two cases most calculators merge: dependent with infinitely many solutions, or inconsistent with none.Descartes' Rule of Signs CalculatorSign changes in f(x) and f(−x) marked one by one, then every possible (positive, negative, complex) combination that adds up to the degree.Simpson's Rule CalculatorIntegrate with the 1/3 and 3/8 rules, with the weight pattern shown, the subinterval count adjusted when it must be, and the error bound.Trapezoidal Rule CalculatorApproximates an integral from a function or from raw measured points, and unevenly spaced points are supported — real data rarely arrives on a regular grid. Draws the trapezoids, gives the error bound and compares to the exact value when one is obtainable.Golden Ratio CalculatorSplit a length in the golden ratio φ = (1+√5)/2: give the total, the larger or the smaller segment and get the other two, drawn to scale.Mass percent calculatorCompute the mass percent of a solute in a solution.Odds Ratio CalculatorCompute the odds ratio from a 2×2 table with its log-odds standard error, the Wald interval at 90/95/99 %, relative risk, risk difference — and the Haldane–Anscombe correction when a cell is zero.Percent off calculatorTake a percentage off a price: the amount you save and the final sale price. Enter the original price and the discount.

Enter A, gives B, C and the Rule of three works out C gives X straight away. For instance, with A = 3, gives B = 12 and C = 5 it returns C gives X = 20.

How to use it

  1. Enter your values: A, gives B, C.
  2. Read the result instantly: C gives X.

Frequently asked questions

What does the Rule of three actually compute?

It takes A, gives B and C and derives C gives X from them. The calculation is live as you type, so the result updates on every change.

What information do I need to provide?

3 values: A, gives B and C. Nothing else is required — no account, no file upload.

Can you show a worked example?

With A = 3, gives B = 12 and C = 5, the calculator returns C gives X = 20. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

What happens if I enter larger values?

It moves a lot. Using A = 6, gives B = 24 and C = 10 instead, C gives X goes from 20 to 40 — which is why it is worth testing a few scenarios rather than trusting a single figure.

What does it give for smaller values?

Scaled down to A = 2, gives B = 6 and C = 3, C gives X comes out at 9. The relationship is worth checking at both ends before you rely on a single result.

When would I actually use this?

The everyday cases: a discount at the till, a rise or fall between two figures, the price before tax, and working backwards from a total.

What is the most common mistake?

Undoing a percentage by applying it again. Take 20% off 100 and you get 80; add 20% to 80 and you get 96, not 100 — the two operations use different bases.

What is the difference between the Rule of three and the Cramer's Rule Calculator?

This one returns C gives X; the Cramer's Rule Calculator returns Result. That is the whole difference — open the one whose figure you need.

Is there a tool for the next step?

Descartes' Rule of Signs Calculator is the closest one after this: Sign changes in f(x) and f(−x) marked one by one, then every possible (positive, negative, complex) combination that adds up to the degree.

What else is worth having open alongside it?

Simpson's Rule Calculator and Trapezoidal Rule Calculator — they come up in the same task often enough to be worth a second tab.

Further reading

All guides →
ExplainerStacked Discounts Do Not Add UpTwenty percent off and then a further ten percent off is not thirty percent off — it is twenty-eight, because the second discount applies to the already-reduced price. The general rule, the cases where order matters, and how sales tax changes the answer.ExplainerRelative Risk and Absolute Risk Are Not the Same StoryA headline saying 50% higher risk can describe a change of two-tenths of a percentage point. Both numbers come from the same 2x2 table, and computing both takes one line each — here is how, with a worked example, number needed to treat, and where the odds ratio stops approximating relative risk.How-toHow to Convert a Percentage to a Fraction: Over 100, Then ReduceA percentage is just a fraction out of 100. Put the number over 100, reduce to lowest terms, and handle decimal percentages like 12.5% by clearing the decimal first. With examples.How-toHow to Calculate a Percentage: 4 Methods with ExamplesA clear guide to percentages: find X% of a number, work out what percent one number is of another, and add or subtract a percentage — with worked examples.How-toPercentage Change: Increase and DecreaseSubtract old from new, divide by the old value, times 100. Here's the formula, why increases and decreases aren't symmetric, and where it's used.How-toHow to Simplify a RatioDivide both sides by their greatest common divisor. Here's what a ratio is, how to reduce it, why units must match first, and how to compare ratios.