Proportion Calculator (a/b = c/d)
Solve a proportion a/b = c/d — enter any three values and leave one blank to solve it, the classic rule of three done automatically.
Fill in any three values and leave one field blank to solve a/b = c/d — or fill in all four to check whether it holds. A cell takes a number, a fraction (3/4), a mixed number (2 1/2) or an expression (sqrt(2), 1.5*3).
2 / 4 = 3 / 6 d = 6
a × d = b × c 2 × d = 4 × 3 2 × d = 12 d = 12 ÷ 2 = 6
Check by working out both sides: Left side: a / b = 2 / 4 = 0.5 = 1/2 Right side: c / d = 3 / 6 = 0.5 = 1/2 0.5 = 0.5 ✓ Check by cross multiplication: a × d = 2 × 6 = 12 b × c = 4 × 3 = 12 12 = 12 ✓
Invertendo — flip both ratios 4 / 2 = 6 / 3 → 2 = 2 ✓ Alternendo — swap the middle terms 2 / 3 = 4 / 6 → 0.666667 = 0.666667 ✓ Componendo — add each denominator to its numerator 6 / 4 = 9 / 6 → 1.5 = 1.5 ✓ Dividendo — take each denominator from its numerator -2 / 4 = -3 / 6 → -0.5 = -0.5 ✓
What this proportion calculator does
A proportion says that two ratios are equal: a/b = c/d. This calculator lets you enter any three of the four values and leave the remaining field blank, and it instantly solves for the missing number. It is the classic "rule of three" you learned in school, done automatically. Everything updates live as you type, so you can change any value and watch the answer recompute immediately — handy for scaling recipes, converting units, resizing images while keeping the aspect ratio, or working out map distances.
How the missing value is found
The tool cross-multiplies. Because a/b = c/d is equivalent to a·d = b·c, each unknown has a simple formula: a = b·c/d, b = a·d/c, c = a·d/b, and d = b·c/a. For example, with a = 2, b = 4 and c = 3, the missing d equals b·c/a = 4·3/2 = 6. Below the answer the calculator also shows the worked steps — the cross-multiplication a·d = b·c and the exact division used — so you can follow (or teach) how the missing value was reached. Leave one field blank and it is solved; fill every field and the page says whether the proportion holds. It guards against dividing by zero instead of returning a misleading result. When no value fits — 0/4 = 3/d — or every value does — 0/4 = 0/d — it says which, and a 0 typed as a denominator is named. For two quantities changing at once — workers and walls deciding the days, say — “Compound — two quantities at once” lays out a table of two quantities and the result, before and after, with a box to tick for each quantity that is inversely proportional, and shows the factors the result is multiplied by.
Frequently asked questions
How do I use this proportion calculator?
Type the three values you know into the a, b, c, and d boxes and leave the one you want to find empty. The answer appears instantly below, and you can copy it with one click.
What is the rule of three?
The rule of three solves a proportion a/b = c/d for one unknown by cross-multiplying: a·d = b·c. This tool applies that rule automatically for whichever field you leave blank.
Does it show the steps?
Yes. Under the result the tool prints the rule-of-three working — the cross-multiplication a·d = b·c, the same with your numbers put in (2 × d = 4 × 3, then 2 × d = 12) and the division that produced the missing value (d = 12 ÷ 2 = 6) — so you can check the reasoning or use it to explain the method.
Can I check a proportion I already have, or type fractions?
Yes. Fill every field and the page says whether the proportion holds, with both ratios reduced and the cross products side by side. Each cell also takes fractions, mixed numbers and small expressions.
Does it handle inverse proportions or a mean term, and show a proportion’s properties?
Yes. “Kind of proportion” switches between Direct (a/b = c/d, the default), Inverse (a × b = c × d, for quantities where one goes down as the other goes up — more workers, fewer hours), Continued (a/b = b/c, where the middle term is the mean proportional, b = √(a × c), and the page says that −b works too) and Compound — two quantities at once. Under a direct proportion that holds, “Properties of this proportion” works out invertendo, alternendo, componendo and dividendo with your numbers.
Can it solve a compound proportion, where two things change at once?
Yes. Pick “Compound — two quantities at once” in “Kind of proportion”: a table takes the initial and final values of two quantities and the initial result, with an “is inversely proportional” box for each quantity where more of it means less of the result. The final result is worked out and its factors are shown. The “Workers, walls and days (compound)” example loads a classic one, and Reset puts those cells back too.