The formula this page uses
a/b = c/d → a × d = b × c → the missing one is found by dividing
Solve proportions for the missing value
Use the free proportion calculator to work through the number relationship, preserve exact values, and check the result with estimation. Choose a focused operation below to calculate, inspect the method, and connect the result to a visual model.
The visual updates with your calculation.
Result—Choose a mode, enter the known values, and calculate.
Show your work Step-by-step method
- The calculation method and verification will appear here.
Arithmetic
Proportion Calculator explained
The short version
- A proportion says two fractions are equal, and one of the four numbers is missing.
- Cross-multiply: multiply each top by the other bottom, then solve the small equation that appears.
- Keep the same kind of thing on top on both sides, or the answer comes out upside down.
What each part means
SymbolWhat it means
a and b — The known pairThe ratio you already have, such as 7 apples for 210 cents.
c and d — The matching pairThe same relationship at a different size. One of these is the unknown.
a × d and b × c — The cross productsThe two diagonal multiplications. In a true proportion they are always equal.
unit rate — a ÷ bThe value of one single item, which is a quick way to check any proportion answer.
Show your work: a full example
- Solve for the missing number3/8 = x/40
- Multiply the two diagonals3 × 40 = 8 × x
- Do the left side120 = 8x
- Divide both sides by 8x = 120 ÷ 8
- Finishx = 15
- Check the fraction really matches15/40 reduces by 5 to 3/8
A second, different case
- A different case: a shopping word problem7 apples cost 210 cents, so what do 12 cost?
- Write it as two matching fractions210/7 = x/12
- Cross-multiply210 × 12 = 7 × x
- Work out the left side2520 = 7x
- Divide by 7x = 2520 ÷ 7 = 360
- Say it in money12 apples cost 360 cents, which is 3 dollars 60 cents
- Check with the unit rate210 ÷ 7 = 30 cents each, and 30 × 12 = 360
Copy-ready example
3/8 = x/40
Solve for the missing number
Questions about the Proportion Calculator
When am I not allowed to cross-multiply?
Only when the equation is genuinely one fraction equals one fraction. If there is anything extra on a side, like 3/8 = x/40 + 2, you have to deal with the extra bit first. Cross-multiplying across a plus sign is the single most common way to wreck a proportion.
What is the difference between direct and inverse proportion?
In direct proportion, doubling one side doubles the other: twice the apples, twice the cost. In inverse proportion, doubling one side halves the other: twice the workers, half the days. Cross-multiplying only works for the direct kind, so check the story before you set it up.
How do I know my answer is sensible?
Compare it with the known pair. Since 12 apples is a bit under twice 7 apples, the price should be a bit under twice 210 cents. It came out at 360, which sits right where you would expect. If your answer is wildly off that, you set the fractions up crossed.
How do I use a proportion on a scale drawing?
Put the drawing measurement over the real measurement on both sides. With a scale of 1 : 25000, a 6 cm line on the map means 1/25000 = 6/x, so x = 150000 cm, which is 1.5 km. Getting both sides into the same unit before you start is the whole battle.
Calculate, interpret, verify.
This workspace keeps the formula and the meaning together. Decimal results are rounded for display; retain full precision when you continue a calculation.
Enter known values
Match each input to the quantities in the problem and keep units consistent.
Use the relationship
The result panel identifies the formula or algorithm and shows the main substitutions.
Read the visual
Use the diagram, plot, or data display to check scale, direction, and plausibility.
Practice unaided
Move to targeted questions once you can explain why the method applies.
A calculator gives you the number. If you also want to be able to do this without one, ratios and proportions walks through the method step by step, with a worked example and the mistakes that cost marks.
Learn the mathematics
Understand arithmetic behind this calculator
A calculator confirms an answer. Working the method yourself is what makes the next problem faster.
GuidesLearn arithmeticConcepts, worked methods, and checks.
PracticePractice arithmetic questionsAnswer review after every attempt.
ReferenceArithmetic formulasConditions and examples for each formula.