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Proportion Solver (a/b = c/x)

How do I solve a proportion?

How it is calculated

The proportion is read as a / b = c / x. Cross-multiplying gives a × x = b × c, so

x = b × c / a

The letters sit in fixed positions: a and c are the two numbers on the top of each fraction, b is the number under a, and x is the unknown under c. The first value a cannot be zero because the formula divides by it; if it is zero or any box is empty, no result is shown. Negative and decimal values work, and the answer is rounded to two decimals.

Worked example

A recipe uses 300 g of flour for 4 servings. How much for 10 servings? Write it as 4 / 300 = 10 / x, so a = 4, b = 300, c = 10.

  1. b × c = 300 × 10 = 3000
  2. x = 3000 / 4 = 750.00

Ten servings need 750 g of flour.

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Common mistakes

  • Putting the numbers in the wrong slots: with a/b = c/x, servings go on top in both fractions and flour below. Swapping one pair gives a different, wrong answer.
  • Mixing units between the two sides, such as grams on one side and kilograms on the other.
  • Using a proportion for something that is not proportional, such as cooking time, which does not double when the quantity doubles.
  • Entering 0 for a: the proportion cannot be solved and no result appears.

About this calculator

This tool solves for the unknown value x in a proportion of the form a/b = c/x by cross-multiplying (a × x = b × c) and rearranging for x, the standard technique for any problem stating that two ratios are equal. Proportions like this describe situations where two quantities scale together at a fixed rate, so knowing three of the four values always pins down the fourth.

It is used by students working through ratio and proportion problems in math class, and in everyday situations like scaling a recipe up or down, converting a map scale into a real-world distance, adjusting a mixture's ingredient ratio for a different batch size, or figuring out how much of one currency or unit corresponds to another given a known exchange rate. Anywhere a "if this much corresponds to that much, then how much corresponds to this new amount" question comes up, this is the underlying calculation.

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Comments (1)

  • Editorial team

    Before trusting the answer, ask whether the relationship really is direct. This solver assumes doubling the top doubles the bottom, which suits recipes, scale drawings and unit prices. For things like workers and days, where more of one means less of the other, the answer would be wrong. A quick check: x should be bigger than b when c is bigger than a. What kind of problem do you usually bring to a proportion?

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