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Miraç Özdemir
Ratios, Proportions & Sharing

Direct and Inverse Proportion Calculator

Find the unknown X and the proportionality constant in a direct proportion A / B = C / X or an inverse proportion A × B = C × X.

Version 2

Things to keep in mind:

  • Mixing up direct and inverse proportion changes the result completely; ask “when one grows, what does the other do?”.
  • Make sure A pairs with B and C pairs with X in the same order (A↔B, C↔X).
  • Proportions assume a linear relation; discounts, tiered prices or efficiency losses can break it.

Calculator

Known values

Proportion type (optional)

Choose direct if both grow together, inverse if one shrinks as the other grows.

First term of the first ratio (A in A / B = C / X). Must be greater than zero.

The term paired with A (B in A / B = C / X).

The known term of the second ratio (C in A / B = C / X). Must be greater than zero.

After the first calculation, the result updates automatically when you change a value.

Result

Enter the values and press Calculate to see the result here.

About this tool

A proportion expresses how two quantities change together. If three values are known, the fourth can be found; this tool uses the rule of three (cross multiplication) to compute the unknown X and the proportionality constant for a direct or inverse proportion. It suits everyday problems such as price–quantity, workers–time or speed–time.

Formula

Direct proportion (both grow together): A / B = C / X

  • X = B × C / A
  • Constant = B / A

Inverse proportion (one grows as the other shrinks): A × B = C × X

  • X = A × B / C
  • Constant = A × B

A and C must be greater than zero because they act as divisors; B may be zero. Results are rounded half-up to 4 decimals.

Example 1 (direct): if 2 kg of apples cost 4, what do 6 kg cost? A = 2, B = 4, C = 6 → X = 4 × 6 / 2 = 12. Example 2 (inverse): if 2 workers finish a job in 4 days, how long do 8 workers need? A = 2, B = 4, C = 8 → X = 2 × 4 / 8 = 1 day. Example 3 (rounding): A = 3, B = 7, C = 2 in a direct proportion gives X = 4.6667 and a constant of 2.3333.

How to read the result: the unknown X is the value that corresponds to C and has the same unit as B. In a direct proportion the constant is the value per unit (B / A); in an inverse proportion it is the fixed product (A × B, for example the total amount of work). For several variables (workers + days + hours) use the Compound Proportion tool, and for percentage problems the percentage tool.

How to use

  1. Choose the proportion type (direct or inverse).
  2. Enter A, B and C.
  3. Press Calculate and read X.

Notes

Results are rounded half-up to 4 decimals. A and C must be greater than zero (they act as divisors); B may be zero. In a direct proportion the layout is “A corresponds to B; C corresponds to X”.

Frequently asked questions

4 questions

  1. For A / B = C / X cross-multiply: X = B × C / A. If 2 kg = 4, then 6 kg = 4 × 6 / 2 = 12.

Next step

Related tools to continue your calculation.

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