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Miraç Özdemir
Ratios, Proportions & Sharing

Compound Proportion Calculator

Solve direct and inverse proportion problems where several variables (workers, days, hours…) change at once, from a known result to the unknown value in one step.

Version 3

Things to keep in mind:

  • Choosing the wrong direct/inverse relation reverses the effect; ask “if the variable grows, does the result grow?” to decide.
  • Proportions assume a linear relation at constant rate; efficiency losses (e.g. too many workers) are not modelled.
  • Old or new values cannot be 0.

Calculator

Known result

The known result under the old conditions (e.g. 120 units, 12 days). It is the starting point of the unknown value.

Variable 1

The old value under which the known result was obtained (e.g. 4 workers).

The new value for the unknown result (e.g. 6 workers).

Variable 1: relationship (optional)

Choose direct if the result grows with the variable, inverse if it shrinks.

Variable 2

Leave at 1 if unused.

Leave at 1 if unused.

Variable 2: relationship (optional)

Choose direct if the result grows with the variable, inverse if it shrinks.

Variable 3

Leave at 1 if unused.

Leave at 1 if unused.

Variable 3: relationship (optional)

Choose direct if the result grows with the variable, inverse if it shrinks.

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

Compound proportion solves problems where the result depends on several variables at the same time. For each variable you enter the old value and the new value and choose whether it affects the result directly or inversely.

Formula

  • Factor for a direct variable = new / old
  • Factor for an inverse variable = old / new
  • Compound multiplier = product of the factors
  • Unknown value = known result × compound multiplier

Example 1 (three direct variables): 4 workers working 6 days at 8 hours a day produce 120 units. How many units do 6 workers produce in 5 days at 10 hours a day? Multiplier = 6/4 × 5/6 × 10/8 = 1.5625; result 120 × 1.5625 = 187.5.

Example 2 (inverse): if 4 workers finish a job in 12 days, 6 workers need 12 × 4/6 = 8 days (more workers, fewer days: inverse); the multiplier is 0.6667.

Example 3 (mixed): 4 workers working 6 days at 8 hours a day produce 120 units. How many units do 6 workers produce in 3 days at 4 hours a day? Treating workers and days as direct and hours as inverse in this example, the multiplier is 6/4 × 3/6 × 8/4 = 1.5000 and the result is 120 × 1.5 = 180. Which variable is inverse depends on the logic of the problem; the tool does not check it.

How to read the result A compound multiplier above 1 means the unknown value is larger than the known result, below 1 smaller, and exactly 1 means the changes cancel out. The multiplier is the combined effect of all variables in a single number.

Leave old and new at 1 for variables you do not use. The result is rounded half-up to 4 decimals. For simple one-variable proportions, the Direct and Inverse Proportion tool is more convenient.

How to use

  1. Enter the known result (e.g. 120 units or 12 days).
  2. For each variable enter the old and new value.
  3. Choose whether the variable affects the result directly or inversely.
  4. Leave unused variables at 1 and press Calculate.

Notes

The result is rounded half-up to 4 decimals. Up to 3 variables are supported. Old and new values must be greater than zero. You decide which variable is direct or inverse from the logic of the problem.

Frequently asked questions

4 questions

  1. A proportion problem where the result depends on several variables at once; for example output depends on workers, days and hours per day together.

Next step

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