Inverse Proportion Calculator

Formula

New output = Known input × Known output ÷ New input

Worked example

With Known input: 2, Known output: 12, New input: 8, new output is 3.

Calculation method

The rule is New output = Known input × Known output ÷ New input.

For this inverse proportion example, changing known input from 2 to 3 while keeping the other inputs fixed changes new output from 3 to 4.5.

Reading new output

A ratio is meaningful only with its order stated. The ratio A ÷ B generally differs from B ÷ A. The known input times known output is held constant, so the new output falls as the requested input rises. In the worked values on this page, known input 2, known output 12, new input 8 produce new output 3.

Practical use

Use proportional reasoning for scale drawings, mixture recipes, rates, and quantities that follow a stable relationship. This fits a fixed-work or fixed-product situation only when adding one resource truly divides the remaining requirement.

Limits and common mistakes

Direct proportion assumes output rises in the same proportion as input. Inverse proportion assumes their product stays constant. Neither assumption applies automatically to every real system. Doubling the new input should halve the projected output under the constant-product assumption.

Why the relationship works

Inverse proportion assumes the product of input and output stays constant: making one factor larger makes the other smaller. This is suitable only when that relationship is justified. It would be wrong to apply it automatically to a situation with fixed costs, limits, or other changing conditions. The inverse proportion rule uses known input, known output, new input in New output = Known input × Known output ÷ New input; read each symbol as the field named on this page.

Interpreting another set of values

For inverse proportion, the fields labeled known input, known output, new input are the known quantities. The calculator solves for new output using New output = Known input × Known output ÷ New input. Keep the order of the compared quantities visible. A result described as first per second is not interchangeable with second per first, and a proportional projection depends on its stated constant-rate assumption. When comparing two calculations, keep their units and input definitions identical.

For a second inverse proportion check, keep the other default inputs fixed and change known input from 2 to 4. New output changes from 3 to 6. This is a comparison of two particular cases. Repeat it near the values relevant to your task; do not assume that every formula changes at a constant rate.

Checks and limits

Make sure the quantities refer to comparable cases and use compatible units. A denominator of zero is undefined. If the relationship is only approximately proportional, treat the answer as an estimate and inspect whether a fixed component or other condition changes between the known and new case. The reported new output is 3 in the worked example. Keep its stated unit or counting convention when checking it against another calculation.