Direct Proportion Calculator

Formula

New output = Known output × New input ÷ Known input

Worked example

With Known input: 2, Known output: 5, New input: 8, new output is 20.

Calculation method

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

For this direct proportion example, changing known input from 2 to 3 while keeping the other inputs fixed changes new output from 20 to 13.333333.

Reading new output

A ratio is meaningful only with its order stated. The ratio A ÷ B generally differs from B ÷ A. The known output per known input is held constant, then applied to the requested new input. In the worked values on this page, known input 2, known output 5, new input 8 produce new output 20.

Practical use

Use proportional reasoning for scale drawings, mixture recipes, rates, and quantities that follow a stable relationship. This fits a situation where each added unit of input contributes the same amount of output.

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 double the projected new output when the known rate is unchanged.

Why the relationship works

Direct proportion assumes the output per unit of input stays constant. Divide the known output by the known input to find that unit rate, then multiply by the new input. This does not model fixed charges, thresholds, or a changing rate. The direct proportion rule uses known input, known output, new input in New output = Known output × New input ÷ Known input; read each symbol as the field named on this page.

Interpreting another set of values

For direct proportion, the fields labeled known input, known output, new input are the known quantities. The calculator solves for new output using New output = Known output × New input ÷ Known 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 direct proportion check, keep the other default inputs fixed and change known input from 2 to 4. New output changes from 20 to 10. 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 20 in the worked example. Keep its stated unit or counting convention when checking it against another calculation.