Inverse Variation Calculator

Find the constant k in y = k/x and predict a new y value.

Result

60.0000
4.0000

How it is calculated

For a relationship y = k / x the product of the two quantities never changes. The tool finds that constant from your known pair, k = known_x × known_y, then predicts y = k / new_x. Both results are shown with four decimals. Known x, known y and new x must all be non-zero: a zero in the known pair would make k = 0, which is not a real inverse relationship, and a zero new x would divide by zero, so any of these shows no result. Negative values are accepted and carry their sign through, so a negative known x gives a negative k. The new x must be in the same unit as the known x.

Worked example

Six workers finish a job in 10 days, and you want the time for 15 workers, assuming the same total work. Step 1: k = 6 × 10 = 60 worker-days. Step 2: y = 60 / 15 = 4. The tool prints a constant k of 60.0000 and a predicted y of 4.0000, so 15 workers need 4 days.

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Common mistakes

  • Using this for a relationship that is proportional rather than inverse. If y rises when x rises, use direct variation.
  • Dividing instead of multiplying to find k. For inverse variation k is x × y, not y / x.
  • Assuming the total stays fixed when it does not, for example workers who do not work equally fast or tasks that cannot be split. The model only holds when the product really is constant.
  • Mixing units between the pair and the new x, such as days in the pair and hours in the new value.
  • Entering 0 in any of the three boxes. A zero known value or a zero new x gives no result, because the relationship has no point at x = 0 and the prediction would be infinite.

About this calculator

Two quantities are in inverse variation when their relationship follows y = k / x, meaning their product stays constant at k, so as x increases y decreases proportionally, and doubling x always halves y. Given one known pair of x and y values, the constant is found by rearranging to k = x × y, and once k is known it predicts y for any new value of x.

This pattern shows up whenever two factors trade off to keep a total fixed: at a constant temperature, gas pressure and volume trade off according to Boyle’s Law (P × V = constant); the time to complete a fixed amount of work decreases as the number of workers increases; and travel time decreases as speed increases for a fixed distance.

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