Inverse Proportion Calculator

What “inversely proportional” means

Two quantities are inversely proportional when their product stays constant. Double one and the other halves; triple one and the other drops to a third. The total amount of work, distance or resource is fixed, and you are just splitting it differently. On a graph this traces a curve (a hyperbola) rather than a straight line — it never touches either axis, because neither quantity can sensibly reach zero while the other stays finite.

The formula: x × y = k

Instead of a constant ratio, an inverse proportion has a constant product:

If 4 workers take 6 days, the total work is 4 × 6 = 24 worker-days. That 24 is the constant k. Any number of workers must still add up to 24 worker-days, so 8 workers take 24 ÷ 8 = 3 days.

The inverse rule of three

For a single unknown you do not need to name k. Multiply across each row rather than diagonally:

The calculator's Inverse mode applies this automatically. Enter the three known values, leave the unknown empty, and it multiplies the complete row and divides by the lone known value in the other row.

Classic inverse-proportion examples

• Workers and time — more people on the same task means fewer days.
• Speed and travel time — at a fixed distance, higher speed means less time.
• Taps filling a tank — more taps open, the shorter the filling time.
• Pressure and volume of a gas — at constant temperature, squeezing the volume raises the pressure (Boyle's law).
• Gears — a smaller gear turns faster than a larger one it meshes with.

How to tell direct from inverse

The test is the same one every time: imagine doubling the first quantity, and ask what should logically happen to the second. If it should double too, the relationship is direct and you cross-multiply. If it should halve, it is inverse and you multiply across rows. Reading the situation correctly matters more than the arithmetic — the numbers are identical, but the wrong method gives an answer that is upside down. A quick sanity check helps: in the worker example, eight workers cannot possibly take longer than four, so an answer bigger than 6 days would signal you had picked the wrong type.