Opposite-direction change
Inverse Proportion Calculator
Calculate the missing value when one quantity increases as the other decreases and their product stays constant.
Calculate the inverse value
Enter one known pair x₁ and y₁, then the new x₂.
Inverse proportion result
Constant product k
Check
Working:
Formula: x₁ × y₁ = x₂ × y₂, so y₂ = (x₁ × y₁) ÷ x₂.
Example
If 4 workers take 12 hours, then the constant product is 48. With 6 workers, the time is 48 ÷ 6 = 8 hours.
When to use inverse proportion
Use inverse proportion when increasing one quantity causes the other to decrease so their product remains the same, such as workers and time for a fixed job.
How inverse proportion works
Multiply the known pair. x₁ × y₁ gives the constant product.
Use the new x value. The new pair must have the same product.
Divide the constant by x₂. This gives y₂.
Inverse proportion FAQs
What is inverse proportion?
Two quantities are inversely proportional when one increases as the other decreases, while their product remains constant.
What is the inverse proportion formula?
Use x × y = k. With one known pair, y₂ = x₁ × y₁ ÷ x₂.
Can I use fractions or decimals?
Yes. Whole numbers, decimals and fractions such as 3/4 are accepted.