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Inverse Proportion Calculator

Calculate a variable inversely proportional to another.

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Overview

Inverse proportion describes a relationship between two variables where their product remains constant. As one value increases, the other decreases proportionally, such as the relationship between speed and time for a fixed distance.

Symbols

Variables

k = Constant (k), x = x Value, y = y Value

Constant (k)
Variable
x Value
Variable
y Value
Variable

Apply it well

When To Use

When to use: Apply this model when two quantities change in opposite directions, such as the time taken for a task versus the number of workers assigned. It is valid only if the product of the variables stays the same and neither variable is zero.

Why it matters: This relationship is vital for understanding physical laws like gas pressure, light intensity, and gravitational pull. It allows scientists and economists to predict how a system will scale when one factor is restricted or expanded.

Avoid these traps

Common Mistakes

  • Using direct proportion.
  • Dividing the wrong way.

One free problem

Practice Problem

Practice Problem 1

A construction crew has a total work requirement (k) of 60 man-hours to complete a project. If there are 15 workers (x) available, how many hours (y) will it take to finish the job?

Constant (k)60
x Value15

Solve for:

Hint: Divide the total work constant k by the number of workers x.

Practice Problem 2

In a physics experiment, the pressure (y) of a gas is inversely proportional to its volume (x). If the measured pressure is 200 Pascals when the volume is 0.5 cubic meters, calculate the constant of proportionality (k).

y Value200
x Value0.5

Solve for:

Hint: The constant k is found by multiplying the two variables x and y together.

Practice Problem 3

The time (y) taken to travel a fixed distance is inversely proportional to the speed (x). If the total distance (k) is 120 kilometers and the trip must be completed in 1.5 hours (y), what speed (x) is required?

Constant (k)120
y Value1.5

Solve for:

Hint: Rearrange the formula to solve for x: x = k ÷ y.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Wikipedia: Inverse proportionality
  2. Britannica: Proportion
  3. Britannica, 'Proportion (mathematics)'
  4. Wikipedia, 'Inverse Proportionality'
  5. Britannica: Inverse proportion
  6. AQA GCSE Maths — Algebra (Proportion)