Two quantities vary inversely when doubling one halves the other: travel time and speed for a fixed distance, the number of workers and the time to finish a job, or pressure and volume of a gas at constant temperature (Boyle’s law). The graph is a hyperbola.
How to use the Inverse Variation Calculator
- Solve for
- Constant of variation k
- Independent variable x
- Dependent variable y
Results update as you type, and everything is calculated in your browser.
How it works
The product x·y is constant and equals k. Choose what you want to find and enter the other two quantities.
Inputs explained
| Field | What to enter |
|---|---|
| Solve for | Choose one: y (dependent variable), x (independent variable), k (constant of variation) |
| Constant of variation k | A number |
| Independent variable x | A number |
| Dependent variable y | A number |
What each result means
- y = [Constant of variation k]÷[Independent variable x]
- x = [Constant of variation k]÷[Dependent variable y]
- k = [Independent variable x]×[Dependent variable y]
Example values
How the main result changes when Constant of variation k changes and everything else stays at the example values above:
| Constant of variation k | y |
|---|---|
| 60 | 7.5 |
| 90 | 11.25 |
| 120 | 15 |
| 150 | 18.75 |
| 180 | 22.5 |
| 240 | 30 |
Formula
y = k ÷ x, k = x · y
Worked example
Inputs — Solve for: y (dependent variable); Constant of variation k: 120; Independent variable x: 8.
Results — y = 15.
Key terms
- Inverse variation
- y = k/x for a constant k.
Frequently asked questions
How do I recognise inverse variation?
The product x·y stays the same for every pair of values.
What does the graph look like?
A hyperbola that never touches the axes.
Is y = 1/x² an inverse variation?
It is an inverse-square variation – y varies inversely with x².
Give a real example.
At 60 km/h a 120 km trip takes 2 h; at 40 km/h it takes 3 h. Speed × time = 120.