# Inverse Variation Calculator

URL: https://speedycalculator.com/calculators/math/inverse-variation/
Last updated: 2026-10-30

> The inverse variation calculator works with y = k/x: enter any two of y, x and the constant k to find the third.

## Inputs

- Solve for
- Constant of variation k
- Independent variable x
- Dependent variable y

## Results

- y
- x
- k

## Formula

```
y = k ÷ x,  k = x · y
```

## Explanation

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

FieldWhat to enterSolve forChoose one: y (dependent variable), x (independent variable), k (constant of variation)Constant of variation kA numberIndependent variable xA numberDependent variable yA 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 ky607.59011.251201515018.7518022.524030

## 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.

## FAQ

**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.


## Sources

- [OpenStax – College Algebra 2e](https://openstax.org/details/books/college-algebra-2e)
- [OpenStax – Intermediate Algebra 2e](https://openstax.org/details/books/intermediate-algebra-2e)