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Inverse Variation Calculator.

For y = k/x, derive k and calculate y at a new x.

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Set your values

Results update as you type.

Variation constant k: 48

Variation constant k

0.000000
Target y: 5.333333

Target y

0.000000
Relation: y = 48 / x

Relation

y = 48 / x

Results update automatically as you type.

Use Cases

Physics: Inverse Square Law

Use inverse variation to model relationships like gravitational force or light intensity, which decrease with the square of distance.

Example: If force is 10 N at distance 2 m, find force at distance 4 m.

Work and Time Problems

Inverse variation applies when the number of workers and time to complete a job are inversely proportional.

Example: If 5 workers take 8 hours, how long for 10 workers?

Frequently Asked Questions

What is inverse variation?
Inverse variation describes a relationship where one variable increases as the other decreases, following the equation y = k/x, where k is the constant of variation. This calculator helps you find k and then compute target y values.
How do I use this calculator?
Enter the known x and y values to calculate the constant k. Then, enter a target x value to find the corresponding y value. The calculator will display the constant and the target y.
What if I need to find x for a given y?
This calculator is designed to find y for a target x. If you need to find x, you can rearrange the formula to x = k/y, but this calculator does not directly compute that.

Tips & Common Mistakes

Tips

  • Ensure the known x and y values are positive and non-zero, as division by zero is undefined.
  • Double-check that the target x is also non-zero to avoid errors.
  • Use the constant k to verify your results: y * x should equal k for any pair.
  • This calculator assumes a simple inverse relationship, not inverse square or other powers.

Common Mistakes to Avoid

  • Entering zero for x or y, which leads to division by zero or an undefined constant.
  • Confusing inverse variation with direct variation, where y = kx instead of y = k/x.
  • Forgetting to use the same units for x and y as in the original problem.

Last updated: August 13, 2026