Inverse Variation Calculator
Find the constant of variation k = x x y and compute new y for inverse proportion y = k/x. Free online inverse variation tool for algebra students and teachers.
About This Calculator
What Is Inverse Variation?
Inverse variation (also called inverse proportion) describes a relationship between two variables where one increases while the other decreases at a proportional rate. This free Inverse Variation Calculator helps you find the constant of variation k and compute unknown values in the equation y = k/x.
The inverse variation formula is y = k/x, where k is the constant of variation. Given any known pair (x, y), the constant is calculated as k = x x y. Once k is known, you can find the corresponding y for any new x value using y = k / x. This calculator is ideal for students learning algebra, teachers preparing lessons, and professionals working with proportional relationships.
How to Use the Inverse Variation Calculator
Enter a known x value and its corresponding y value that satisfy the inverse variation relationship. Then enter a new x value to find the matching y. The calculator instantly computes the constant of variation k and displays the inverse variation equation so you can verify the relationship.
Key Features
- Computes the constant of variation k from any known (x, y) pair
- Finds the unknown y for a new x value automatically
- Displays the complete inverse variation equation y = k/x
- Supports positive and negative numbers, decimals, and fractions
- Free to use with no registration or download
Frequently Asked Questions
What is inverse variation and how does it work?
Inverse variation describes a relationship where one variable increases while the other decreases proportionally, expressed as y = k/x where k is the constant of variation. If x doubles, y halves, and vice versa.
How do you find the constant of variation k in inverse variation?
The constant of variation k is found by multiplying the known x and y values: k = x x y. Once k is known, you can find any unknown y by dividing k by the new x value: y = k / x.
What are some real-world examples of inverse variation?
Common examples include speed and travel time (faster speed means less time for the same distance), pressure and volume of a gas (Boyle's law), and the number of workers and time to complete a task (more workers means fewer hours).
Can x or y be zero in an inverse variation?
No, neither x nor y can be zero in an inverse variation because the equation y = k/x would be undefined at x = 0. The graph of inverse variation never touches the x-axis or y-axis.
What is the difference between direct and inverse variation?
In direct variation (y = kx), both variables increase or decrease together. In inverse variation (y = k/x), one variable increases while the other decreases. Direct variation graphs are straight lines through the origin, while inverse variation graphs are hyperbolas.
How do you write an inverse variation equation from a table of values?
Multiply each x value by its corresponding y value. If all products are equal, the variables vary inversely with constant k = x x y. Then write the equation as y = k/x using that constant.
Is this calculator free to use?
Yes, all calculators on Calculy including the Inverse Variation Calculator are completely free to use with no registration or download required.