Calculator
Choose the variation type, pick what to solve, then enter the known values. Results appear above this form after submission.
Formula used
Direct variation
Model: y = kx
Constant: k = y / x
Unknowns: y = kx, x = y / k
Inverse variation
Model: y = k / x
Constant: k = xy
Unknowns: y = k / x, x = k / y
Use direct variation when the ratio y/x remains fixed. Use inverse variation when the product xy remains fixed.
How to use this calculator
- Select direct or inverse variation.
- Choose the solving mode that matches your problem.
- Enter a known pair, a constant, or a target value as needed.
- Add unit labels if you want clearer output.
- Press Submit to see the result above the form.
- Review the working steps, graph, and generated value table.
- Use the export buttons to save the result as CSV or PDF.
Example data table
| Type | Known values | Constant k | Equation | Example output |
|---|---|---|---|---|
| Direct | x = 4, y = 20 | 5 | y = 5x | If x = 7, then y = 35 |
| Direct | k = 2.5, x = 12 | 2.5 | y = 2.5x | y = 30 |
| Inverse | x = 3, y = 18 | 54 | y = 54 / x | If x = 9, then y = 6 |
| Inverse | k = 48, y = 6 | 48 | y = 48 / x | x = 8 |
FAQs
1. What is direct variation?
Direct variation means two variables change proportionally. If one doubles, the other doubles too when the constant stays fixed. Its equation is y = kx.
2. What is inverse variation?
Inverse variation means one variable increases while the other decreases so their product remains constant. Its standard form is y = k / x.
3. How do I know which model to use?
Use direct variation when the ratio y/x stays the same. Use inverse variation when the product xy stays the same for each valid pair.
4. What does the constant k represent?
k is the fixed relationship value. In direct variation it equals y/x. In inverse variation it equals xy.
5. Can this calculator solve missing x or y values?
Yes. It can find k, solve for y from x and k, solve for x from y and k, and use one known pair to calculate a new matching value.
6. Why does inverse variation reject x = 0?
Inverse variation uses division by x. Division by zero is undefined, so x cannot be zero in the equation y = k / x.
7. What does the graph show?
The graph plots the equation based on your calculated or entered constant. Direct variation makes a straight line through the origin. Inverse variation makes a curve.
8. What can I export from the result?
You can export a CSV file containing the summary, steps, and generated table. You can also create a PDF copy of the visible result area.