Direct & Inverse Variation Calculator
Find the constant of variation and predict new values.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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Request a ToolHow to Use the Direct and Inverse Variation Calculator
This tool finds the constant of variation and can predict new values.
- Select the type. Choose direct (y = kx) or inverse (y = k/x) variation.
- Enter a known pair. Provide x1 and y1 values that satisfy the relationship.
- Predict a value (optional). Enter x2 to calculate the corresponding y2.
About Direct and Inverse Variation
In direct variation, y = kx, meaning y increases proportionally with x. The constant k = y/x. In inverse variation, y = k/x, meaning y decreases as x increases. The constant k = x * y. These relationships are fundamental in science and everyday math. For example, speed and time (for a fixed distance) show inverse variation, while distance and time (at constant speed) show direct variation.
Frequently Asked Questions
What is the constant of variation?
The constant of variation (k) is the fixed ratio or product that relates x and y. For direct variation, k = y/x. For inverse variation, k = x * y.
How do I know if a relationship is direct or inverse?
If both variables increase or decrease together, it is direct. If one increases while the other decreases, it is inverse.
Can x1 be zero?
No. If x1 is zero, the constant k cannot be determined because division by zero is undefined.