Variation Calculator
Choose direct or inverse variation, then enter a known pair and a new x.
This result is an estimate only. Double-check important figures before relying on them.
How it is calculated
- Direct: k = y₁ ÷ x₁, then y₂ = k × x₂
- Inverse: k = x₁ × y₁, then y₂ = k ÷ x₂
For proportions in general, use the ratio calculator.
Worked example
y = 6 when x = 2:
- Direct: k = 3, so at x = 5, y = 15
- Inverse: k = 12, so at x = 4, y = 3
Why your number may differ
Real relationships are rarely exactly proportional. The answer is exact only for an ideal direct or inverse variation.
Frequently asked questions
What is direct variation?
y varies directly with x when y = kx. When x doubles, y doubles. The ratio y ÷ x stays constant.
What is inverse variation?
y varies inversely with x when y = k ÷ x. When x doubles, y halves. The product x × y stays constant.
How do I solve a variation problem?
Use the known pair to find k, then use k with the new x to find the new y.