Direct and Inverse Variation Calculator
Determine the constant of variation k from a known pair, then predict y for a new x under direct or inverse proportionality.
Variation type
Value of y at the new x
- 1
Constant of variation k = y₁ ÷ x₁
6 ÷ 2 = 3 - 2
Predicted y₂ = k × x₂
3 × 5 = 15
How does this calculator work?
Pick direct or inverse variation and enter a known x-y pair. Direct uses y = k·x with k = y₁/x₁; inverse uses y = k/x with k = x₁·y₁. The tool finds the constant k, predicts y for a new x, and plots the line or hyperbola with both points marked.
Formula
How this is calculated
Choose the variation type. In direct variation two quantities rise and fall together, modeled by y = k·x; the constant of variation is k = y₁/x₁ from any known pair (x₁, y₁). In inverse variation one quantity grows as the other shrinks, modeled by y = k/x; here the constant is k = x₁·y₁, since the product of the two quantities stays fixed.
Once k is known, the calculator predicts y for the new x value you enter. For direct variation it multiplies, y₂ = k·x₂; for inverse variation it divides, y₂ = k/x₂. The plotted curve shows the full relationship — a straight line through the origin for direct variation, a hyperbola for inverse variation — with the known point and the predicted point marked.
Units carry through unchanged: k absorbs whatever units make the equation balance. Edge cases are guarded: direct variation needs x₁ ≠ 0 to compute k, and inverse variation needs the new x₂ ≠ 0 to avoid division by zero. Non-numeric entries produce no result.
Frequently asked questions
In direct variation the ratio y/x is constant, so doubling x doubles y. In inverse variation the product x·y is constant, so doubling x halves y. Check which quantity stays fixed across your data pairs.
It is the fixed number linking the variables. For direct variation k = y/x (the slope of the line); for inverse variation k = x·y (the fixed product). Both are computed from your known pair.
Direct variation divides by x₁ to find k, and inverse variation divides by the new x₂ to find y, so a zero in those positions is undefined and the calculator returns no result.
Also known as
TG we-Calculate Editorial Team. (2026). Direct and Inverse Variation Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/direct-inverse-variation-calculator
TG we-Calculate Editorial Team. "Direct and Inverse Variation Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/direct-inverse-variation-calculator.
TG we-Calculate Editorial Team, "Direct and Inverse Variation Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/direct-inverse-variation-calculator
@misc{wecalculate_direct_inverse_variation_calculator, title = {Direct and Inverse Variation Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/direct-inverse-variation-calculator}}, year = {2026}, note = {TG we-Calculate} }
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