Power Function Calculator — y = a·xⁿ

Formula

How this is calculated

A power function has the form y = a · xⁿ, where a is a constant multiplier, x is the variable input and n is the degree. For integer exponents the function produces well-known shapes: even degrees give symmetric U-shaped curves about the y-axis (like a parabola for n = 2), while odd degrees give S-shaped curves that pass through the origin (like a cubic for n = 3). Fractional exponents — such as n = 0.5 for a square root — produce concave root curves, and negative exponents generate hyperbolic decay toward zero.

The calculator evaluates y = a · xⁿ at your chosen x using 64-bit floating-point arithmetic and plots the curve over a range so you can see its shape. For non-integer n with negative x the result enters the complex plane and those x values are omitted from the plot. Results are rounded when the true value is irrational or very large.

Power functions appear throughout science and engineering: quadratic drag (n = 2), square-root scaling in diffusion (n = 0.5), gravitational inverse-square law (n = −2). The coefficient a scales the curve vertically without changing its qualitative shape.