Laplace transform calculator

Compute the Laplace transform L{f(t)} = F(s) of any function. Shows step-by-step work with transform pairs.

f(t) =

What is the Laplace transform?

The Laplace transform converts a time-domain function f(t) into a frequency-domain function F(s). It's defined as L{f(t)} = ∫₀^∞ f(t)e^(-st) dt.

Common transform pairs

L{1} = 1/s. L{t} = 1/s². L{tⁿ} = n!/s^(n+1). L{e^(at)} = 1/(s−a). L{sin(bt)} = b/(s²+b²). L{cos(bt)} = s/(s²+b²).

Why is it useful?

The Laplace transform turns differential equations into algebraic equations, which are much easier to solve. It's fundamental in electrical engineering, control systems, and signal processing.