Laplace Calculator

Inverse Laplace Transform Calculator

Online Inverse Laplace Transform Calculator

Calculate Inverse Laplace Transform
Enter a function F(s) to find its inverse Laplace transform f(t)

Examples

Laplace Transform

L{et/2}\mathcal{L}\{e^{t/2}\}L{e−2tsin⁡2(t)}\mathcal{L}\{e^{-2t}\sin^2(t)\}L{8π}\mathcal{L}\{8\pi\}L{sin⁡(at)}\mathcal{L}\{\sin(at)\}L{t2}\mathcal{L}\{t^2\}

Inverse Laplace Transform

L−1{1s2+1}\mathcal{L}^{-1}\{\frac{1}{s^2 + 1}\}L−1{ss2+4}\mathcal{L}^{-1}\{\frac{s}{s^2 + 4}\}L−1{1s(s+1)}\mathcal{L}^{-1}\{\frac{1}{s(s+1)}\}L−1{1s2}\mathcal{L}^{-1}\{\frac{1}{s^2}\}L−1{ss2+a2}\mathcal{L}^{-1}\{\frac{s}{s^2 + a^2}\}

What is Inverse Laplace Transform?

The Inverse Laplace Transform is a mathematical operation that converts a function from the frequency domain (s-domain) back to the time domain. It is denoted as f(t)=L−1{F(s)}f(t)=\mathcal{L}^{-1}\{F(s)\}, where F(s) is the Laplace transform of the original function f(t). This transformation is crucial in engineering and physics for solving differential equations and analyzing system responses. The Inverse Laplace Transform is particularly useful in control systems, signal processing, and electrical engineering where we need to determine how a system behaves over time based on its frequency-domain representation.