Home Calculators Laplace Transform

Laplace Transform Calculator

Compute forward and inverse Laplace transforms with step-by-step derivations, properties used, poles, region of convergence, and a full clickable transform table.

L{f(t)} = integral from 0 to inf of e^(-st) f(t) dt  |  Supports linearity, s-shift, t-shift, t-multiplication

Transform Input

Type a function or click any row in the table below

Supported: 1, t, t^n, e^(at), sin(bt), cos(bt), sinh(bt), cosh(bt), t*e^(at), t*sin(bt), t*cos(bt), e^(at)*sin(bt), e^(at)*cos(bt), t^n*e^(at), u(t-a), delta(t-a) — and scaled versions like 3*sin(2t)

Complete Transform Table

Click any row to auto-fill and calculate

f(t) F(s) = L{f(t)} Category

Result Summary

f(t) = ?
↕
F(s) = ?
Direction—
Type—
ROC—
Poles—

Properties Used

Quick Reference

L{1} = 1/s L{t^n} = n!/s^(n+1) L{e^(at)} = 1/(s-a) L{sin(bt)} = b/(s^2+b^2) L{cos(bt)} = s/(s^2+b^2) L{sinh(bt)} = b/(s^2-b^2) L{cosh(bt)} = s/(s^2-b^2) L{delta(t)} = 1 L{u(t-a)} = e^(-as)/s L{e^at*f(t)} = F(s-a)