Use the next Laplace transform calculator to check your answers. It has three input fields:

  • Field 1: add your function and you can use parameters like \sin a*t
  • Field 2: specify the function variable which is t in the above example
  • Field 3: specify the Laplace variable, s in this case.

Illustrative example about how to use Laplace transform calculator

As an example, let’s consider the following problem:

Find the Laplace Transform of f(t)=3e^{-2t}+t^2

1. Using the Laplace transform calculator

  • We just write the above function in the corresponding field. The function depends on t and we consider s as the Laplace variable. Check the following screenshot:
Laplace transform calculator example
  • Then we hit the calculate button to get the following:
Laplace transform calculator with steps

Hence the Laplace transform of the function f(t)=3e^{-2t}+t^2 is given by:

\displaystyle F(s)=\frac{2}{s^3}+ \frac{3}{s+2}

2. Using the Laplace definition

Taking the Laplace transform of given expression and using the linearity property, we get:


Using the table of Laplace transforms (exponential and t to the power 2), we get

\displaystyle \mathscr{L}\{3e^{-2t}+t^2\}=\frac{3}{s+2}+\frac{2}{s^3}

which is the same as the one provided by the Laplace transform calculator!

This calculator widget has been developed by venkateshb in