Math Calculator

Inverse Laplace Transform Calculator

Select a standard F(s) form and parameters to recover the time-domain f(t).

Choose F(s)

Pick the transform form and enter a or ω when required.

F(s)

Clear

About this calculator

How to use Inverse Laplace Transform Calculator, plus the formulas and logic behind the results.

Tool description

Uses the standard inverse Laplace table for introductory DE courses (unilateral transforms).

How to use

Select the F(s) template.
Enter a or ω if the form needs it.
Select Calculate to view f(t).
Combine results by linearity for sums of terms.

Formulas & reference

L⁻¹{1/s} = 1
L⁻¹{1/s²} = t
L⁻¹{1/(s−a)} = e^{at}
L⁻¹{ω/(s²+ω²)} = sin(ωt)
L⁻¹{s/(s²+ω²)} = cos(ωt)

Inverse Laplace tips

Match your F(s) to a table entry first
ω ≠ 0 for the sin/cos forms
Linearity: invert each term then add
Use the forward Laplace tool to check

Calculation logic

Maps the selected rational F(s) to its elementary inverse from the transform table.

Partial fractions for arbitrary rationals are not performed here.