Inverse Laplace Transform Calculator

Find inverse Laplace transforms for standard expressions.

Use this calculator as a study checker

Enter the problem carefully, review the interpreted input, and compare each step with your own work. Calculus results can depend on notation, variables, bounds, domains, and assumptions.

Check the method before copying the answer.
Use the examples below to test nearby problems.
Read the calculus guides for worked explanations.

Solution

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Enter an expression or choose an example to calculate.

Inverse Laplace Transform Examples

What this calculator is for

The inverse Laplace transform converts an s-domain expression back into a time-domain function. Use it to check your setup, compare steps with your own work, and review the meaning of the final expression before copying it into homework.

How inverse Laplace transforms are found

Simplify the expression in \(s\).
Use partial fractions if the denominator factors.
Match each term to a known inverse transform.

Manual example

Problem: \(\mathcal{L}^{-1}\{1/s^2\}\).
The table pair \(\mathcal{L}\{t\}=1/s^2\) applies.
Final result: \(t\).

Common mistakes to avoid

Skipping partial fractions when the expression is not table-ready.
Confusing \(1/s\) and \(1/s^2\).
Dropping exponential shift factors.

When to double-check the result

Complicated rational functions may have multiple equivalent forms. Check that the final time-domain expression transforms back correctly.