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Inverse Laplace Calculator

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Inverse Laplace Calculator
Look up F(s) → f(t) transform pairs with worked examples
Select F(s) Form
F(s) = 1/s  →  f(t) = 1 (unit step)
Inverse Laplace Result
f(t) = 1 (unit step) (t ≥ 0)
Common Transform Pairs Reference
F(s)f(t) = L⁻¹{ F(s) }
1/s1 (unit step)
1/s²t
n!/sⁿ⁺¹tⁿ
1/(s+a)e^(−at)
s/(s²+ω²)cos(ωt)
ω/(s²+ω²)sin(ωt)
s/(s²−ω²)cosh(ωt)
ω/(s²−ω²)sinh(ωt)
Click a row to select. All transforms valid for t ≥ 0.

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What is Inverse Laplace Calculator?

Inverse Laplace Calculator converts functions from the Laplace (frequency) domain back to the time domain, making it easier to solve differential equations in engineering and physics.

Inverse Laplace Calculator Formula / Method

Nosingleclosedformula;usestablelookup,partialfractions,andinversetransformpairs:No single closed formula; uses table lookup, partial fractions, and inverse transform pairs:
L−1F(s)=f(t)ℒ⁻¹{F(s)} = f(t)

Inverse Laplace Calculator Step-by-Step

  1. Enter all required inputs shown in the calculator.
  2. Check units/scales or grading format where applicable.
  3. Apply the calculator method for this tool.
  4. Review the computed output.
  5. Use the result for planning, verification, or comparison.

Inverse Laplace Calculator Worked Example

FindinverseLaplaceofF(s)=1/(s2+4)Find inverse Laplace of F(s) = 1 / (s² + 4)

Result: f(t) = (1/2) sin(2t)

Where Inverse Laplace Calculator Is Applied

Essential in control systems engineering, electrical engineering, mechanical vibrations, signal processing, and solving differential equations in physics.

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