Laplace Transform Calculator

Compute Laplace transforms of common functions: exponential, sine, cosine, polynomial, and Heaviside step.

Function

Parameter (a/w/n)

Evaluate at s

Tab to move between fields

F(s) Formula

1/(s - 2)

F(s) Value

Pole(s)2

Residue1

How to Use This Calculator

Select the function type: exponential (e^at), sine, cosine, polynomial (tⁿ), unit step, or delta function.
Enter the function parameter (e.g., the decay constant a for e^(at) or the frequency ω for sin(ωt)).
The Laplace transform F(s) = ∫₀^∞ f(t)e^(−st) dt is displayed using the standard closed-form result for each function type.
The s-domain plot shows F(s) as a function of the complex frequency parameter s for s > 0.
Poles (values of s where F(s) is undefined) and residues are listed and are key for inverse transforms and stability analysis.
Laplace transforms convert differential equations into algebraic equations, making them much easier to solve.

What each input means

Function: Time-domain function to transform
Parameter (a/w/n): Parameter: rate for exp, frequency for trig, degree for polynomial, delay for step
Evaluate at s: Complex frequency variable s to evaluate F(s) at

Identify Input Parameters
Function = 1, Parameter (a/w/n) = 2, Evaluate at s = 3 = 3 input(s) provided
Calculate F(s) Formula
1/(s - 2) = 1/(s - 2)
Calculate F(s) Value
1 = 1
Calculate Pole
Pole = number | string;
2 = 2
Calculate Residue
1 = 1

Engine last updated August 5, 2026. Checked against 5 independently-derived tests — how we verify calculators.

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