What is a Laplace transform?
An integral transform that maps a time function f(t) to a complex-frequency function F(s).
Laplace Transform Calculator
Select a standard time-domain function and parameters to obtain F(s) = L{f(t)}.
Choose f(t)
Pick the function type and enter a, n, or ω as needed.
About this calculator
How to use Laplace Transform Calculator, plus the formulas and logic behind the results.
Tool description
Uses the standard unilateral Laplace transform table for introductory differential equations courses.
How to use
- Select the form of f(t) from the list.
- Enter a, n, or ω depending on the chosen form.
- Select Calculate to view F(s).
- Compare with your Laplace transform table.
Formulas & reference
L{1} = 1/sL{t} = 1/s²L{tⁿ} = n!/sⁿ⁺¹L{e^{at}} = 1/(s−a)L{sin(ωt)} = ω/(s²+ω²)L{cos(ωt)} = s/(s²+ω²)
Laplace tips
- Transforms are unilateral (t ≥ 0)
- n must be a non-negative integer for tⁿ
- ω is the angular frequency for sin/cos
- Use inverse Laplace tool to go F(s) → f(t)
Calculation logic
Looks up the closed-form transform for the selected elementary function and substitutes parameters.
Assumes Re(s) is large enough for convergence; educational table lookup only.
Laplace Transform Calculator FAQ
Common questions about this calculator and how to use the results.
Which f(t) are supported?
1, t, tⁿ, e^{at}, sin(ωt), and cos(ωt).
What is the transform of e^{2t}?
1/(s−2) for Re(s) > 2.
Can n be a decimal?
For tⁿ this tool expects a non-negative integer n.
Is linearity included?
Compute each term separately and add transforms by linearity.
Is this free?
Yes. LeCalculators tools are free to use.