Laplace Transform Calculator (Common Functions)
Laplace transform F(s) of standard time functions with region of convergence, poles, and the numeric value at a complex s.
How to use the Laplace Transform Calculator
- Enter or select: Function f(t) for t ≥ 0, a, ω, n (for tⁿ), Re(s), Im(s).
- The results (F(s), Region of convergence, Poles, Re F(s), Im F(s), |F(s)|) are calculated instantly as you type.
- Use “Copy link” to share the calculation with the same input values.
Formula
- F(s) = ∫₀^∞ f(t) e^(−st) dt
- L{sin ωt} = ω/(s² + ω²)
- L{e^(−at)} = 1/(s + a)
- L{tⁿ} = n!/sⁿ⁺¹
About this tool
Evaluating F(s) outside the region of convergence uses the analytic continuation of the transform, not the defining integral.