Laplace Transform Calculator

Calculate Laplace transforms of common functions used in differential equations and signal processing.

Transform Parameters

Laplace Transform Definition

L{f(t)} = ∫₀^∞ f(t)e^(-st) dt = F(s)

F(s) = L{f(t)}

1.00000000

Transform Pair

Time Domain

f(t) = 1

Frequency Domain

F(s) = 1/s

Region of Convergence

s > 0

Properties

  • • Linearity: L{af + bg} = aF + bG
  • • Time Shift: L{f(t-a)u(t-a)} = e^(-as)F(s)
  • • Derivative: L{f'(t)} = sF(s) - f(0)
  • • Integral: L{∫f(t)dt} = F(s)/s