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