Inverse Laplace Transform Calculator
Find the time-domain function from a standard-form Laplace transform F(s).
Inputs
f(t) value
0.36787944
f(t) =
f(t) = e^(-1t)
Step by step
Values used
F(s) form = 1/(s-a) → e^(at); n (power) = 2; a (exponential rate) = -1; ω (angular frequency) = 2; Evaluate f(t) at t = = 1
Inverse Laplace
f(t) = L⁻¹{F(s)}
f(t) value
= 0.36787944
f(t) =
= f(t) = e^(-1t)
How it works
Finds the inverse Laplace transform f(t) = L⁻¹{F(s)} for standard forms. Supported inverse transforms: • L⁻¹{n!/s^(n+1)} = tⁿ • L⁻¹{1/(s-a)} = e^(at) • L⁻¹{ω/(s²+ω²)} = sin(ωt) • L⁻¹{s/(s²+ω²)} = cos(ωt) • L⁻¹{1/(s-a)²} = t·e^(at) • L⁻¹{ω/((s-a)²+ω²)} = e^(at)sin(ωt) • L⁻¹{(s-a)/((s-a)²+ω²)} = e^(at)cos(ωt)
Formula
Inverse Laplace
f(t) = L⁻¹{F(s)}
- f(t)
- Time-domain function
- F(s)
- S-domain transform
Frequently Asked Questions
How do I handle more complex F(s)?
Use partial fraction decomposition to break F(s) into the standard forms listed above, then invert each term separately.
What about the e^(-as) factor?
A factor e^(-as) in F(s) corresponds to a time delay: L⁻¹{e^(-as)F(s)} = f(t-a)·u(t-a).