Laplace Transform of u(t)
The Laplace transform of u(t) is 1/s. See the table rule behind it, then edit the function to transform anything else.
L{u(t)} = 1/s. The Heaviside unit step is 1 for t ≥ 0, so its transform is 1/s.
Use t as the variable. Examples: t^3, e^(-2t), sin(3t), t*cos(2t), 4t^2+3. Write δ(t) as delta(t).
The result
L{u(t)} = 1/s
- L{1} = 1/s Table rule: L{1} = 1/s
The Heaviside unit step is 1 for t ≥ 0, so its transform is 1/s.
More special transforms
Other transforms
Frequently asked questions
What is the Laplace transform of u(t)? ▾
L{u(t)} = 1/s. The Heaviside unit step is 1 for t ≥ 0, so its transform is 1/s.
Which rule gives the transform of u(t)? ▾
L{1} = 1/s applied to 1.
How do I get back from F(s) to f(t)? ▾
Use the inverse Laplace transform. Split F(s) into partial fractions and invert each piece with the same table read backwards — the inverse Laplace transform calculator does this step by step.
About this Calculator
The Laplace transform of u(t) is 1/s. See the table rule behind it, then edit the function to transform anything else.