Laplace Transform of δ(t)
The Laplace transform of δ(t) is 1. See the table rule behind it, then edit the function to transform anything else.
L{δ(t)} = 1. The Dirac delta transforms to the constant 1 — it excites every frequency equally.
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{δ(t)} = 1
- L{1·δ(t)} = 1 Table rule: L{δ(t)} = 1
The Dirac delta transforms to the constant 1 — it excites every frequency equally.
More special transforms
Other transforms
Frequently asked questions
What is the Laplace transform of δ(t)? ▾
L{δ(t)} = 1. The Dirac delta transforms to the constant 1 — it excites every frequency equally.
Which rule gives the transform of δ(t)? ▾
L{δ(t)} = 1 applied to 1·δ(t).
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 δ(t) is 1. See the table rule behind it, then edit the function to transform anything else.