Inverse Laplace Transform of 1/s²

The inverse Laplace transform of 1/s² is t. See the partial fraction expansion and the transform pair used for each term, then edit F(s) to try your own.

L⁻¹{1/s²} = t. A double pole at the origin is a ramp.

Numerator N(s)

e.g. 2s+3

Denominator D(s)

Expanded or factored, e.g. (s+1)(s^2+4)

Try an example

The result

L⁻¹{1/s²} = t

Partial fractions: 1/s^2

Invert 1/s^2 — L⁻¹{A/(s − a)^2} = A·t^1e^(at)/1!

A double pole at the origin is a ramp.

More inverse transforms

L⁻¹{1/s} L⁻¹{1/s³} L⁻¹{1/(s − 3)} L⁻¹{1/(s + 2)} L⁻¹{1/(s² + 4)} L⁻¹{s/(s² + 9)} L⁻¹{1/(s² − 4)} L⁻¹{1/(s(s + 1))}

Frequently asked questions

What is the inverse Laplace transform of 1/s²? ▾

It is f(t) = t. A double pole at the origin is a ramp.

What are the partial fractions here? ▾

F(s) splits into 1/s^2, and each piece is inverted separately.

How can I check this answer? ▾

Transform t forward again with the Laplace transform calculator — you should get back 1/s².

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