Inverse Laplace Transform Calculator

Use our free inverse Laplace transform calculator to compute f(t) numerically from any F(s) using the Gaver-Stehfest algorithm. Supports evaluation, table generation, and the Final Value Theorem.

Math

Mode

F(s) =

t value

t start (table)

t end (table)

Steps (table)

Formula

Compute f(t) from F(s) numerically using the Gaver-Stehfest algorithm, which evaluates F(s) at real s values and sums weighted terms. Supports single evaluation, tables across a t range, and the Final Value Theorem.

f(t) = ℒ⁻¹{F(s)} via Gaver-Stehfest (N=10)

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Enter F(s) using x as the s variable.
2Select mode: single t, table, or final value theorem.
3For single: enter t.
4For table: enter t range and steps.
5Click Calculate.

Examples

ℒ⁻¹{1/(s+1)} at t=1

1.ℒ⁻¹{1/(s+1)} = e^{-t}
2.f(1) = e⁻¹ ≈ 0.36788

Result: 0.3678794412

Final Value of 1/(s+1)

1.f(∞) = lim_{s→0} sF(s)
2.s/(s+1) → 0

Result: 0

Frequently Asked Questions

The inverse operation that recovers f(t) from F(s).

Gaver-Stehfest (N=10) — a purely real numerical inversion method.

f(∞) = lim_{s→0} sF(s), giving the steady-state value.

Smooth F(s) with known inverse transforms work best. Oscillatory or highly resonant F(s) may be less accurate.

The calculator uses x as the variable. Enter F(s) using x: e.g., 1/(x+1) for 1/(s+1).

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CalculateMe Team

Last updated: 2026-07-15

Frequently Asked Questions

The inverse operation that recovers f(t) from F(s).

Gaver-Stehfest (N=10) — a purely real numerical inversion method.

f(∞) = lim_{s→0} sF(s), giving the steady-state value.

Smooth F(s) with known inverse transforms work best. Oscillatory or highly resonant F(s) may be less accurate.

The calculator uses x as the variable. Enter F(s) using x: e.g., 1/(x+1) for 1/(s+1).

Inverse Laplace Transform Calculator

Formula

How It Works

Examples

ℒ⁻¹{1/(s+1)} at t=1

Final Value of 1/(s+1)

Frequently Asked Questions

What is the inverse Laplace transform?

What algorithm is used?

What is the Final Value Theorem?

What functions work well?

Why use x for s?

Related Calculators

Inverse Laplace Transform Calculator

Formula

How It Works

Examples

ℒ⁻¹{1/(s+1)} at t=1

Final Value of 1/(s+1)

Frequently Asked Questions

What is the inverse Laplace transform?

What algorithm is used?

What is the Final Value Theorem?

What functions work well?

Why use x for s?

Related Calculators