Laplace Transform Calculator

Use our free Laplace transform calculator to compute F(s) numerically for any function, generate a table of F(s) values, or apply the Initial Value Theorem.

Math

Mode

f(x) =

s value

s start (table)

s end (table)

Steps (table)

Formula

Compute the Laplace transform F(s) of any function f(t) using numerical integration over [0, 200] with the trapezoidal rule. Supports evaluation at a single s, tables across a range, and the Initial Value Theorem.

F(s) = ∫₀^∞ f(t)e^{-st} dt

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

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

Examples

ℒ{t²} at s=1

1.ℒ{t²} = 2/s³
2.F(1) = 2

Result: 2

Initial Value f(0⁺) for e^{-x}

1.f(0⁺) = lim sF(s) as s→∞
2.F(s)=1/(s+1), sF(s)=s/(s+1)→1

Result: 1

Frequently Asked Questions

An integral transform that converts a function of time to a function of complex frequency s.

Numerical integration of F(s) = ∫₀²⁰⁰ f(t)e^{-st} dt using the trapezoidal rule.

f(0⁺) = lim_{s→∞} sF(s), giving the function's value at time 0⁺.

Yes, any expression with x (time variable) using sin, cos, exp, polynomials, etc.

Good accuracy for smooth, decaying functions. For functions that don't decay, the integral may not converge.

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CalculateMe Team

Last updated: 2026-07-15

Frequently Asked Questions

An integral transform that converts a function of time to a function of complex frequency s.

Numerical integration of F(s) = ∫₀²⁰⁰ f(t)e^{-st} dt using the trapezoidal rule.

f(0⁺) = lim_{s→∞} sF(s), giving the function's value at time 0⁺.

Yes, any expression with x (time variable) using sin, cos, exp, polynomials, etc.

Good accuracy for smooth, decaying functions. For functions that don't decay, the integral may not converge.

Laplace Transform Calculator

Formula

How It Works

Examples

ℒ{t²} at s=1

Initial Value f(0⁺) for e^{-x}

Frequently Asked Questions

What is the Laplace transform?

What method is used?

What is the Initial Value Theorem?

Can I use any function?

How accurate is it?

Related Calculators

Laplace Transform Calculator

Formula

How It Works

Examples

ℒ{t²} at s=1

Initial Value f(0⁺) for e^{-x}

Frequently Asked Questions

What is the Laplace transform?

What method is used?

What is the Initial Value Theorem?

Can I use any function?

How accurate is it?

Related Calculators