Inverse Laplace Transform Calculator
Compute the inverse Laplace transform of a function F(s) using partial fraction decomposition and known transform pairs. Enter F(s) as a rational function in s.
Published by:
isCalculator Editorial Team
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How to use this tool?
How to Use the Inverse Laplace Transform Calculator
This calculator computes the inverse Laplace transform f(t) of a rational function F(s) = numerator / denominator.
- Enter the numerator (e.g.,
s+2) in the top field. - Enter the denominator (e.g.,
s^2+4s+3) in the bottom field. - Click "Calculate Inverse Laplace".
- View the result f(t) and step-by-step decomposition below.
Input format: Use s for the variable. Write powers as s^2, s^3, etc. Constants are plain numbers (e.g., 5). Example: (s+2)/(s^2+4s+3).
Notes: The calculator supports denominators up to degree 3. If the numerator degree is ≥ denominator degree, polynomial division is performed first. Results include impulse functions (δ) for polynomial parts and exponentials for real/complex roots.
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Frequently Asked Questions
It handles rational functions where the denominator is a polynomial of degree up to 3. It uses partial fraction decomposition and known Laplace transform pairs.
Use standard notation with 's' as the variable. For example, (s+2) for numerator and (s^2+4s+3) for denominator. Coefficients can be decimals.
The calculator performs polynomial division first and handles the remainder via partial fractions. The result includes impulse functions and their derivatives.
