Inverse Laplace Transform Calculator
Compute inverse Laplace transforms with step-by-step solutions. Convert F(s) to f(t) for differential equations and system analysis.
Inverse Laplace Transform Calculator
Compute inverse Laplace transforms with step-by-step solutions
Transform Input
Laplace Transform Expression
Use 's' as the complex frequency variable. Example: 1/(s^2 + a^2)
Common Transform Pairs
| F(s) | f(t) | Copy |
|---|---|---|
| 1 | δ(t) | |
| 1/s | 1 | |
| 1/s^2 | t | |
| 1/s^n | t^(n-1)/(n-1)! | |
| 1/(s-a) | e^(at) | |
| 1/(s^2+a^2) | sin(at)/a | |
| s/(s^2+a^2) | cos(at) | |
| 1/(s^2-a^2) | sinh(at)/a |
Results
Your inverse transform results will appear here
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Simple steps to compute inverse Laplace transforms!
Enter Laplace Transform
Input your F(s) expression using standard mathematical notation.
Compute Inverse Transform
Our algorithm matches your input against known transform pairs.
Get Step-by-Step Solution
See the reasoning behind each transformation with detailed steps.
Key Features
What makes our Inverse Laplace Calculator special!
Standard Transform Pairs
Recognizes common Laplace transform forms and their inverses.
Complex Form Handling
Processes expressions with exponents, polynomials, and trigonometric functions.
Mathematical Syntax
Understands standard mathematical notation (^ for exponents, etc.).
Who Can Benefit
Our Inverse Laplace Calculator helps various users:
Engineering Students
Solve differential equations and control systems problems.
Mathematics Students
Understand integral transforms and their applications.
Researchers
Quickly verify inverse transforms during analysis.
Educators
Demonstrate transform concepts with interactive examples.
Math Calculators
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Try NowUser Reviews
Rated Excellent 4.98/5 on There's An AI For That (TAAFT) - The #1 AI Aggregator
- Jun 17, 2025
Saved My Homework!
This calculator helped me verify my differential equations solutions instantly.
Engineering StudentVerified Review - Jun 15, 2025
Perfect for Teaching
I use this in my signals and systems class to demonstrate transform concepts.
Professor JohnsonVerified Review - Jun 13, 2025
Accurate Results
Matches exactly with my advanced math textbook tables.
Math MajorVerified Review - Jun 11, 2025
Great Learning Tool
The step-by-step solutions help me understand the process, not just the answer.
Physics StudentVerified Review
Frequently Asked Questions
Is this Inverse Laplace Calculator free?
Yes, our Inverse Laplace Transform Calculator is completely free to use with no limitations.
What types of expressions can it handle?
The calculator recognizes standard forms like 1/(s²+a²), s/(s²+a²), 1/(s-a), e^(-as)/s, and more. It also handles numeric variations of these forms.
Does it show the steps?
Yes, the calculator provides step-by-step explanations showing how it arrived at each inverse transform.
Can it handle partial fraction decomposition?
Currently the calculator focuses on direct transform recognition. For complex expressions requiring partial fractions, consider breaking them down into simpler components first.
What notation should I use?
Use standard mathematical notation: '^' for exponents (e.g., s^2), '*' for multiplication (optional), and standard function names (sin, cos, exp, etc.).
Is this suitable for engineering applications?
Yes, the calculator is particularly useful for electrical engineering, mechanical engineering, and other fields that use Laplace transforms for system analysis.
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