Laplace transform calculator
Type a function of t, such as 3 + 2t^2 − 4exp(−2t) + 5sin(3t), and get its Laplace transform F(s), term by term from the standard table.
Sums of constants, tⁿ, exp(at), sin(bt), cos(bt), sinh(bt) and cosh(bt), also multiplied by exp(at).
Fill in the fields; the answer appears here straight away.
How it's worked out
How it works
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Enter the values
Type the numbers or the formula. Decimals may use a point or a comma. No idea? Click Fill in an example.
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Instant answer
The answer appears as you type, with the most important intermediate values.
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See the working
Under "How it's worked out" you see the steps, handy for checking your own calculation.
Supported terms
Constants, tⁿ, e^(at), sin(bt), cos(bt), sinh(bt) and cosh(bt), and those terms multiplied by e^(at) (the shift rule). Because the Laplace transform is linear, sums and constant multiples work too.
Examples from the table
- L{1} = 1/s
- L{tⁿ} = n! / sⁿ⁺¹
- L{e^(at)} = 1 / (s − a)
- L{sin(bt)} = b / (s² + b²)
- L{e^(at)·cos(bt)} = (s − a) / ((s − a)² + b²)
The result is valid for s greater than the real part of every a. To go back from F(s) to f(t), use the inverse Laplace transform calculator.
Frequently asked questions
Is the laplace transform free?
Yes. The laplace transform is completely free, with no account, sign-up or usage limit.
How accurate is the result?
The tool calculates with your browser's number precision. For important calculations, always double-check what you entered.
Does it work on my phone?
Yes. The tool works in any modern browser on a phone, tablet or computer.