Laplace Transform Calculator

The Laplace transform of a standard function is a table entry with your constants substituted into it, and this page does exactly that rather than pretending to parse algebra. Pick one of twelve forms, from a constant through the exponential, sine, cosine and hyperbolic entries to the delayed step and impulse, type its constants, and the tool writes f(t) back with your numbers in it alongside F(s), the table entry used and the region of convergence. A second tab transforms a polynomial in t up to degree three, one term at a time. Anything needing symbolic algebra, such as an expression typed as free text, a product of two forms or a piecewise definition, is refused rather than approximated.

Calculator Type

Pick the shape of f(t) from the table, type the constants in it, and read off F(s).

The whole of f(t) is multiplied by this, and so is F(s). Leave it at 1 for the bare table entry.
Used by the e^(at), t^n e^(at), e^(at) sin, e^(at) cos, sinh and cosh forms.
Used by the four sine and cosine forms. It must not be zero there.
Used by the t^n and t^n e^(at) forms only.
Used by the delayed step and the delayed impulse only.
Optional, and only for a real s inside the region of convergence. The symbolic answer does not depend on it.
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A polynomial up to degree three, transformed term by term. The transform is linear, so each t^n becomes n!/s^(n+1) and the pieces are added.

f(t) = a t^3 + b t^2 + c t + d.
Leave a coefficient at zero to drop that term.
f(t) = a t^3 + b t^2 + c t + d.
f(t) = a t^3 + b t^2 + c t + d.
Optional, and only for a real s inside the region of convergence. The symbolic answer does not depend on it.
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