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Maclaurin Series Calculator

The Taylor series at 0 for twelve standard functions — sin, cos, eˣ, ln(1+x), √(1+x), arcsin, arctan and more — with exact fractions such as 1/120, the general term and the error at a chosen x.

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Open Maclaurin Series Calculator and you get an answer straight away, with no account to create. You will find it under Calculus, with Fourier Series Coefficients Calculator and Taylor Series Calculator for the neighbouring cases.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Maclaurin Series Calculator do?

The Taylor series at 0 for twelve standard functions — sin, cos, eˣ, ln(1+x), √(1+x), arcsin, arctan and more — with exact fractions such as 1/120, the general term and the error at a chosen x.

When would I actually use this?

Checking a derivative or an integral you worked out by hand, finding where a function turns, and getting a numeric answer when no closed form exists.

What is the most common mistake?

Integrating across a discontinuity as if it were not there. A numeric method will happily return a finite value for an integral that diverges — check the domain before trusting the number.

How is Maclaurin Series Calculator different from Fourier Series Coefficients Calculator?

They sit next to each other but answer different questions: Fourier Series Coefficients Calculator is the one to open when you need it to a₀, aₙ and bₙ over any period, computed exactly by integration by parts when f is a polynomial and by Gauss–Legendre quadrature otherwise, with the truncated series plotted against f so the Gibbs overshoot is visible. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Taylor Series Calculator is the closest one after this: Type any f(x) — tan(x), sqrt(1+x), ln(1+x), exp(x)/cos(x) — pick the expansion point and get exact rational coefficients up to order 20, the derivatives f⁽ⁿ⁾(a) and the detected general term.

What else is worth having open alongside it?

Infinite Series Sum Calculator and Power Series Calculator — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

Symbolic results are exact; numeric ones come from adaptive quadrature or a standard step method, and the tool reports which. Where both are available, compare them — a large gap means the problem is ill-conditioned.

Further reading

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