About the Taylor Series Calculator

Expands a function into a Taylor or Maclaurin series with term-by-term working.

What it is

Computes f(a), f'(a), f''(a), and so on up to your chosen order using math.js symbolic differentiation, then builds the series Σ f⁽ᵏ⁾(a)/k! · (x−a)ᵏ term by term.

Features

Center & order selection

Any center point a and order up to 10.

Term-by-term derivatives

Each derivative order shown as it's computed and evaluated.

General term recognition

Standard functions like eˣ, sin x, and 1/(1−x) show summation notation.

Comparison graph

Original function overlaid with the Taylor polynomial.

Ready to use it?

Free, no sign-up required.

Open the Taylor Series Calculator