๐Taylor Series Calculator
Expand a function into a Taylor (or Maclaurin, at a=0) series with term-by-term working and a comparison graph.
Calculations run entirely in your browser using math.js for parsing, symbolic differentiation, and evaluation. No data is sent to a server.
Free Taylor Series Calculator With Steps
Need a polynomial approximation of a function, or want to see how Taylor series actually build up term by term? Our free Taylor series calculator expands any function around a center point instantly. Enter your function, choose the center (0 gives you the Maclaurin series) and the order, and see each derivative term computed and added to the series one at a time.
For common functions like e^x, sin x, and 1/(1-x), it also recognizes the general term pattern and shows the summation notation, connecting the worked-out terms to the formula you'd see in a textbook. A live graph overlays your function with the polynomial approximation, so you can see visually how accuracy improves with more terms and where it starts to diverge.
Enter your function to get started. No sign-up, no downloads, no limits โ just clear, worked-out calculus whenever you need it. See the About page or the FAQ for more.