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Taylor Series Calculator

Compute Taylor/Maclaurin series coefficients for common functions.

Introduction

Taylor Series Calculator — Compute Taylor/Maclaurin series coefficients for common functions. Enter Function, Number of terms to get an instant, accurate result.

Formula

Generates the Maclaurin (Taylor-at-0) series coefficients for eˣ, sin(x), or cos(x) up to the requested number of terms, using each function's known term pattern (e.g. sin(x) alternates 0, x/1!, 0, −x³/3!, 0, x⁵/5!, …).

Step-by-step

  1. Enter the Function.
  2. Enter the Number of terms.
  3. Click Calculate to see your result instantly.

Real-world example

Example: With Function = exp, Number of terms = 5, the Taylor Series Calculator gives Function: exp, Coefficients: 1, 1, 0.5, 0.1667, 0.0417.

Frequently Asked Questions

Is this expanded around x = 0?
Yes — this generates the Maclaurin series, which is the Taylor series specifically centered at x = 0.
Which functions are supported?
eˣ, sin(x), and cos(x).
What inputs does the Taylor Series Calculator need?
You'll need to provide: Function, Number of terms. All fields use sensible defaults, so you can see a working example immediately and then adjust the values to match your own numbers.
How accurate is the Taylor Series Calculator?
The Taylor Series Calculator applies the formula exactly as calculated — Generates the Maclaurin (Taylor-at-0) series coefficients for eˣ, sin(x), or cos(x) up to the requested number of terms, using each function's known term pattern (e.g. sin(x) alternates 0, x/1!, 0, −x³/3!, 0, x⁵/5!, …). — so results are precise for the inputs you provide. Accuracy depends on entering correct, realistic input values.
Is the Taylor Series Calculator free to use?
Yes, the Taylor Series Calculator is completely free, requires no signup, and runs instantly in your browser.

About the Taylor Series Calculator

The Taylor Series Calculator uses a real, verifiable formula — Generates the Maclaurin (Taylor-at-0) series coefficients for eˣ, sin(x), or cos(x) up to the requested number of terms, using each function's known term pattern (e.g. sin(x) alternates 0, x/1!, 0, −x³/3!, 0, x⁵/5!, …). — so results are accurate every time, not an approximation.