Taylor Series Expansion Calculator (e^x, sin x, cos x)
Taylor polynomial approximation for common functions.
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ⓘ Live results
Results
- Taylor approximation
- 2.71666667
- Exact value
- 2.71828183
- Absolute error
- 0.00161516
- Terms used
- 6
Quick answer
A Taylor series approximates a function near a point by summing derivative-based polynomial terms; more terms improve accuracy.
f(x) ≈ Σ f^(n)(0)/n! * x^n
How to use the Taylor Series Expansion Calculator (e^x, sin x, cos x)
- 1Choose the function to approximate (e^x, sin x or cos x).
- 2Enter the x value and how many series terms to include.
- 3Compare the Taylor approximation with the exact function value.
Worked example
Using the values the calculator loads with:
Inputs
- Functione^x
- Evaluate at x1
- Number of terms6
Results
- Taylor approximation2.71666667
- Exact value2.71828183
- Absolute error0.00161516
- Terms used6
Frequently asked questions
Why does accuracy improve with more terms?
Each extra term captures higher-order curvature of the function, shrinking the truncation error.
Why center at 0?
This is the Maclaurin series, the standard case for these functions; centering elsewhere shifts every term.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.