How does the Taylor Series Calculator work?

f(x) ≈ f(a) + f'(a)(x−a) + f''(a)(x−a)²/2! + ... Then: sin(x) = x − x³/6 + x⁵/120 − ... Then: cos(x) = 1 − x²/2 + x⁴/24 − ... Then: eˣ = 1 + x + x²/2 + x³/6 + ....

Can you give an example of how to use the Taylor Series Calculator?

Example: Input sin(0.5 rad) using 3 terms gives a result of 0.5 − 0.5³/6 + 0.5⁵/120 = 0.4794 (Exact: 0.47943; error < 0.0001).

Is the Taylor Series Calculator free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Taylor Series Calculator?

Our Taylor Series Calculator uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Taylor Series Calculator

∑Taylor Series Calculator

Value of x

Number of terms

A Taylor series approximates any smooth function as an infinite polynomial around a point. Truncating it gives a polynomial approximation — the basis for how calculators compute sin, cos, and eˣ.

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Did You Know?

Taylor series explain why CPUs can compute transcendental functions using only addition and multiplication — they evaluate polynomial approximations in hardware.

References

›Taylor series — Wikipedia

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Taylor Series Calculator

∑Taylor Series Calculator

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∑Taylor Series Calculator