Taylor Series Expansion Calculator (e^x, sin x, cos x)
Taylor polynomial approximation for common functions.
Enter your values
Choose one of: e^x, sin(x), cos(x).
Enter the evaluate at x you are working with.
Enter the number of terms you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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
At a glance
| What it does | Taylor polynomial approximation for common functions. |
|---|---|
| Category | Math |
| Inputs needed | Function, Evaluate at x, Number of terms |
| Main output | Taylor approximation |
| Formula | f(x) ≈ Σ f^(n)(0)/n! * x^n |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Function
- Choose one of: e^x, sin(x), cos(x).
- Evaluate at x
- Enter the evaluate at x you are working with.
- Number of terms
- Enter the number of terms you are working with.
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.
What do I need to enter into the Taylor Series Expansion Calculator (e^x, sin x, cos x)?
Just 3 values: function, evaluate at x, number of terms. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Taylor Series Expansion Calculator (e^x, sin x, cos x) work out the answer?
A Taylor series approximates a function near a point by summing derivative-based polynomial terms; more terms improve accuracy. It applies the formula f(x) ≈ Σ f^(n)(0)/n! * x^n and shows the working so you can check each step by hand.
Is the Taylor Series Expansion Calculator (e^x, sin x, cos x) free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.