Polynomial Calculator
Enter a polynomial's coefficients from the highest degree down and an x value; the tool evaluates the polynomial at that x using Horner's method and reports P(x) plus the degree. It does not factor, expand, or find roots.
What this calculator does
The Polynomial Calculator estimates your result instantly from the values you enter, using standard math & conversions formulas. Enter a polynomial's coefficients from the highest degree down and an x value; the tool evaluates the polynomial at that x using Horner's method and reports P(x) plus the degree. It does not factor, expand, or find roots. Calculations run in your browser, so nothing you type is sent to a server, and the output is an estimate rather than a certified or official figure.
Result
About Polynomial Calculator
The Polynomial Calculator evaluates a polynomial at a single value of x. You supply the coefficients from the highest degree down (comma separated) and the x to plug in, and it returns P(x) computed by Horner's rule, along with the polynomial's degree.
Reach for it when you need the numeric value of a polynomial at a point rather than its factors or roots.
Formula & Mathematical Calculation
P(x) = f(Coefficients (highest degree first), Evaluate at x)
Calculated according to standard math formulas implemented in the calculator core.
Calculation Example
Enter Coefficients = 1,-3,2 (that is x² - 3x + 2) and Evaluate at x = 5.
The tool shows P(x) = 12 and Degree = 2, with the note "Evaluated by Horner rule: P(5) = 12 (degree 2)."
Key Benefits
- Evaluates a polynomial of any degree at a chosen x value
- Uses Horner's method for a numerically stable result
- Reports the polynomial's degree from the number of coefficients you entered
- Reads coefficients from a single comma-separated field
How to Use this Calculator
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Enter the coefficients
In the Coefficients field, list the coefficients from highest degree first, separated by commas, for example 1,-3,2. -
Enter the x value
Type the value at which to evaluate the polynomial into the Evaluate at x field. -
Calculate and read the results
Click Calculate, then read the P(x) box for the value and the Degree box for the polynomial's degree.
Assumptions & Limitations
What the calculation assumes
- Every value you enter is treated as an exact, known amount.
- Any rate or interval you enter is assumed to hold for the whole period unless the form asks for it separately.
- Results use standard published formulas and account only for the values entered above.
- Rounding is applied for display; the underlying calculation uses your full precision.
- Results are returned in the same units you enter, unless the tool states the output unit.
What it does not cover
- Polynomial Calculator produces a calculated result for reference and learning, not a certified or official measurement.
- Real-world outcomes differ when tolerances, rounding rules or local standards apply.
- Definitions and standards vary by region and change over time; verify the convention that applies to your case.
- Figures are only as accurate as the inputs you supply — check them before acting on the result.
- For work where the result carries real consequences, confirm it against an authoritative source.
Frequently Asked Questions
Free to use, no account needed. Calculations run in your browser, so nothing you type is sent to a server. Results are estimates — how we build and check our calculators.