Polynomial Evaluation Calculator
Plug an x value into any polynomial and instantly get P(x), computed efficiently with Horner’s method.
Polynomial value at the chosen x
- 1
Leading coefficient a₀
1 - 2
Iteration 1: r × x + next coefficient
1 × 4 + -3 = 1 - 3
P(x)
1 × 4 + 2 = 6
How does this calculator work?
Enter your polynomial’s coefficients (highest degree first) and an x value. The calculator uses Horner’s method to evaluate P(x) exactly, reports the degree and leading coefficient, and plots the curve over a window around your point so you can see where the value lands.
Formula
How this is calculated
Enter the polynomial coefficients from the highest-degree term to the constant term, separated by commas or spaces. For example, the list 1, -3, 2 represents the polynomial x² − 3x + 2 (degree 2). The x value field is the point at which the polynomial is evaluated.
The value P(x) is computed with Horner’s method, which rewrites the polynomial as nested multiplication: aₙxⁿ + … + a₀ = (((aₙ)x + aₙ₋₁)x + …)x + a₀. Starting from the leading coefficient, the routine repeatedly multiplies the running result by x and adds the next coefficient. This uses only n multiplications and n additions, making it faster and more numerically stable than computing each power of x separately.
The degree equals the number of coefficients minus one, and the leading coefficient is the first value in the list. The chart plots the polynomial over the interval [x − 5, x + 5] using about 60 samples, with the evaluated point highlighted. Coefficients may be negative or zero, but every term must be present in order (use 0 for missing powers, e.g. 1, 0, -4 for x² − 4).
Frequently asked questions
Highest-degree term first, down to the constant. For 2x³ + 0x² − 5x + 7 enter 2, 0, -5, 7. Always include a 0 for any missing power so the positions line up.
Horner’s method needs only n multiplications and n additions instead of recomputing x², x³, …, so it is faster and accumulates less floating-point error for high-degree polynomials.
Yes. Any real number works for x, and coefficients may be negative or fractional too. The result and the plotted curve update accordingly.
Also known as
TG we-Calculate Editorial Team. (2026). Polynomial Evaluation Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/evaluate-polynomial-calculator
TG we-Calculate Editorial Team. "Polynomial Evaluation Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/evaluate-polynomial-calculator.
TG we-Calculate Editorial Team, "Polynomial Evaluation Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/evaluate-polynomial-calculator
@misc{wecalculate_evaluate_polynomial_calculator, title = {Polynomial Evaluation Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/evaluate-polynomial-calculator}}, year = {2026}, note = {TG we-Calculate} }
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