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Math

Polynomial Evaluation Calculator

Evaluate a polynomial at a chosen x using coefficients listed from highest power to constant.

Exact method explained belowEditable inputs
Calculation notebook
Calculation notebook

The formula and worked example below explain the calculation.

See the method

Enter your values

Runs on your device

Your answer

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter coefficients, highest power first, value of x.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

Horner’s method starts with the leading coefficient and repeatedly multiplies the accumulated value by x before adding the next coefficient.

A WORKED EXAMPLE

Using coefficients, highest power first = 2, 0, -3, 4, value of x = 2, the result is 14. Change these example inputs to match your task; use the method above to check each step.

Understanding your result

Each position represents a power. The list 2, 0, −3, 4 means 2x³ − 3x + 4; omitting the zero changes the polynomial.

What to keep in mind

Degree at most 30. Large coefficients or inputs may overflow; non-finite results are rejected. Finite-precision arithmetic is used. Check the domain and the stated convention before using an approximation.

Common questions

Why must I include zero coefficients?

Each position represents a power. The list 2, 0, −3, 4 means 2x³ − 3x + 4; omitting the zero changes the polynomial.

How can I check the result?

Horner’s method starts with the leading coefficient and repeatedly multiplies the accumulated value by x before adding the next coefficient. The worked example uses editable inputs. Calculations run on your device; no external API or account is required.

Methodology maintained by ClarityKit. How these tools are built and checked.