Polynomial Interpolation
Given a set of (x, y) points, find the unique polynomial of degree n−1 that passes through all of them, and evaluate it anywhere. The tool builds the Newton divided-difference form (and cross-checks with Lagrange), displays the polynomial, and verifies it reproduces every input point. Everything runs locally in your browser.
Points (one per line: "x y" or "x,y")
Newton form coefficients
Polynomial
Evaluation
For n points with distinct x values there is exactly one polynomial of degree ≤ n−1 through them. The Newton form P(x) = c₀ + c₁(x−x₀) + c₂(x−x₀)(x₁) + … builds coefficients from the divided-difference table; the Lagrange form is a weighted sum of basis polynomials. Both represent the same polynomial and are cross-checked here. Unlike linear regression (which approximates), interpolation passes through every point exactly — so it can oscillate wildly between points (Runge's phenomenon) with many points. The expanded power form is also shown; for many points its coefficients can lose precision. Pairs with the Linear Regression and Calculus Toolkit tools. Everything runs locally — nothing leaves your browser.