Lagrange Interpolation Polynomial Calculator

About this calculator

Lagrange interpolation constructs the unique lowest-degree polynomial that passes exactly through a given set of (x, y) points, built as a weighted sum of "basis" polynomials — each one designed to equal 1 at its own x-value and 0 at every other data point's x-value. Unlike fitting a line or curve by least-squares regression, which minimizes overall error but generally misses most points, Lagrange interpolation guarantees the polynomial threads through every single point exactly, which is exactly what you want when the data points are trusted, exact values rather than noisy measurements.

This calculator takes your set of x,y data points, builds the Lagrange polynomial symbolically, and evaluates it at any x value you choose. Numerical methods students verifying interpolation by hand, engineers estimating a value between sparse tabulated data (like steam tables or lookup charts), and programmers implementing curve-fitting from scratch use it to check their derivations or quickly get an interpolated estimate without coding the algorithm themselves.