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Lagrange Interpolation

Interpolate points and evaluate at a given x.

Points (x y, one per line)
Result

Enter points.

Technical Description & Theory

What is Interpolation Lagrange Calculator and Why it Matters?

Polynomial interpolation reconstructs a smooth function from discrete samples and is foundational in approximation theory.

Mathematical Formula and Theory

P(x)=Σ yᵢ ℓᵢ(x), ℓᵢ(x)=∏_{j≠i}(x−xⱼ)/(xᵢ−xⱼ). Unique of degree at most n−1.

How to Use This Calculator - Step by Step

  • Enter data pairs and evaluation point.
  • Click Interpolate.

Solved Example with Full Calculation

Points (0,1),(1,2),(2,0),(3,5). P(1.5)≈1.4375.