Lagrange Interpolation Calculator
Find the unique polynomial passing through given points using Lagrange interpolation.
Data Points
P1:
P2:
P3:
P4:
P(1.5)
3.2500000000
Polynomial of degree 3
Lagrange Basis Contributions at x = 1.5
L_0(1.5) × y_0-0.0625 × 1 = -0.0625
L_1(1.5) × y_10.5625 × 2 = 1.1250
L_2(1.5) × y_20.5625 × 5 = 2.8125
L_3(1.5) × y_3-0.0625 × 10 = -0.6250
Verification (passes through all points?)
P(0) = 1.000000 = 1
P(1) = 2.000000 = 2
P(2) = 5.000000 = 5
P(3) = 10.000000 = 10
Interpolated Values
(0.00, 1.00)
(0.15, 1.02)
(0.30, 1.09)
(0.45, 1.20)
(0.60, 1.36)
(0.75, 1.56)
(0.90, 1.81)
(1.05, 2.10)
(1.20, 2.44)
(1.35, 2.82)
(1.50, 3.25)
(1.65, 3.72)
(1.80, 4.24)
(1.95, 4.80)
(2.10, 5.41)
(2.25, 6.06)
(2.40, 6.76)
(2.55, 7.50)
(2.70, 8.29)
(2.85, 9.12)
(3.00, 10.00)
Lagrange Interpolation
Formula
P(x) = Σᵢ yᵢ × Lᵢ(x)
Lᵢ(x) = Πⱼ≠ᵢ (x-xⱼ)/(xᵢ-xⱼ)
Properties
- Unique polynomial of degree ≤ n-1 through n points
- Lᵢ(xⱼ) = 1 if i=j, 0 otherwise
- Exact at interpolation nodes
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Editorial Note
MyCalcBuddy Editorial Team
This page is maintained as an educational calculator reference.
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Formula Source: Handbook of Mathematical Functions
by Abramowitz & Stegun
🔄Last reviewed: May 2026
✓Formula checks are based on standard references and internal QA review.