Lagrange Interpolation Calculator
Enter your data points and instantly compute the exact Lagrange interpolating polynomial. Then find f(x) at any point.
| Point # | x-value | y-value f(x) |
|---|---|---|
| 1 | ||
| 2 | ||
| 3 | ||
| 4 | ||
| 5 |
ℓᵢ(x) = Πⱼ₌₀ⁿ,ⱼ≠ᵢ (x − xⱼ)/(xᵢ − xⱼ)
Interpolating Polynomial:
P(x) = Σ yᵢ × ℓᵢ(x)
About the Lagrange Interpolation Calculator
The Lagrange Interpolation Calculator is a scientifically precise online tool that computes the exact interpolating polynomial using the world-famous Lagrange Interpolation method — the gold standard in numerical analysis and applied mathematics. Named after Joseph-Louis Lagrange, this method constructs a polynomial that passes through all given data points with mathematical perfection. Whether you're a student, engineer, scientist, or farmer analyzing growth data, this free calculator delivers trusted, peer-reviewed results instantly. For practical agricultural applications, visit Agri Care Hub.
What is Lagrange Interpolation?
Lagrange interpolation finds the unique polynomial of degree at most n−1 that passes through n given points (xᵢ, yᵢ). The formula constructs basis polynomials ℓᵢ(x) such that ℓᵢ(xⱼ) = δᵢⱼ (Kronecker delta), ensuring the final polynomial P(xᵢ) = yᵢ for all i.
P(x) = Σᵢ yᵢ ℓᵢ(x) where ℓᵢ(x) = Πⱼ≠ᵢ (x − xⱼ)/(xᵢ − xⱼ)
Scientific Accuracy & Standards
This calculator implements the exact Lagrange algorithm as published in leading textbooks (Burden & Faires, 2011; Kincaid & Cheney, 2002) and used in MATLAB, Mathematica, and SciPy. It supports up to 20 points with full double-precision arithmetic — results are identical to professional software.
Importance of Lagrange Interpolation
Widely used in:
- Engineering: Signal processing, control systems, finite element analysis
- Agriculture: Crop growth modeling, yield prediction from sample dates
- Physics: Trajectory calculation, thermodynamic interpolation
- Computer Graphics: Bézier curves, animation paths
- Education: Teaching numerical methods worldwide
When & Why You Should Use This Calculator
Use it when you need to:
- Predict plant height on day 45 from weekly measurements
- Interpolate missing sensor readings
- Fit experimental data perfectly
- Solve university assignments accurately
- Teach or learn interpolation theory
User Guidelines
- Enter your (x, y) data points
- Add/remove points using buttons
- Input the target x-value
- Click “Calculate” — get instant, exact result
Agricultural Applications
In precision farming — supported by Agri Care Hub — Lagrange interpolation helps:
- Model daily crop growth from weekly samples
- Predict harvest dates accurately
- Interpolate soil moisture between sensor locations
- Calibrate equipment using known standards
Conclusion
The Lagrange Interpolation Calculator is the definitive online tool for exact polynomial interpolation. With its elegant design, instant computation, and full scientific rigor, it serves students, researchers, and professionals worldwide. Learn more at the Lagrange Interpolation Wikipedia page or explore farming solutions at Agri Care Hub.