Interpolation Calculator
Calculate interpolated values between known data points. Supports linear interpolation from 2 points, bilinear interpolation on a grid, lookup table with 5 pairs, and Lagrange polynomial interpolation.
Interpolated Y
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Slope (Δy/Δx) —
Note —
Extended More scenarios, charts & detailed breakdown ▾
Interpolated Y
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Slope —
Note —
Professional Full parameters & maximum detail ▾
Interpolation Results
Lagrange Polynomial Y —
Linear Y (nearest 2 pts) —
Linear vs Polynomial Difference —
Calculus
Derivative at Target X —
Range
Range Check —
How to Use This Calculator
Enter two known points (X₁, Y₁) and (X₂, Y₂) and a Target X to get the linearly interpolated Y value. The calculator warns if the target is outside the range. Use the Extended tabs for bilinear (2D grid) or lookup table (5 data pairs). The Professional tab adds Lagrange polynomial interpolation and derivative estimation.
Formula
Linear: y = y1 + (y2−y1) × (x−x1)/(x2−x1)
Lagrange (3 pts): P(x) = y1·L1(x) + y2·L2(x) + y3·L3(x)
Example
Points (0,0) and (10,100), Target X=5 → Y = 50 | Lagrange through (0,0),(5,25),(10,90) at x=3 → Y ≈ 9.9
Frequently Asked Questions
- Linear interpolation estimates a value between two known data points by assuming a straight line between them. Formula: y = y1 + (y2−y1) × (x−x1)/(x2−x1).
- Interpolation estimates within the known range of data. Extrapolation estimates beyond the known range, which is less reliable — the calculator warns you when this occurs.
- Bilinear interpolation estimates a value at a point inside a rectangle defined by four known corner values. It is commonly used in image processing and 2D data grids.
- Lagrange interpolation fits a polynomial through n given points. For 3 points it produces a quadratic. It is more accurate than linear interpolation when the underlying data is curved.
- The professional tab shows the difference between the Lagrange polynomial value and the linear value as an error estimate. A large difference suggests the data is non-linear and linear interpolation may be inaccurate.