Linear and Bilinear Interpolation Calculator
Estimate unknown values between known data points using linear interpolation or bilinear interpolation on a rectangle.
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Linear mode uses x0,y0,x1,y1. Bilinear mode uses x0,x1,y0,y1,Q11,Q21,Q12,Q22 and x,y.
What this calculator teaches
Interpolation estimates a value inside known data, not beyond it. Linear interpolation works along one dimension. Bilinear interpolation extends the idea to a rectangle in two dimensions.
Engineering tables, thermodynamics charts, maps, images, and sensor grids often require interpolation.
Formula & Symbols
| Concept | Formula | Meaning |
|---|---|---|
| Linear interpolation | y = y0 + (x-x0)(y1-y0)/(x1-x0) | Estimate between two known points. |
| Bilinear interpolation | weighted average of four corners | Interpolate in x, then y, or use area weights. |
Step-by-Step Examples
- Known points are (2,10) and (6,18).
- x=4 is halfway between 2 and 6.
- The y-value is halfway between 10 and 18.
Where students use this
Common Mistakes to Avoid
Interpolation is inside the known interval. Outside is extrapolation and is less reliable.
For bilinear interpolation, keep Q11, Q21, Q12, Q22 tied to their corners.
The formula handles unequal spacing, but the coordinates must be correct.
Frequently Asked Questions
Related Math Calculators
Formula Explorer connections
Interpretation: This method approximates a mathematical solution through iteration, discretization, interpolation or numerical quadrature. Assumption: Accuracy depends on step size, initial guesses, smoothness, conditioning and stopping criteria. Compare error and convergence rather than trusting a single approximation.