AJ Designer

Bilinear Interpolation Calculator

P equals the bilinear interpolation of four corner values Q11, Q21, Q12, Q22 at point x, y
Bilinear interpolation diagramA rectangular grid with four red corner values Q11, Q21, Q12, and Q22. A green interior point P marks the interpolated value at (x, y).Q₁₁Q₂₁Q₁₂Q₂₂Px₁xx₂y₁yy₂

Red = known valuesBlue = interpolation pointGreen = result

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How It Works

Bilinear interpolation estimates a value inside a rectangle on a two-dimensional grid. You provide the four corner values Q11, Q21, Q12, and Q22, then the calculator interpolates across one axis and then the other to estimate the value P at the interior point (x, y).

Example Problem

A survey grid stores elevation at four corners of a rectangular cell. Estimate the elevation at an interior point using the four known corner heights.

  1. Enter x1, x, x2 and y1, y, y2 so the target point lies inside the rectangular grid cell.
  2. Enter the four corner elevations Q11, Q21, Q12, and Q22 in their correct positions on the grid.
  3. The calculator interpolates across x for the top and bottom edges, then interpolates those two intermediate values across y to return P.

Key Concepts

Bilinear interpolation extends linear interpolation to two dimensions. The method assumes the value changes smoothly across the rectangular cell, so it works best for gridded data where the target point lies between the known corner coordinates.

Applications

  • Geographic information systems: estimating elevation, rainfall, or temperature between sampled grid points
  • Computer graphics: resizing textures or images using nearby pixel values on a 2D grid
  • Engineering tables: estimating values from two-variable lookup tables such as pressure-temperature or load-deflection grids

Common Mistakes

  • Swapping x and y coordinates in bilinear interpolation — the four corner values must correspond to the correct grid positions
  • Assigning Q11, Q21, Q12, and Q22 to the wrong corners — one misplaced value changes the whole surface estimate
  • Using a point outside the rectangle without realizing it becomes extrapolation rather than interpolation

Frequently Asked Questions

What is bilinear interpolation?

Bilinear interpolation is a two-dimensional interpolation method that estimates a value inside a rectangle using four known corner values. It performs linear interpolation in one direction and then again in the other direction.

When should I use bilinear interpolation instead of linear interpolation?

Use linear interpolation when your data varies along a single axis between two known points. Use bilinear interpolation when your data is arranged on a two-dimensional grid and you need a value inside a rectangular cell.

When should I use bicubic interpolation instead?

Bicubic interpolation is often preferred when you need smoother gradients or visual results, especially in image processing. Bilinear interpolation is simpler and faster, but bicubic can better preserve smooth transitions when the data changes more gradually.

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