Bilinear Interpolation Calculator

Your details

The smaller x-coordinate of the rectangle. Must be less than x2.
The larger x-coordinate of the rectangle. Must be greater than x1.
The smaller y-coordinate of the rectangle. Must be less than y2.
The larger y-coordinate of the rectangle. Must be greater than y1.
Known function value at the bottom-left corner (x1, y1).
Known function value at the bottom-right corner (x2, y1).
Known function value at the top-left corner (x1, y2).
Known function value at the top-right corner (x2, y2).
The x-coordinate of the point where you want to estimate the value. Must lie between x1 and x2.
The y-coordinate of the point where you want to estimate the value. Must lie between y1 and y2.
Interpolated value P(x, y)
4

Estimated function value at the target point, computed by bilinear interpolation.

R1 - interpolated at (x, y1)9
R2 - interpolated at (x, y2)-1
Weight on x1 side0.75
Weight on x2 side0.25
R1 at y1 (bottom edge)9
R2 at y2 (top edge)-1
P(x, y) final result4

Interpolated value at (1, 2): P = 4

  • The target point (1, 2) lies 25.0% of the way from x1 to x2 and 50.0% of the way from y1 to y2.
  • Corner values range from -4 to 12; the interpolated result 4 falls within that range.
  • Bilinear interpolation is exact at all four corners and varies linearly along any horizontal or vertical line through the cell.

Next stepFor higher accuracy over larger regions, consider subdividing the grid into smaller cells and re-applying bilinear interpolation within each cell.

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