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Bilinear Interpolation on a Unit Rectangle Calculator

f(x,y) from the four corner values of a rectangle.

Compute f(x, y) inside a rectangle [x₁, x₂] × [y₁, y₂] from its four corner values f₁₁, f₂₁, f₁₂, f₂₂ using bilinear interpolation: f(x,y) = (1−tx)·(1−ty)·f₁₁ + tx·(1−ty)·f₂₁ + (1−tx)·ty·f₁₂ + tx·ty·f₂₂, with tx = (x−x₁)/(x₂−x₁) and ty similarly.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

f(x,y) = bilinear blend of the four corners.

In depth

Compute f(x, y) inside a rectangle [x₁, x₂] × [y₁, y₂] from its four corner values f₁₁, f₂₁, f₁₂, f₂₂ using bilinear interpolation: f(x,y) = (1−tx)·(1−ty)·f₁₁ + tx·(1−ty)·f₂₁ + (1−tx)·ty·f₁₂ + tx·ty·f₂₂, with tx = (x−x₁)/(x₂−x₁) and ty similarly.