Bilinear Interpolation Calculator
Result
Bilinear Interpolation Calculator Perform bilinear interpolation to estimate a value at an arbitrary point (x,y) within a rectangular grid of known values. — free online calculator.
Formula
- Bilinear Interpolation Calculator calculates its result from x₁ (left), x₂ (right), y₁ (bottom), y₂ (top), f(x₁,y₁) — bottom-left, f(x₁,y₂) — top-left, f(x₂,y₁) — bottom-right, f(x₂,y₂) — top-right, Query point x, Query point y. It uses the formula f(x,y) = [q11(x₂-x)(y₂-y) + q21(x-x₁)(y₂-y) + q12(x₂-x)(y-y₁) + q22(x-x₁)(y-y₁)] / [(x₂-x₁)(y₂-y₁)]. Change any input to recalculate the result instantly.
- The main inputs are x₁, x₂, y₁, y₂, f(x₁,y₁) — bottom-left, f(x₁,y₂) — top-left, f(x₂,y₁) — bottom-right, f(x₂,y₂) — top-right, Query point x, Query point y. Enter them in the units and format shown in the calculator.
- Keep comparable quantities in compatible units whenever the formula combines or compares them.
- Changing any input above recalculates the result with the same calculation engine used by this page.
Example: Bilinear Interpolation
- x₁: 0 left
- x₂: 1 right
- y₁: 0 bottom
- y₂: 1 top
- f(x₁,y₁) — bottom-left: 10
- f(x₁,y₂) — top-left: 20
- f(x₂,y₁) — bottom-right: 30
- f(x₂,y₂) — top-right: 40
- Query point x: 0.5
- Query point y: 0.5
Using x₁ (left) = 0, x₂ (right) = 1, y₁ (bottom) = 0, y₂ (top) = 1, f(x₁,y₁) — bottom-left = 10, f(x₁,y₂) — top-left = 20, f(x₂,y₁) — bottom-right = 30, f(x₂,y₂) — top-right = 40, Query point x = 0.5, Query point y = 0.5, the calculated result is 25.
Sample result: Calculating…
Frequently asked questions
What does the Bilinear Interpolation calculate?
Bilinear Interpolation Calculator Perform bilinear interpolation to estimate a value at an arbitrary point (x,y) within a rectangular grid of known values. — free online calculator.
Which values should I enter?
Enter x₁, x₂, y₁, y₂, f(x₁,y₁) — bottom-left, f(x₁,y₂) — top-left, f(x₂,y₁) — bottom-right, f(x₂,y₂) — top-right, Query point x, Query point y using the units and format shown beside each field.
What formula does this calculator use?
The calculator uses the following relationship: f(x,y) = [q11(x₂-x)(y₂-y) + q21(x-x₁)(y₂-y) + q12(x₂-x)(y-y₁) + q22(x-x₁)(y-y₁)] / [(x₂-x₁)(y₂-y₁)].
Why might my result differ from another source?
Results can differ when another source uses different units, rounding rules, conventions or assumptions. Compare the inputs and definitions before comparing results.
Does the result update automatically?
Yes. Changing an input updates the result using the same calculation engine shown on this page.