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Bilinear Interpolation — result sheet
Interpolate a value inside an ordered rectangle from four finite corner values and an in-range x-y target.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: s=(x-x0)/(x1-x0), t=(y-y0)/(y1-y0), p=(1-s)(1-t)f00+s(1-t)f10+(1-s)tf01+stf11.
Bilinear interpolation applies linear weighting across x and y inside an ordered rectangle, combining the four corner values according to the target's two normalized coordinates.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Left x0 — The lower x boundary of the rectangle.; minimum -1000000; maximum 1000000
- Right x1 — The upper x boundary; it must exceed x0.; minimum -1000000; maximum 1000000
- Lower y0 — The lower y boundary of the rectangle.; minimum -1000000; maximum 1000000
- Upper y1 — The upper y boundary; it must exceed y0.; minimum -1000000; maximum 1000000
- Target x — The target x must be inside the rectangle.; minimum -1000000; maximum 1000000
- Target y — The target y must be inside the rectangle.; minimum -1000000; maximum 1000000
- Corner f00 — Value at (x0, y0).; minimum -1000000; maximum 1000000
- Corner f10 — Value at (x1, y0).; minimum -1000000; maximum 1000000
- Corner f01 — Value at (x0, y1).; minimum -1000000; maximum 1000000
- Corner f11 — Value at (x1, y1).; minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Left x0 | 0 |
| Right x1 | 10 |
| Lower y0 | 0 |
| Upper y1 | 20 |
| Target x | 2.5 |
| Target y | 5 |
| Corner f00 | 0 |
| Corner f10 | 10 |
| Corner f01 | 20 |
| Corner f11 | 30 |
s = 0.25, t = 0.25, and the interpolated value is 7.5.
Assumptions and limits
- x0 is less than x1, y0 is less than y1, and the target x-y pair lies inside the closed rectangle.
- The four corner values are finite samples of a locally bilinear surface; no curvature, extrapolation, or unit conversion is inferred.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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