What this calculator does
Bilinear interpolation works out estimates a value at a point inside a rectangular grid from the four surrounding known values. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
FormulaP = Q11(x2−x)(y2−y) + Q21(x−x1)(y2−y) + Q12(x2−x)(y−y1) + Q22(x−x1)(y−y1), all divided by (x2−x1)(y2−y1)
The inputs explained
| Field | What to enter |
|---|---|
| x1 | A number. Starts at 0. |
| x2 | A number. Starts at 10. |
| y1 | A number. Starts at 0. |
| y2 | A number. Starts at 10. |
| Value at (x1, y1) | A number. Starts at 20. |
| Value at (x2, y1) | A number. Starts at 30. |
| Value at (x1, y2) | A number. Starts at 40. |
| Value at (x2, y2) | A number. Starts at 60. |
| Target x | A number. Starts at 4. |
| Target y | A number. Starts at 6. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with x1
Every other input is held at the calculator’s starting values while x1 varies. Select any row to load that scenario into the calculator.
How the answer changes with x1