Input Values
Provide two X bounds, two Y bounds, and the four corner values.
Example Data Table
This sample uses default values. Click “Load Example” to fill the form.
| Point | X | Y | Value (Q) |
|---|---|---|---|
| Q11 (X1, Y1) | 10 | 100 | 30 |
| Q21 (X2, Y1) | 20 | 100 | 50 |
| Q12 (X1, Y2) | 10 | 200 | 40 |
| Q22 (X2, Y2) | 20 | 200 | 80 |
| Target (X, Y) | 14 | 150 | ? |
Tip: if you use clamp mode and enter X=200, it will use X*=20.
Formula Used
Double linear interpolation blends values in two directions. You first interpolate along the X axis at two Y levels, then interpolate those two results along the Y axis.
tX = (X* − X1) / (X2 − X1)
tY = (Y* − Y1) / (Y2 − Y1)
R1 = Q11 + tX (Q21 − Q11) [at Y1]
R2 = Q12 + tX (Q22 − Q12) [at Y2]
P = R1 + tY (R2 − R1)
tY = (Y* − Y1) / (Y2 − Y1)
R1 = Q11 + tX (Q21 − Q11) [at Y1]
R2 = Q12 + tX (Q22 − Q12) [at Y2]
P = R1 + tY (R2 − R1)
X* and Y* are either your target values (extrapolate) or clamped values (clamp).
How to Use This Calculator
- Enter X1, X2, Y1, and Y2 as bounds.
- Enter the four corner values: Q11, Q21, Q12, Q22.
- Type your target X and Y.
- Select a mode: clamp for safe bounds, extrapolate for outside values.
- Choose precision and enable steps if you want details.
- Press Calculate. Results appear above the form.
- Use Download CSV or Download PDF after calculating.
Note: If X1 equals X2 or Y1 equals Y2, the fractions are undefined.