Bilinear Interpolation Calculator
Bilinear Interpolation: calculate results from explicit inputs, with a formula and worked example.
Formula
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Real finite inputs. Numeric results use floating-point arithmetic; this is not a symbolic computer algebra system. Interpolation only, without extrapolation.
Example Calculation
- x₀: 0
- x₁: 2
- y₀: 0
- y₁: 2
- f(x₀,y₀): 0
- f(x₁,y₀): 2
- f(x₀,y₁): 2
- f(x₁,y₁): 4
- Target x: 1
- Target y: 1
For corner values 0,2,2,4 on [0,2]×[0,2], the center value is 2.
Frequently asked questions
How do I use this calculator?
Enter x₀, x₁, y₀, y₁, f(x₀,y₀), f(x₁,y₀), f(x₀,y₁), f(x₁,y₁), target x, target y. The result updates automatically. Use Reset to restore the example values.
What method does it use?
u=(x−x₀)/(x₁−x₀); v=(y−y₀)/(y₁−y₀); f=(1−u)(1−v)f₀₀+u(1−v)f₁₀+(1−u)vf₀₁+uvf₁₁. Real finite inputs. Numeric results use floating-point arithmetic; this is not a symbolic computer algebra system. Interpolation only, without extrapolation.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.