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How It Works
Interpolation estimates an unknown value that falls between two or more known data points. Instead of guessing, it uses the existing data to calculate a mathematically reasonable in-between value. This calculator supports both one-dimensional (linear) and two-dimensional (bilinear) interpolation.
Linear Interpolation
Linear interpolation estimates an unknown value between two known data points by assuming a constant rate of change (straight line) between them. It is the simplest form of interpolation and works well when data changes uniformly.
y₂ = y₁ + (x₂ − x₁) · (y₃ − y₁) / (x₃ − x₁)
Enter two known data points (x₁, y₁) and (x₃, y₃) from your table, plus the x₂ value where you want to interpolate.
Bilinear Interpolation
Bilinear interpolation (double interpolation) extends linear interpolation to two dimensions. It estimates a value at a point (x, y) using four known corner values from a grid. First it interpolates in the x-direction, then in the y-direction.
P = f(x, y) from Q₁₁, Q₂₁, Q₁₂, Q₂₂
Enter the four corner values from your 2D table along with the boundary coordinates and the point (x, y) where you want to interpolate.
Example Problem
A table shows temperature 20°C at depth 10 m and 28°C at depth 30 m. Estimate the temperature at 18 m.
- x₁ = 10, y₁ = 20; x₃ = 30, y₃ = 28; x₂ = 18
- y₂ = 20 + (18 − 10)(28 − 20)/(30 − 10) = 20 + 3.2 = 23.2°C
Frequently Asked Questions
What is the difference between interpolation and extrapolation?
Interpolation estimates a value between known data points. Extrapolation estimates beyond the known range and is generally less reliable because it assumes the same trend continues outside the data.
When should I use bilinear instead of linear interpolation?
Use bilinear interpolation when your data is arranged in a 2D grid and you need to estimate a value at an interior point. Linear interpolation works for one-dimensional data (a single row or column of values).
Is linear interpolation accurate for non-linear data?
It produces a rough approximation. For highly curved data, polynomial or spline interpolation gives better results. Linear interpolation is most accurate when the data changes at a nearly constant rate.
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