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Linear Interpolation Calculator

The linear interpolation calculator helps you estimate an unknown value between two known data points.
It is useful when you need to interpolate between two values in engineering tables, sensor data, calibration data or other numerical datasets.

The standard linear interpolation formula is:

\[
y = y_1 + \frac{x-x_1}{x_2-x_1}(y_2-y_1)
\]

Where \(x_1\) and \(x_2\) are the known input values, \(y_1\) and \(y_2\) are their corresponding output values, and \(x\) is the value you want to interpolate.

How to Use the Linear Interpolation Calculator

Enter the two known points \(x_1, y_1\) and \(x_2, y_2\), then enter the target value \(x\).
The interpolation calculator will automatically calculate the corresponding value \(y\).

Linear Interpolation Calculator For Example:

\[
x_1=10,\quad y_1=100
\]

\[
x_2=20,\quad y_2=200
\]

If:

\[
x=15
\]

then:

\[
y=150
\]

This method is also commonly used for linear interpolation tables, Excel calculations, sensor scaling and engineering lookup data.

Bilinear Interpolation Calculator

Bilinear interpolation is used to estimate a value inside a 2D grid using four known surrounding points.
It can be considered a two-dimensional extension of linear interpolation.

Instead of interpolating between two values, bilinear interpolation performs the calculation in two directions, usually along the \(x\)-axis and then the \(y\)-axis.

The bilinear interpolation formula can be written as:

\[
f(x,y)
=
\frac{
f_{11}(x_2-x)(y_2-y)
+
f_{21}(x-x_1)(y_2-y)
+
f_{12}(x_2-x)(y-y_1)
+
f_{22}(x-x_1)(y-y_1)
}{
(x_2-x_1)(y_2-y_1)
}
\]

Enter the four known values around the target point, together with the \(x\) and \(y\) coordinates.
The bilinear interpolation calculator will estimate the value at the selected position.

Bilinear Interpolation Example

Suppose four known values are located at the corners of a rectangular grid:

\[
f(0,0)=10,\qquad f(10,0)=20
\]

\[
f(0,10)=30,\qquad f(10,10)=40
\]

We want to estimate the value at the center point:

\[
x=5,\qquad y=5
\]

First, perform linear interpolation along the \(x\)-direction:

\[
f(5,0)=10+\frac{5-0}{10-0}(20-10)=15
\]

\[
f(5,10)=30+\frac{5-0}{10-0}(40-30)=35
\]

Then interpolate these two results along the \(y\)-direction:

\[
f(5,5)=15+\frac{5-0}{10-0}(35-15)
\]

\[
f(5,5)=25
\]

Therefore, the bilinear interpolation result at \((5,5)\) is:

A bilinear interpolation calculator performs these two interpolation steps automatically using the four surrounding values.