Mathematics

Polynomial Interpolation

Interpolate up to 20 points with distinct x values and evaluate the polynomial at a chosen coordinate.

01Input and settings

The calculation runs in your browser. You can use the tool without installing software.

02Result

Waiting for input
Waiting for input

Enter your values or load the example to see the result here.

About this tool: Polynomial Interpolation

Interpolate up to 20 points with distinct x values and evaluate the polynomial at a chosen coordinate.

Enter 2–20 x; y pairs, one per line, with distinct x coordinates. The interpolating polynomial passes through every point; it is different from a least-squares regression line. Values outside the data interval are extrapolations, and high-degree curves can oscillate substantially.

How the calculation works

P(x) = Σ yᵢ ∏ⱼ≠ᵢ (x−xⱼ)/(xᵢ−xⱼ)

Worked example

Pairs: x; y, one per line
0; 1
1; 2
2; 5
Predict for x
1.5
P(1.5) = 3.25

Questions and answers

What does this tool do?

Interpolate up to 20 points with distinct x values and evaluate the polynomial at a chosen coordinate. Enter 2–20 x; y pairs, one per line, with distinct x coordinates. The interpolating polynomial passes through every point; it is different from a least-squares regression line. Values outside the data interval are extrapolations, and high-degree curves can oscillate substantially.

What affects precision and input format?

Enter 2–20 x; y pairs, one per line, with distinct x coordinates.

Where are the calculations performed?

The calculation runs in your browser. You can use the tool without installing software.

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