Polynomial Interpolation Calculator
Interpolate distinct X/Y knots with one global polynomial using the barycentric evaluation formula.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Normalize the X scale, form barycentric weights and return a knot value directly when the query equals a knot.
p(x)=Σ(wi yi/(x−xi))/Σ(wi/(x−xi)); wi=1/Πj≠i(xi−xj)
Worked example
Knots (0,0),(1,1),(2,4) lie on y=x², giving interpolated y=2.25 at x=1.5.
Assumptions and input details
2–15 well-separated distinct X values; high-degree interpolation and extrapolation can oscillate and amplify rounding error. This is exact knot interpolation, not noisy-data regression or a shape-preserving spline.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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