Interpolation Calculator
Interpolation Calculator works out Interpolated value and Method from x values, y values and Interpolate at. The default figures on this page give interpolated value of 4; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
3 steps
- Bracketing points: (1, 2) and (3, 6).
- Slope = (6 - 2) / (3 - 1) = 2.
- Value = 2 + 2 x (2 - 1) = 4.
Polynomial coefficients (ascending powers)table
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
2 sources
What the Interpolation Calculator calculates
Estimates the value between tabulated data points using linear, Lagrange, Newton divided-difference, natural cubic spline, nearest-neighbour or log-linear interpolation, and can also interpolate in reverse.
How to use this Interpolation Calculator
Enter x values, y values, Interpolate at and Method. Interpolated value updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Interpolated value, Method and Interval used.
The method follows Burden & Faires, Numerical Analysis, chapter 3 (Interpolation and Polynomial Approximation) and NIST Digital Library of Mathematical Functions, section 3.3 (Interpolation).
Linear between (1,2) and (3,6) at x = 2 example
With x values: 1,3, y values: 2,6, Interpolate at: 2, Method: linear, the calculator returns Interpolated value: 4, Slope of the segment: 2. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects Interpolated value, Method and Interval used. The inputs you can vary are x values, y values, Interpolate at, Method, Solve for and Allow extrapolation outside the data range.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
How to do interpolation on a calculator?
Estimates the value between tabulated data points using linear, Lagrange, Newton divided-difference, natural cubic spline, nearest-neighbour or log-linear interpolation, and can also interpolate in reverse. Open “How this is worked out” beside the result to see each step for your own figures.
How to do interpolation on TI-84 calculator?
It needs x values, y values, Interpolate at, Method, Solve for and Allow extrapolation outside the data range. Nothing else is required, and the figures stay in your browser.
How do I calculate interpolation?
The result gives Interpolated value, Method, Interval used, Slope of the segment, Interpolating polynomial and Polynomial coefficients (ascending powers), each labelled with its unit so the figure can be read on its own.
How to perform interpolation calculations manually?
The page opens with worked default figures: interpolated value of 4. Replace them with your own and every figure updates as you type.
What information do I need for the Interpolation Calculator?
You need x values, y values, Interpolate at, Method, Solve for and Allow extrapolation outside the data range. The page opens with default figures that give interpolated value of 4, so you can see the scale before entering your own.
What does this Interpolation Calculator show?
It shows Interpolated value, Method, Interval used, Slope of the segment, Interpolating polynomial, Polynomial coefficients (ascending powers), Newton divided differences and Outside the data range, with the working and any warnings for your entries.