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Linear Interpolation Calculator

Estimate an unknown value between two data points with linear interpolation.

How it is calculated

Linear interpolation estimates y at a chosen x by assuming the data follow a straight line between two known points (x1, y1) and (x2, y2). The slope is m = (y2 − y1) / (x2 − x1) and the estimate is y = y1 + (x − x1) × m. The tool shows both y and the slope with two decimals. It works for an x outside the two points too, which is extrapolation and is usually less reliable. The two x values must differ, otherwise the slope is undefined. The estimate is only as good as the straight-line assumption.

Worked example

Known points (10, 20) and (20, 50); estimate y at x = 14. Slope = (50 − 20) / (20 − 10) = 30 / 10 = 3. Distance from the first point: 14 − 10 = 4. y = 20 + 4 × 3 = 32. The estimated value is 32.00, with a slope of 3.00. Check: 14 is 40% of the way from 10 to 20, and 40% of the way from 20 to 50 is 32.

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Common mistakes

  • Pairing coordinates wrongly, e.g. entering y1 with x2.
  • Using two points that are far apart on a curved relationship, where a straight line misses the real value.
  • Choosing x outside the two points and treating the extrapolated number as reliable.
  • Entering the same x for both points, which gives no result.
  • Using the two nearest table entries to a target is right; using the first and last entries of the table is not.

About this calculator

This calculator estimates an unknown y value on the straight line connecting two known points using linear interpolation: y = y1 + (x − x1)·(y2 − y1)/(x2 − x1). It assumes the relationship between x and y is linear between the two given points.

Engineers, scientists, and spreadsheet users rely on it to fill gaps in lookup tables, calibration curves, and sensor readings — for example, finding a property value at a temperature that falls between two tabulated points. Enter the two known points and the x value to interpolate to get the estimated y.

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