Extrapolation Calculator
Project a y-value beyond your known data by extending the straight line through two points. Enter two readings and a target x that lies past them, and the calculator predicts y along the same linear trend.
Enter Values
How to use this calculator
- Enter two known points as x1, y1 and x2, y2.
- Enter a target x that lies beyond the range of the two points (before x1 or after x2).
- Read the extrapolated y, the slope, and a warning if your target x actually falls inside the known range (which would make it interpolation instead).
How it works
The tool computes the slope of the line through the two points, slope = (y2 − y1) / (x2 − x1), then applies y = y1 + slope × (x − x1) at your target x. The maths is identical to interpolation — the difference is that the target x lies outside the known range, so the line is extended rather than filled in. This assumes the linear relationship continues indefinitely, an assumption that weakens the further you project.
Worked example
Worked example. From (0, 32) and (100, 212) — the Celsius-to-Fahrenheit anchor points — the slope is (212 − 32) / (100 − 0) = 1.8. Projecting to x = −40 gives y = 32 + 1.8 × (−40 − 0) = −40, the temperature where the two scales meet.
Common mistakes
- Extrapolating far beyond the data and trusting the number — the linear trend may not hold.
- Setting x1 equal to x2, which makes the slope undefined.
- Forgetting that a target x inside [x1, x2] is interpolation, not extrapolation, and is more reliable.
Frequently asked questions
Why is extrapolation less reliable than interpolation?
Interpolation stays within measured data, where the straight-line assumption is anchored on both sides. Extrapolation projects beyond the data, where nothing guarantees the trend continues, so error grows with distance.
How far can I safely extrapolate?
There is no fixed limit — reliability depends on how linear the underlying process is. As a rule, the closer your target x is to the known range, the more trustworthy the estimate.
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Tip: Enter any known values to calculate the remaining results.
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