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Concept Explainer · STEM Learning

Interpolation vs. Extrapolation — Why Estimating Between Your Data Is Safer Than Estimating Beyond It

Both are estimates made from the same fitted curve. Only one of them is backed by direct evidence on both sides.

Every model, curve fit, or trend line eventually gets used to estimate a value you didn't directly measure. Interpolation estimates a value that falls within the range of data you actually measured — bracketed by real observations on both sides. Extrapolation estimates a value that falls outsidethat range — extending the same fitted relationship into territory you have never observed at all. The math used to compute either one can look identical: plug an x-value into the fitted equation and read off y. But the confidence you're entitled to have in the answer is not the same, and treating them as equally trustworthy is a routine, well-documented source of engineering and scientific error.