Extrapolation Calculator
Linear extrapolation extends the straight line through two known points (x₁,y₁) and (x₂,y₂) to estimate y at some other x-value, even one outside the range you measured. Enter your two points and the x you want a prediction for.
The Line Through Two Points
Any two distinct points determine exactly one straight line. Its slope is m = (y₂ − y₁)/(x₂ − x₁), and its intercept is b = y₁ − m·x₁. Once you have m and b, predicting y at any x is just y = m·x + b.
Worked Example
With (0,0) and (2,4), the slope is (4−0)/(2−0) = 2 and the intercept is 0, so the line is y = 2x. Extrapolating to x = 5 gives y = 10 — straightforward as long as the underlying relationship really is linear that far out.
A Word of Caution
Extrapolation trusts that the pattern between your two points keeps going unchanged. For physical, biological, or economic data, trends frequently flatten, reverse, or accelerate outside the range you actually measured — treat extrapolated values as a first estimate, not a guarantee.
Frequently Asked Questions
What is linear extrapolation?
It's using the straight line through two known data points to estimate a value outside that pair — the slope between the points is assumed to keep holding true beyond them.
How accurate is extrapolation far from the known points?
Accuracy drops the further the target x is from x₁ and x₂, because the method assumes the trend stays perfectly linear — real data often curves, plateaus, or changes direction outside the measured range.
What if x1 equals x2?
The line is vertical and has no defined slope, so extrapolation is impossible — the calculator flags this rather than dividing by zero.
How is extrapolation different from interpolation?
Interpolation estimates a value for an x that falls between x₁ and x₂; extrapolation estimates a value for an x outside that range, which carries more risk since you're assuming the trend continues unchanged.
Can I extrapolate backward, below x1?
Yes — a targetX smaller than both x₁ and x₂ works the same way, following the line's slope in the opposite direction.