Linear interpolation calculator
y from x or x from y between two points, with slope, y-intercept, line equation and extrapolation alert.
Result
Awaiting the quantities required for the calculation.
Calculation, assumptions and sources
OverviewTwo points (x1, y1) and (x2, y2) give y for a given x, or x for a given y, assuming a linear relationship between the two quantities.
Two points (x1, y1) and (x2, y2) give y for a given x, or x for a given y, assuming a linear relationship between the two quantities. The calculation gives the slope, the y-intercept and the line equation, and flags an extrapolation when the sought value falls outside the interval of the two points.
Method & formulasm = (y2 − y1) / (x2 − x1)
Two points (x1, y1) and (x2, y2) define a unique line, y = m×x + b, which its inverted form solves for x.
- Interpolation
- estimation of y (or x) for a value between x1 and x2 (or between y1 and y2), within the observed interval.
- Extrapolation
- estimation outside this interval, which assumes the linear relationship extends beyond the measured points.
- Slope (m)
- change in y for a one-unit change in x; negative if y decreases when x increases.
- Y-intercept (b)
- value of y at x = 0 on the extended line, not necessarily observed.
Validity domainThe calculation assumes a linear relationship over the whole interval considered.
The calculation assumes a linear relationship over the whole interval considered. It is undefined when the two x-values are equal (no slope) and, in the inverse direction, when the two y-values are equal (a horizontal line gives no x).