Find a missing y or x value between two points with linear interpolation: enter x1, y1, x2, y2 and the target to get the value, slope and line equation.
Assumptions Read first
- Uses simple linear interpolation (or extrapolation) between two known points: Y3 = Y1 + ((X3 − X1) × (Y2 − Y1)) / (X2 − X1).
- X1, Y1 and X2, Y2 define a straight-line relationship; no curve fitting, smoothing, or weighting is applied.
- All inputs must be numeric, and X1 ≠ X2 (to avoid a zero denominator).
- Units must be consistent: X1, X2, X3 share the same unit; Y1, Y2 (and thus Y3) share the same unit.
- Best used when the true relationship is approximately linear between X1 and X2; extrapolation (X3 outside the X1–X2 range) is permitted but may be less reliable.
- Outputs are purely computational; no error bounds or data validation beyond basic checks are provided.
When to Use This Calculator
- Estimate a missing Y value at a target X using two known data points.
- Fill gaps in tables, charts, or schedules when linear change is reasonable.
- Perform quick two-point calibration or mapping between scales.
- Not ideal for strongly nonlinear relationships or when multiple data points are available—consider regression, polynomial, or spline methods instead.
Input Definitions
- X1 — first known value of the independent variable.
- Y1 — dependent value corresponding to X1.
- X2 — second known value of the independent variable (must differ from X1).
- Y2 — dependent value corresponding to X2.
- X3 — target independent variable at which to estimate Y3.
- Y3 — computed estimate of the dependent variable at X3 (read-only).
- Unit note — keep X-units consistent across X1, X2, X3 and Y-units consistent across Y1, Y2, Y3.
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Interpolation Formula
The following formula is used to calculate a linear interpolation.
- Where Y3 is the missing value of the interpolation
- X3,X2,X1 are coordinate points
- Y2,Y1 are known coordinate points
Linear Interpolation Definition
Interpolation estimates values between known points. Extending beyond those points is extrapolation. A two-point linear model assumes a straight-line relationship; it does not establish a future trend.
For points (x₁, y₁) and (x₂, y₂), the slope is (y₂ − y₁)/(x₂ − x₁). At a target x, y = y₁ + (x − x₁) × slope. Targets within the endpoint interval are interpolated; those outside it are extrapolated.
The reverse mode finds x from y on the same line. Equal x coordinates are invalid. A horizontal line has either no x solution or infinitely many x solutions for a supplied y.
How to perform a linear interpolation?
Performing a linear interpolation is as simple as using the equation above. First, find the known coordinate points, then plug the values into the calculator or formula.
FAQ
Interpolation estimates values between known points. Extending beyond those points is extrapolation.
