Interpolation Calculator
Interpolate between two points and evaluate the value at any x.
Table of Contents
How to Use
- Enter the first point (x0, y0)
- Enter the second point (x1, y1)
- Provide the target x where you want to estimate y
- Run the calculation to see the interpolated value and slope
How linear interpolation works
Linear interpolation connects two known points with a straight line and evaluates the line at a chosen x. It assumes the change between the points is roughly linear.
- Slope m = (y1 - y0) / (x1 - x0)
- Parameter t = (x - x0) / (x1 - x0)
- Interpolated value y = y0 + t · (y1 - y0)
When to use interpolation vs extrapolation
Interpolation (0 ≤ t ≤ 1) is usually reliable when values change smoothly between measured points. Extrapolation (t < 0 or t > 1) projects beyond known data and should be used cautiously.
For curved relationships, use more points or polynomial/spline methods rather than relying on a single straight line.
Frequently Asked Questions
- What is the parameter t?
- t measures progress along the segment from x0 to x1. t = 0 at x0, t = 1 at x1, and values in between correspond to interpolation.
- Can I trust extrapolated values?
- Extrapolated results can be rough because they extend beyond the known points. Use them only when you expect the trend to stay linear outside the sampled range.
- What if x0 equals x1?
- The slope would be undefined. Provide two distinct x-values so the line segment can be constructed.