Interpolation Calculator

Interpolation is a mathematical method used to estimate an unknown value that falls within the range of a discrete set of known data points. Linear interpolation assumes that the relationship between two consecutive data points is a straight line.

Interpolation estimates a value INSIDE the range of your known data points. Extrapolation estimates a value OUTSIDE the range of your known data points. Extrapolation is generally much less reliable because you have to assume the trend continues unchanged outside your observed data.

The standard formula is y = y1 + (x − x1) × (y2 − y1) / (x2 − x1). It essentially calculates the slope between the two known points, multiplies that slope by how far the target x is from the first point, and adds that to the first y value.

Linear interpolation works best when your data points are close together, or when the underlying relationship between variables is relatively linear (a straight line). It becomes less accurate for highly curved or volatile data.

If your data is highly curved (e.g., exponential, logarithmic, or polynomial trends), linear interpolation will introduce significant errors. In these cases, polynomial interpolation, spline interpolation (like cubic splines), or curve fitting is more appropriate.

Yes. In advanced mode, you can provide a larger table of data points. The calculator will automatically find which two known points your target x falls between, and perform linear interpolation just between those two specific points. This is called piecewise linear interpolation.

Interpolation is heavily used in engineering (reading values from thermodynamic tables), statistics (estimating percentiles), computer graphics (smoothing animations), and finance (estimating interest rates on the yield curve).

If x1 and x2 are identical, you cannot perform linear interpolation because it requires dividing by (x2 − x1), which would result in division by zero. The two known points must have different x values.