Enter two known data points (X1, Y1 and X2, Y2) plus the X value you want to interpolate, and the Linear Interpolation Calculator returns the estimated Y value along with the slope and Y-intercept of the line. Works for both interpolation (within range) and extrapolation (beyond range). Also try the calculate Arc Length (L), Sag (Max Deflection) & y at X Start — Catenary Curve.
Interpolated Y Value
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Slope (m)
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Y-Intercept (b)
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Result Type
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Linear interpolation is a method of estimating an unknown value that falls between two known data points by assuming a straight-line relationship between them. The formula is: y = y1 + (x - x1) × (y2 - y1) / (x2 - x1). It's widely used in mathematics, engineering, finance, and data analysis.
Interpolation estimates a value within the range of the two known points, while extrapolation estimates a value outside that range. For example, if your known X values are 1 and 10, finding Y at X = 5 is interpolation, but finding Y at X = 15 is extrapolation. Extrapolated values carry more uncertainty because they assume the linear trend continues beyond the measured data.
Enter the coordinates of your two known points (X1, Y1 and X2, Y2), then enter the X value you want to find the Y for. The calculator applies the linear interpolation formula and returns the estimated Y value along with the slope and Y-intercept of the line connecting your two points.
Interpolation fills in gaps in a dataset where measurements were not taken. It allows analysts, scientists, and engineers to estimate intermediate values without conducting additional experiments or measurements. This is especially useful in fields like physics, finance, medicine, and engineering where data collection is expensive or time-consuming.
Linear interpolation is most accurate when the relationship between your two variables is truly linear, or when the two known points are close together. Accuracy decreases when the actual relationship is curved (non-linear) or when you're extrapolating far beyond the known data range. For curved data, polynomial or spline interpolation methods may be more appropriate.
Linear interpolation assumes a straight-line relationship between the two known points, which may not reflect the true behavior of the data. It can introduce errors when the underlying relationship is nonlinear, and extrapolated results beyond the known range can be especially unreliable. It also only uses two data points, ignoring any broader trends in a larger dataset.
The slope (m) represents the rate of change between the two known points, calculated as (Y2 - Y1) / (X2 - X1). It tells you how much Y changes for every one-unit increase in X. The equation of the line is y = mx + b, where b is the Y-intercept (the value of Y when X equals zero).
Yes. The Linear Interpolation Calculator accepts any real number for all input fields, including negative values and decimals. This makes it suitable for a wide range of scientific, financial, and engineering applications where data points may not be positive whole numbers.