Linear Interpolation Calculator

Linear interpolation estimates an unknown value that lies between two known data points. Given points (x1, y1) and (x2, y2), it assumes that y changes at a constant rate as x moves from the first point to the second. The interpolation formula is y = y1 + ((x - x1) / (x2 - x1))(y2 - y1). This calculator evaluates that formula and also displays the interpolation fraction, which shows how far the target x has traveled across the interval. The fraction is zero at x1, one at x2, and between zero and one for a target inside the interval. For example, a fraction of 0.4 means the target is forty percent of the horizontal distance from the first point to the second. The same fraction is applied to the vertical change from y1 to y2. This proportional approach makes interpolation easy to understand and gives exact results whenever the underlying relationship is truly linear. The two x coordinates must differ because a vertical pair of points does not define y as a single-valued linear function of x. The y values may be equal, producing a constant result. The points can be entered in either order; reversing both endpoints leaves the interpolated value unchanged. A target outside the endpoint interval is also mathematically accepted, but that operation is linear extrapolation rather than interpolation and may carry more uncertainty. Interpolation is widely used to estimate measurements between table entries, convert scales, fill gaps in time series, blend positions in graphics, calibrate instruments, and approximate engineering data. Its reliability depends on whether the change between endpoints is reasonably straight. Curved, discontinuous, or rapidly changing relationships may require polynomial interpolation, splines, or a domain-specific model. Always preserve compatible units: x1, x2, and the target x must share one unit, while y1 and y2 must share another. To verify the answer, compute the horizontal fraction first, multiply it by y2 minus y1, and add that change to y1.