Linear Interpolation Calculator

Linear interpolation assumes that the change between two known points follows a straight line. Given two coordinates, (x₁, y₁) and (x₂, y₂), the calculator first determines the slope (m) of the line using the formula: slope = (y₂ - y₁) / (x₂ - x₁). Next, it finds the y-intercept using the equation: intercept = y₁ - (slope * x₁). To find an unknown y-value for a given intermediate x-value (let us call it x₃), the formula applied is: y₃ = slope * x₃ + intercept. This straightforward geometric approach provides a reliable approximation for any point falling strictly between your baseline coordinates.

Imagine you have two known data points: Point 1 is at coordinates (2, 10) and Point 2 is at coordinates (6, 30). You need to find the corresponding y-value for x = 4. First, calculate the slope: m = (30 - 10) / (6 - 2) = 20 / 4 = 5. Next, determine the y-intercept using Point 1: intercept = 10 - (5 * 2) = 0. Finally, apply the linear equation for your target x-value of 4: y = (5 * 4) + 0 = 20. Therefore, the estimated intermediate value at x = 4 is precisely 20.

Always ensure your input data represents a genuinely linear relationship; applying linear interpolation to exponential or curved datasets will introduce significant estimation errors. Additionally, check that your target x-value sits comfortably between your lower and upper bounds (x₁ and x₂), as trying to estimate values outside this range is known as extrapolation, which drastically reduces accuracy.