Interpolate a y-value for a given x between two known points using linear interpolation (LERP). Supports extrapolation, multi-point error analysis, and shows slope, equation, and interpolation para...
Linear interpolation is the simplest and most widely used method for estimating unknown values between two known data points. Given two points (x₀, y₀) and (x₁, y₁), linear interpolation finds the y-value that corresponds to any target x by assuming a straight-line relationship between the points.
The formula y = y₀ + (x − x₀)(y₁ − y₀)/(x₁ − x₀) — often called LERP in computer graphics and game development — is fundamental across engineering, science, finance, and data analysis. Whether you're reading values between entries in a lookup table, animating between keyframes, or estimating sensor data between samples, linear interpolation provides a quick, reliable estimate.
This calculator computes the interpolated value along with the slope, y-intercept, linear equation, and the interpolation parameter t (where t = 0 at the first point and t = 1 at the second). It automatically detects whether your target x falls within the interval (interpolation) or outside it (extrapolation) and flags the result accordingly.
In multi-point mode, you can supply additional known data points to evaluate how well the linear model fits real data. The tool computes the error between the actual y-values and the linearly predicted values, giving you a quick measure of linearity. Use the presets to explore common scenarios from temperature conversion to population estimation.
Linear Interpolation Calculator helps you solve linear interpolation problems quickly while keeping each step transparent. Instead of redoing long algebra by hand, you can enter x₀ (first x), y₀ (first y), x₁ (second x) once and immediately inspect Interpolated y, Slope (m), y-Intercept (b) to validate your work.
This is useful for homework checks, classroom examples, and practical what-if analysis. You keep the conceptual understanding while reducing arithmetic mistakes in multi-step calculations.
y = y₀ + (x − x₀) × (y₁ − y₀) / (x₁ − x₀). Equivalently: y = (1 − t) × y₀ + t × y₁ where t = (x − x₀) / (x₁ − x₀). Slope m = (y₁ − y₀) / (x₁ − x₀), y-intercept b = y₀ − m × x₀.
Result: Interpolated y shown by the calculator
Using the preset "Temperature 0–100°C", the calculator evaluates the linear interpolation setup, applies the selected algebra rules, and reports Interpolated y with supporting checks so you can verify each transformation.
This calculator takes x₀ (first x), y₀ (first y), x₁ (second x), y₁ (second y) and applies the relevant linear interpolation relationships from your chosen method. It returns both final and intermediate values so you can audit the process instead of treating it as a black box.
Start with the primary output, then use Interpolated y, Slope (m), y-Intercept (b), Interpolation Parameter (t) to confirm signs, magnitude, and internal consistency. If anything looks off, change one input and compare the updated outputs to isolate the issue quickly.
A strong workflow is manual solve first, calculator verify second. Repeating that loop improves speed and accuracy because you learn to spot common setup errors before they cost points on multi-step algebra problems.
Linear interpolation (LERP) estimates a value between two known data points by assuming a straight-line relationship. It's the simplest form of interpolation and works well when the underlying function is approximately linear between the points.
Interpolation estimates values within the range of known data points (x is between x₀ and x₁). Extrapolation estimates values outside that range. Extrapolation is generally less reliable because the linear assumption may not hold beyond the measured interval.
The parameter t represents the fractional position between the two points: t = 0 at the first point and t = 1 at the second. Values between 0 and 1 indicate interpolation; values outside indicate extrapolation.
Linear interpolation works best when the underlying relationship is approximately linear between your data points, the points are close together, or you need a quick approximation. For curved data, consider polynomial or spline interpolation.
LERP is shorthand for linear interpolation, commonly used in game development and computer graphics. The function lerp(a, b, t) returns a + t × (b − a), blending between values a and b based on parameter t.
This calculator uses two-point linear interpolation. For more points, you'd use piecewise linear interpolation (connect consecutive points with straight lines), polynomial interpolation (Lagrange or Newton), or spline interpolation.