Linear Interpolation Calculator

Visualize and calculate linear interpolation effortlessly. Enter your points and get instant results with an interactive graph.

Enter Coordinates

Input the coordinates for two points and the x-value for interpolation.

Point 1 - X (x₁):

Point 1 - Y (y₁):

Point 2 - X (x₂):

Point 2 - Y (y₂):

Interpolate X:

Interpolation Visualization

Result

Slope (m):

Intercept (b):

Interpolated Y at x = :

Formula:

$$y = m \cdot (x - x_1) + y_1$$

Calculation Steps:

Slope (m) Calculation:
Y-intercept (b) Calculation:
Interpolated Y-value Calculation:

Understanding Linear Interpolation

Linear interpolation is a method to estimate a value within two known values. Imagine you have two points on a graph and you want to find a point in between that lies on the straight line connecting them. That's linear interpolation! It's commonly used to fill in gaps in data or to estimate values when you only have a couple of data points.

This calculator helps you perform this estimation quickly and visually. Just enter your two points and the x-value you're interested in, and we'll show you the interpolated y-value and plot it on a graph.

It's useful in many areas, from making graphs smoother to estimating values in science and engineering.

Formula and Concepts

Slope (m): Represents the steepness of the line. Formula: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$
Interpolation Formula: Calculates the y-value for a given x. Formula: $$y = y_1 + m \cdot (x - x_1)$$
Visualization: The graph visually represents the two points and the interpolated point on the line, making it easier to understand the concept.