Interpolation Calculator

Estimate Values Between Data Points

Calculate interpolated values between known data points using linear, polynomial, or other interpolation methods. Our calculator helps you estimate unknown values within a dataset range for scientific and engineering applications.

Estimate a Value Using Linear Interpolation

Enter two known points and an x-value to estimate the corresponding y-value using linear interpolation.

X₁:

Y₁:

X₂:

Y₂:

X (Value to Interpolate at):

Understanding Linear Interpolation

Linear interpolation is a method of estimating an unknown value of a function between two known values. It assumes that the change between the two values is linear and calculates the unknown value accordingly.

The Linear Interpolation Formula

The formula for linear interpolation between two points $(X_1, Y_1)$ and $(X_2, Y_2)$ is:

Y = Y_1 + \frac{Y_2 - Y_1}{X_2 - X_1} \times (X - X_1)

Where:

$X$ is the value at which you want to estimate $Y$ .
$Y$ is the interpolated value at $X$ .
$X_1, Y_1$ and $X_2, Y_2$ are the known data points.

Applications of Linear Interpolation

Linear interpolation is widely used in engineering, physics, finance, and other fields where estimating values within two known points is necessary.

What is Interpolation?

Interpolation estimates values between known data points. Linear interpolation (most common) assumes straight line between points: y = y₁ + (x - x₁) × (y₂ - y₁)/(x₂ - x₁). Polynomial interpolation fits curves through multiple points. Used when data is continuous but only sampled at discrete intervals.

Types of Interpolation

Linear: connects two points with straight line (simple, less accurate). Polynomial: fits curve through multiple points (more accurate, can oscillate). Spline: piecewise polynomials (smooth, stable). Lagrange: polynomial through all points. Choose based on data characteristics and accuracy needs.

Applications

Interpolation is used in: reading values from tables, image resizing and resampling, animation frame generation, scientific data analysis, weather prediction, financial modeling, and engineering simulations. Essential when you need values between measured or calculated points.