Interpolation is a fundamental concept in mathematics and statistics used to estimate unknown values that lie between known data points. It plays a crucial role in various fields such as engineering, science, finance, and computer graphics. In this article, we will explore the concept of interpolation and create an interpolation calculator to understand its practical application.

**What is Interpolation?**

Interpolation is the process of estimating values within a range based on known data points. It involves constructing a function or curve that passes through the given points, allowing us to determine the value of any intermediate point. Interpolation is commonly used when we have a set of discrete data points and need to approximate the value of a function at points between these data points.

**Types of Interpolation**

There are several methods of interpolation, including linear interpolation, polynomial interpolation, spline interpolation, and more. Each method has its own advantages and is suitable for different types of data sets.

**Linear Interpolation**: Linear interpolation involves fitting a straight line between two adjacent data points and estimating the value of the function at any point along this line.**Polynomial Interpolation**: Polynomial interpolation uses a polynomial function to pass through all the given data points. The degree of the polynomial depends on the number of data points and the desired accuracy.**Spline Interpolation**: Spline interpolation divides the data set into smaller segments and fits separate polynomial functions to each segment. This results in a smoother curve compared to polynomial interpolation.

**Creating an Interpolation Calculator**

Now, let’s create a simple interpolation calculator using HTML and JavaScript to demonstrate how interpolation works in practice.

**HTML Structure**

The HTML structure of the interpolation calculator includes input fields for X1, Y1, X2, Y2, and X3, along with a button to calculate the interpolated value of Y3.

**JavaScript Function**

A JavaScript function is written to calculate the interpolated value of Y3 based on the provided data points using the formula:

*y*3=*y*1+(*x*3−*x*1)/(*x*2−*x*1) X (*y*2−*y*1)

**Conclusion**

Interpolation is a powerful tool used to estimate values within a range of known data points. By understanding different interpolation methods and their applications, we can make informed decisions and draw accurate conclusions from data sets. The interpolation calculator created in this article provides a practical example of how interpolation is implemented in real-world scenarios. Whether in mathematics, engineering, or other fields, interpolation remains an indispensable technique for data analysis and problem-solving.