# Interpolation Calculator

Interpolation Calculator helps to compute the interpolated value for the given coordinates. Interpolation is the process of finding a new value for a function when we already know any two values.

## What is Interpolation Calculator?

Interpolation Calculator is an online tool that helps to calculate the interpolated value, y, for a linear function when we are given certain coordinates. The linear interpolation formula is used to find the new value of the function. To use the * interpolation calculator*, enter the values in the input boxes.

### Interpolation Calculator

NOTE: Enter the values up to two digits only.

## How to Use Interpolation Calculator?

Please follow the steps given below on how to find the interpolates value using the online interpolation calculator:

**Step 1:**Go to Cuemath's online interpolation calculator.**Step 2:**Enter the coordinates in the given input boxes.**Step 3:**Click on**"Calculate"**to find the interpolated value for the given coordinates.**Step 4:**Click on**"Reset"**to clear the fields and enter the new values.

## How Does Interpolation Calculator Work?

When we want to estimate the value of a function between any two points, we use the interpolation method. Interpolation is a technique that is used to find a new value between two points on the curve of a given function. Suppose we know the coordinates of two points (\(x_{1}\), \(y_{1}\)) and (\(x_{2}\), \(y_{2}\)). We also know the point where the interpolation has to be performed. This is denoted by x. Then the formula for linear interpolation is given as follows:

Linear Interpolation(y) = \(y_{1} + (x - x_{1})\frac{(y_{2}-y_{1})}{x_{2}-x_{1}}\)

Here, y is the interpolated value. We can substitute the given values in the aforementioned equation to determine the interpolated value y.

Linear interpolation is used for data forecasting, predicting the stock market, and many other scientific applications. Linear interpolation is a technique for curve fitting when working with linear polynomials. It can be used for constructing new data points within some known data points.

## Solved Examples on Interpolation

**Example 1:** Find the interpolated value of y at x = 2 if given some set of values are (-2, 3), (4, 6). Verify it using the online interpolation calculator.

**Solution:**

Using the interpolation formula, \(y_{1} + (x - x_{1})\frac{(y_{2}-y_{1})}{x_{2}-x_{1}}\)

Given: x = 2, x_{1} = -2, y_{1} = 3, x_{2} = 4 , y_{2} = 6

y = 3 + (2 - (-2)) (6 - 3) / (4 - (-2))

y = 3 + 4 × (-3 /-6)

y = 5

**Example 2:** Find the interpolated value of y at x = -3 if given some set of values are (5, 3.5), (10, 6). Verify it using the online interpolation calculator.

**Solution:**

Using the interpolation formula, \(y_{1} + (x - x_{1})\frac{(y_{2}-y_{1})}{x_{2}-x_{1}}\)

Given: x = -3, x_{1} = 5, y_{1} = 3.5, x_{2} = 10 , y_{2} = 6

y = -3.5 + (-3 - 5)) (6 - (3.5)) / (10 - 5)

y = -1 / 2.

Similarly, you can use the interpolation calculator to find the interpolated value for given coordinates:

- Find the interpolated value of y at x = 4 if given some set of values are (-2, -7), (-4, 8)
- Find the interpolated value of x at x = 3 if given some set of values are (5, -3), (1, -2)

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