Mathematical Calculators

# Linear Interpolation Calculator

This free online calculator calculates the linear interpolation and the linear extrapolation. It also provides the slope of the linear equation.

#### Linear interpolation calculator

#### Table of contents

The extrapolation of data using previous data is known as interpolation. For example, in the stock market, you may state that the price has risen 10% in the last year, so you'll extrapolate that the stock will gain 10% in the following year as well. In actuality, this may not be the case, but it is an example of interpolation based on previous data.

## What is the linear interpolation?

Linear interpolation is easy to understand with an example. Imagine that you are baking and you want to find out how many cookies you get for a certain amount of flour. First time you used 400 grams of flour, and you got 20 cookies. On the second time you used 200 grams of flour and got 10 cookies. On the third time you have 250 grams of flour, but you would like to find out in advance how many cookies you can get. If the relationship between the amount of flour and amount of cookies is linear, you can find out the result using the linear interpolation!

If you are trying to look out for a value that was not in the tested region, it is called the linear extrapolation. In this case it could be one kilogram of flour.

## What is linear interpolation formula?

If you want to find 'y', the linear interpolation formula is the following:

y = (x - x₁) * (y₂ - y₁) / (x₂ - x₁) + y₁

In this equation:

(x₁, y₁) = coordinates of the first data point

(x₂, y₂) = coordinates of the first data point

(x, y) = coordinates of the result point

## What is the linear extrapolation formula?

The equation for the linear extrapolation is identical with the formula of the linear interpolation. Only thing that you need to keep in mind is that when using the linear extrapolation, very often the results are not confirmed by experimental data. That is why you need to be sure that the relationship between your data points is linear before you use the linear extrapolation.

## How to use linear interpolation calculator?

We can use our cookie example for values in the calculator. So we are finding out how many cookies we can bake with 150 grams of flour?

x₁ = 400

y₁ = 20

x₂ = 200

y₂ = 10

x = 250

Fill in these values to the calculator. You should see the result of:

y = 12.5

The linear interpolation calculator will also calculate you the slope of the linear equation.

## How to extrapolate using this calculator?

You can use this linear interpolation calculator also for the linear extrapolation! Just fill in all the values like you would otherwise, and you get the result of the linear extrapolation.

Article author

John Cruz

John is a PhD student with a passion to mathematics and education. In his freetime John likes to go hiking and bicycling.

###### Linear Interpolation Calculator English

Published: Wed Sep 29 2021

In category Mathematical calculators

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