# Extrapolation Calculator

## Extrapolation Calculator

Are you trying to find a value outside a known range of data points? That’s what an Extrapolation Calculator helps you do. It estimates unknown values by extending a known sequence of values.

What is Extrapolation?

### How to Use the Extrapolation Calculator

**Input Fields**

**Enter X1 (e.g., 2):**The first known x-coordinate.**Enter Y1 (e.g., 4):**The first known y-coordinate.**Enter X2 (e.g., 6):**The second known x-coordinate.**Enter Y2 (e.g., 8):**The second known y-coordinate.**Enter X3 or Y3 (e.g., 10):**The x-coordinate or y-coordinate for which you want to find the corresponding y or x value.

**Example Values:**

Let’s say you have two points: (2, 4) and (6, 8). You want to find the y-value for x = 10.

### Formula

The formula for linear extrapolation is:

`$Y3=Y1+\left(\frac{X3-X1}{X2-X1}\right)\times (Y2-Y1)$`

**Variables**

Variable | Description |
---|---|

$X1$ | First x-coordinate |

$Y1$ | First y-coordinate |

$X2$ | Second x-coordinate |

$Y2$ | Second y-coordinate |

$X3$ | Third x-coordinate (for Y3 calculation) |

$Y3$ | Third y-coordinate (for X3 calculation) |

## Calculation Examples

### Example 1

**X1:**2**Y1:**4**X2:**6**Y2:**8**X3:**10

**Calculation:**

1. Calculate the slope:

`$\text{slope}=\frac{Y2-Y1}{X2-X1}=\frac{8-4}{6-2}=1$`

2. Apply the formula:

`$Y3=4+\left(\frac{10-2}{6-2}\right)\times (8-4)=4+2\times 4=12$`

**Result:** Y3 = 12

### Example 2

**X1:**1**Y1:**3**X2:**4**Y2:**7**Y3:**15

**Calculation:**

1. Calculate the slope:

`$\text{slope}=\frac{7-3}{4-1}=\frac{4}{3}$`

2. Apply the formula to find X3:

`$X3=1+\left(\frac{15-3}{\frac{4}{3}}\right)=1+9=10$`

**Result:** X3 = 10

Thank you for using our tool.