This is an overview.

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## What Is Interpolation?

Interpolation is a mathematical technique used to estimate values within a set of known data points. It fills gaps between observed data points by assuming a smooth or linear relationship between them. Interpolation can be linear or non-linear, depending on the data nature and accuracy.

### How to Do Linear Interpolation for Linear Dataset in Excel?

If your dataset is linear, you can implement a linear interpolation method. The image below displays a set of formulas that you can use to perform linear interpolation on a linear set of data.

### How to Do Linear Interpolation for Non-linear Dataset in Excel? (Taking All X & Y Values into Consideration)

If your dataset is non-linear, you may get different interpolation results if you follow different methods. You can perform linear interpolation either by taking all X & Y values or only the adjacent X & Y values.

#### 1. Using the FORECAST Function

- Use the following formula in
**C15:**

`=FORECAST(C14,C5:C12,B5:B12)`

- Press
**Enter**.

#### 2. Using SLOPE and INTERCEPT Functions

**Slope** =** SLOPE(C5:C12,B5:B12)**

**Intercept** =** INTERCEPT(C5:C12,B5:B12)**

- In
**C15**, enter the following formula**:**

`=E6*C14+E8`

- Press
**Enter.**

(This method follows the straight line equation, **y = mx + c**)

#### 3. Using the Excel Scatter Plot (Linear Trendline)

- Select the X and Y coordinate values and click
**Insert**>>**Charts**>>**Scatter**.

- Click
**Chart Elements**. Check**Trendline**. Uncheck**Gridlines**. - Change the chart title.

- Double-click Trendline.
- Select
**Trendline Options**>>**Linear**>>**Display Equation on Chart**.

The linear equation is visible. You can enter an X value and get the corresponding Y value.

- In
**C17**, enter the following formula:

`=0.7337*C16 + 4.0858`

- Press
**Enter**.

### How to Do Linear Interpolation in a Non-linear Dataset in Excel? (Taking Adjacent X & Y Values into Consideration)

#### 1. Using a General Mathematical Interpolation Formula

- Use the following formula in
**C15**:

`=C7+(C14-B7)*(C8-C7)/(B8-B7)`

- Press
**Enter**.

#### 2. Using the FORECAST Function

Formulas for **INDEX & MATCH**

- For X
_{1 }:`=INDEX(B5:B12,MATCH(C14,B5:B12,1))`

- For X
_{2 }:`=INDEX(B5:B12,MATCH(C14,B5:B12,1)+1)`

- For Y
_{1 }:`=INDEX(C5:C12,MATCH(C14,B5:B12,1))`

- For Y
_{2 }:`=INDEX(C5:C12,MATCH(C14,B5:B12,1)+1)`

Formulas for **XLOOKUP**

- For X
_{1 }:`=XLOOKUP($C$14, B5:B12,B5:B12,,-1,1)`

- For X
_{2 }:`=XLOOKUP($C$14, B6:B13,B6:B13,,1,1)`

- For Y
_{1 }:`=XLOOKUP($C$14, B5:B12,C5:C12,,-1,1)`

- For Y
_{2 }:`=XLOOKUP($C$14, B5:B12,C5:C12,,1,1)`

- In
**C15**, enter the following formula:

`=FORECAST(C14,F8:F9,F6:F7)`

- Press
**Enter**.

#### 3. Combining the FORECAST, OFFSET, and MATCH Functions

- In
**C15**, enter the following formula:

`=FORECAST($C$14, OFFSET($C$5:$C$12,MATCH($C$14, $B$5:$B$12,1)-1, 0,2), OFFSET($B$5:$B$12,MATCH($C$14, $B$5:$B$12,1)-1,0,2))`

- Press
**Enter**.

**Formula Breakdown**

**MATCH($C$14, $B$5:$B$12, 1):**Finds the position of the largest value less than or equal to the lookup value in**B5:B12**.**OFFSET($B$5:$B$12, MATCH($C$14, $B$5:$B$12, 1)-1, 0, 2):**Creates a new range by shifting**B5:B12**by the number of rows specified by the result of the**MATCH**function minus 1, with a resulting range height of 2 rows.**OFFSET($C$5:$C$12, MATCH($C$14, $B$5:$B$12, 1)-1, 0, 2):**Creates a new range by shifting**C5:C12**by the number of rows specified by the result of the**MATCH**function minus 1, with a resulting range height of 2 rows.**FORECAST($C$14, OFFSET($C$5:$C$12, MATCH($C$14, $B$5:$B$12, 1)-1, 0, 2), OFFSET($B$5:$B$12, MATCH($C$14, $B$5:$B$12, 1)-1, 0, 2)):**Performs linear interpolation using the**FORECAST**function, using the value in**C14**as the X value and interpolating between two adjacent data points based on their corresponding X and Y values (shifted using**OFFSET**).

## How to Do Non-linear Interpolation in Excel?

### How to Do Non-linear Interpolation Using the GROWTH Function?

- In
**C15**, enter the following formula:

`=GROWTH(C5:C12,B5:B12,C14)`

- Press
**Enter.**

### How to Do Non-linear Interpolation Using a Scatter Plot with a Trendline?

- Select the X and Y coordinate values and click
**Insert**>>**Charts**>>**Scatter.**

- Click
**Chart Elements**. - Check
**Trendline**. - Uncheck
**Gridlines**. - Change the chart title.

- Double-click Trendline.
- Select
**Trendline Options**>>**Exponential**>>**Display Equation on Chart**.

The linear equation is visible. Enter the X value and get the corresponding Y value.

- In
**C17**, enter the following formula:

`=4.2258*EXP(0.0936*C16)`

- Press
**Enter.**

## Practical Examples of Interpolation in Excel

### How to Use the FORECAST.LINEAR Function to find Density?

- Select
**F5**>> enter the formula >> press**Enter.**

`=FORECAST.LINEAR(F4,C5:C11,B5:B11)`

### How to Apply the TREND Function to Get Interpolated Density?

- Select
**F5**>> use the following formula >> press**Enter.**

`=TREND(C5:C11,B5:B11,F4,TRUE)`

### How to Do Interpolation With the SLOPE and INTERCEPT Functions?

- Select
**F5**>> enter the following formula >> press**Enter.**

`=F4*SLOPE(C5:C11,B5:B11)+INTERCEPT(C5:C11,B5:B11)`

## How to Prevent Interpolation Errors in Excel?

**#DIV/0 **is often displayed because **x1** and **x2** are the same. To prevent this error:

- Select
**F11**>>use the formula >> press**Enter**to see**#DIV/0.**

`=FORECAST(F10,F7:F8,F5:F6)`

Improve the formula.

- Select
**F11**>> enter the following formula >> press**Enter.**

`=IF(F5=F6,F7,FORECAST(F10,F7:F8,F5:F6))`

No **#DIV/0** will be displayed.

## Things to Keep in Mind

- Make sure your data is organized in columns or rows, with the independent variable (X) values in one column and the dependent variable (Y) values in another column.
- Ensure that your X values are sorted in ascending order. If your data is not sorted, the interpolation results may be incorrect.
- Make sure there are no duplicate X values in your dataset. Excel’s interpolation functions rely on unique X values.

## Frequently Asked Questions

**1. Is there an interpolation function in Excel?**

**Answer:** Yes, Excel provides several functions that can be used for interpolation. The most commonly used function for linear interpolation is the **FORECAST **function. For non-linear interpolation, Excel does not have a built-in function, but you can use other functions like **TREND**, **GROWTH**, or **LINEST **to perform various types of curve fitting and extrapolation.

**2. What are the differences between extrapolation and interpolation?**

**Answer:** Interpolation is the technique of estimating values within the range of known data points.

Extrapolation involves estimating values beyond the range of known data points. It extends the trend or relationship observed to predict values outside the range.

**3. Is Interpolated data a reliable source of information?**

**Answer:** The reliability of interpolated data depends on the quality of the original data and the appropriateness of the interpolation method.

## Excel Interpolation: Knowledge Hub

- How to Interpolate Missing Data in Excel
- How to Do Linear Interpolation in Excel
- How to Do VLOOKUP and Interpolate in Excel
- How to Interpolate Between Two Values in Excel
- How to Do Interpolation with GROWTH & TREND Functions in Excel
- How to Use Non Linear Interpolation in Excel
- How to Interpolate in Excel Graph
- Do 2D Interpolation in Excel
- 3D Interpolation in Excel
- Linear Interpolation Excel VBA
- Calculate Logarithmic Interpolation
- Perform Exponential Interpolation
- Do Polynomial Interpolation
- Apply Cubic Spline Interpolation
- Interpolate Time Series
- Perform Bilinear Interpolation

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