How to Interpolate Values in Excel Like a Pro

Interpolating values in Excel is a useful skill that allows you to estimate values between two known data points. With interpolation, you can calculate smooth transitions between discrete data points to better understand trends and make forecasts. While Excel has a dedicated FORECAST function for interpolation you can also do it manually using simple formulas. In this comprehensive guide we’ll explore the ins and outs of interpolating values in Excel using different methods.

What is Interpolation?

Interpolation refers to the process of estimating unknown values between two known data points. It helps you find values that lie between your discrete data points on a continuous line or curve. Interpolation enables smooth transitions between data points, giving you a better sense of the overall trend.

In Excel, interpolation is useful when:

• You need to estimate weekly sales figures when you only have monthly data.
• You want to calculate monthly website traffic when you have annual figures.
• You need to forecast next year’s revenue based on data from the past 5 years.

Instead of making wild guesses about the intermediate values, interpolation gives you a scientifically derived estimate based on the existing data points. The interpolated values connect your data points smoothly rather than in sudden jumps.

Excel Interpolation Methods

There are a few different ways to interpolate values in Excel

1. Linear Interpolation

Linear interpolation calculates values between two points on a straight line, It assumes the rate of change between the known points is constant,

To do linear interpolation in Excel:

1. Enter the two known y-values in cells A1 and A2.

2. In another cell, enter the formula:

   =(A2-A1)/(ROW(A2)-ROW(A1))

This calculates the rate of change between the two points.

1. In cell A3, enter the formula:

   =A1+B1

Where B1 contains the rate of change formula.

1. Copy the formula down from A3 to cells below it to interpolate values along the straight line.

The intervals between the calculated values will be equal.

2. Polynomial Interpolation

Polynomial interpolation fits a polynomial curve through more than two known points. It makes sense when the data demonstrates non-linear behavior.

To do polynomial interpolation in Excel:

1. Enter at least three y-values in consecutive cells (A1, A2, A3 etc.)

2. Select these cells and use Excel’s Growth trendline option.

3. Display the equation on the chart and use it to calculate additional points.

The curve connects the given points smoothly according to their relative positions.

3. Lagrange Polynomial Interpolation

The Lagrange polynomial formula lets you fit a polynomial through a number of points while passing through each point exactly.

The formula is more complex but has the advantage of interpolating multiple data points accurately.

4. Cubic Spline Interpolation

Cubic spline interpolation fits a special cubic polynomial between each pair of data points. The curves have the same slope and curvature at the junctions, resulting in a smooth overall fit.

Implementing cubic spline interpolation requires advanced numerical methods. However, Excel provides the cubic spline option for trendlines to achieve this automatically.

Using Excel’s FORECAST Function

The easiest way to interpolate values in Excel is using the built-in FORECAST function. FORECAST performs linear regression analysis to fit a straight line through your data points and returns the y-value for a given x-value.

To use FORECAST:

1. Enter the known y-values in a column (A1:A5)

2. Enter the known x-values horizontally in row 1 (B1:F1)

3. In another cell, use the FORECAST formula:

   =FORECAST(x,known_y’s,known_x’s)

Where x is the x-value you want to interpolate.

FORECAST calculates the projected y-value based on the linear regression line. It’s great for interpolating a few values but becomes cumbersome with large datasets.

Interpolation vs. Extrapolation

Interpolation refers to estimating values within the range of known data points. Extrapolation means projecting beyond the range, based on assumed trends.

Be careful when extrapolating – the trends beyond your data may not continue as smoothly as within the range. Interpolation is usually safer for making sound forecasts.

Examples of Interpolating Values in Excel

Let’s look at some examples of different interpolation techniques in Excel for practice:

1. Basic Linear Interpolation

![Basic linear interpolation][]

Given the years and population figures in A1:B3, we can interpolate to find the population in 2007 using linear interpolation.

The formula in B4 is: =B1+((B3-B1)/(A3-A1))*(A4-A1)

It calculates the y-value in 2007 based on the change rate between 2000 and 2010.

2. Polynomial Interpolation![Polynomial interpolation][]

Here we have quarterly sales figures for the past 3 years. To interpolate sales for Q3 and Q4 of 2022, we’ll use a polynomial trendline.

Right click the data points, select Add Trendline and choose the Polynomial order. The equation gives the interpolated estimates.

3. Using FORECAST![FORECAST example][]

Here FORECAST interpolates the value in cell A7 based on the y-values A1:A6 and x-values B1:B6 using linear regression.

The formula in A7 is: =FORECAST(B7,A1:A6,B1:B6)

FORECAST returns the projected y-value in 2022 based on the data from 2016 to 2021.

Tips for Interpolating Values

Here are some best practices for interpolating values accurately in Excel:

• Use at least 3-4 data points – Two points only allow linear interpolation. More points enable non-linear regression for curve fitting.
• Check for outliers – Outlier data can skew interpolations. Consider removing anomalies before interpolating.
• Be wary of extrapolation – Only extrapolate gently beyond your data range. The trends can change quickly.
• Check interpolated values – Ensure they align logically with the raw data points. Adjust the methods if needed.
• Use interpolation for estimates – Don’t rely too heavily on interpolated values for critical business forecasts.

Interpolating in Excel helps derive meaningful insights from discrete data points. Mastering interpolation methods such as linear, polynomial and cubic regression enables you to forecast trends accurately. Use Excel’s inbuilt FORECAST function for quick linear estimates.

We looked at the key concepts behind interpolation, Excel’s capabilities and useful examples. Interpolating values is a valuable analytics skill for better data-driven decisions. Use it wisely by following the best practices!