How to Make First Derivative Graph on Excel

Trying to understand how fast your numbers are changing can be more important than the numbers themselves. Using Excel, you can go beyond tracking simple totals and actually visualize the momentum, or rate of change, in your data by graphing its first derivative. This tutorial will walk you through calculating and plotting the first derivative to uncover hidden trends in your marketing campaigns, sales figures, or any other time-series data.

Graphed

Build AI Agents for Marketing

Build virtual employees that run your go to market. Connect your data sources, deploy autonomous agents, and grow your company.

Build Your First Agent

Understanding the First Derivative (Without the Textbook Math)

Forget the complicated calculus definitions for a moment. In the context of business data, the first derivative is just a fancy term for the rate of change. It’s the speed and direction of your data. Think of it as the slope of your trend line at any given point.

While a standard line graph shows you what your website traffic was, the derivative graph shows you how fast it was growing or declining at any given time. This is incredibly useful for spotting critical changes in momentum.

Why Should You Care About Rate of Change?

Visualizing the rate of change helps you answer much deeper questions about your data, such as:

• Marketing Analytics: Is our new campaign’s traffic growth accelerating, or is it starting to slow down? At what point did we see the fastest increase in user sign-ups?
• Sales Performance: Is our monthly recurring revenue (MRR) growth picking up steam or leveling off? Visualizing the derivative of MRR helps spot plateau points before they become a major issue.
• E-commerce Trends: Did that flash sale cause an initial spike in sales that quickly tapered off, or did it create sustained momentum? The derivative shows you how long the positive impact lasted.

Plotting the derivative gives you a leading indicator. You can see when growth is losing steam long before the actual numbers start to decline, giving you time to act.

AI Agents for Marketing

Crash Course

Graphed

Free PDF · the crash course

AI Agents for Marketing Crash Course

Learn how to deploy AI marketing agents across your go-to-market — the best tools, prompts, and workflows to turn your data into autonomous execution without writing code.

Download the PDF

Step 1: Get Your Data Ready in Excel

Before you can calculate anything, you need to structure your data properly. All you need is a simple, two-column table. It's crucial that your independent variable is sorted in ascending order.

For this tutorial, let’s use a simple example of monthly user sign-ups for a SaaS company.

• Column A (The 'X' variable): This is your independent variable, which is usually a unit of time like Day, Week, or Month. Make sure these are formatted as regular numbers (1, 2, 3...) or as dates that Excel can recognize.
• Column B (The 'Y' variable): This is your dependent variable - the metric you want to analyze. Examples include Website Sessions, Revenue, or in our case, User Sign-ups.

Your data should look something like this:

For the date/time column to work correctly in our formula, it's often easiest to use regular numbers (Day 1, Day 2) or ensure Excel has formatted them as dates. If using dates like "Jan-23," Excel automatically treats them numerically in the background, which is perfect for our calculation.

Step 2: Calculate the First Derivative Using a Simple Formula

Now, let's calculate the rate of change. We'll add a third column to our table and call it "Rate of Change" or "Derivative." We’re essentially calculating the slope between each successive data point using the classic formula:

• (Change in Y) / (Change in X) or (y2 - y1) / (x2 - x1)

That might seem intimidating, but in Excel, it’s a straightforward formula.

1. In cell C2, type the heading "Rate of Change."
2. We can't calculate a rate of change for the very first data point because there's nothing before it. So, we'll start our formula in the second row of data, cell C3.
3. In cell C3, enter the following formula:

=(B3-B2)/(A3-A2)

Let’s break that down:

• (B3-B2) calculates the change in our metric (the user sign-ups) between the current month and the previous month.
• (A3-A2) calculates the change in time (the number of months passed). In our case, the change between consecutive months should be 1, but this formula makes your calculation accurate even if your time intervals aren't perfectly consistent. Excel still only thinks this has a value of 1 when using dates separated equally (e.g., days).

1. Press Enter. You’ll now see the rate of change for that first interval.
2. To apply this formula to the rest of your data, simply click on cell C3, then click and hold the small square (the "fill handle") in the bottom-right corner of the cell. Drag it all the way down to your last row of data.

Your table now includes a third column showing exactly how much the user sign-ups changed from one month to the next.

Graphed

Build AI Agents for Marketing

Build virtual employees that run your go to market. Connect your data sources, deploy autonomous agents, and grow your company.

Build Your First Agent

A Note for Consistent Time Intervals

If your X variable is a simple series of numbers with a consistent interval of 1 (e.g., Day 1, Day 2, Day 3), your (A3-A2) will always equal 1. In this very common scenario, you can simplify the formula to just calculate the raw change:

=B3-B2

Either formula will work, but the first one, =(B3-B2)/(A3-A2), is more robust and mathematically accurate, so it's a good habit to use.

Step 3: Visualize the Data and its Derivative Together

Now for the fun part: creating a chart that visualizes both our original data and its derivative. A combo chart is the perfect tool for this because it allows us to use different chart types and axes for different data sets.

1. Highlight all three columns of your data, including the headers (from A1 to your last data row in column C).
2. Navigate to the Insert tab on Excel's ribbon. In the Charts section, click "Recommended Charts" and go to the "All Charts" tab. Select Combo from the list on the left.
3. Now, you need to configure the combo chart. Excel will list your two data series ("User Sign-ups" and "Rate of Change").

• For your original data ("User Sign-ups"), a Clustered Column or a Line chart works well. Let’s use a line chart for this example.
• For your "Rate of Change" series, choose a Line chart.
• This is the most important step: For the "Rate of Change" series, check the box under Secondary Axis.

Why is the Secondary Axis so important?

Your original data (thousands of sign-ups) likely operates on a much larger scale than your rate of change data (change of a few hundred). Without a secondary axis, your rate of change line would look flat and meaningless, squished at the bottom of the chart. The secondary axis gives it its own Y-axis (on the right side of the chart) so you can see both trendlines clearly.

1. Click OK. Excel will now generate your combo chart.

You can then clean up the chart by adding a title, formatting the lines, and labeling your axes. Your final result should be a clear, insightful visual.

AI Agents for Marketing

Crash Course

Graphed

Free PDF · the crash course

AI Agents for Marketing Crash Course

Learn how to deploy AI marketing agents across your go-to-market — the best tools, prompts, and workflows to turn your data into autonomous execution without writing code.

Download the PDF

How to Read and Interpret Your New Graph

Having the graph is one thing, knowing what it means is another. Here’s how to decipher the story your two trend lines are telling you.

Let's use our user sign-up example:

• When the orange line (Derivative) is above zero: The blue line is going up. Our sign-ups are growing. The higher the orange line, the faster the growth. You can see our growth accelerated rapidly from Month 4 to Month 7, where the rate of change peaked.
• When the orange line is sloping downwards (but still above zero): This is a crucial insight. From Month 7 to Month 10, the orange line is decreasing. This means that although we were still gaining users each month, the rate of that growth was slowing down. This is your early warning that momentum is fading.
• When the orange line crosses zero: This is the peak. In our chart, this happens around Month 10. The rate of change becomes negative, which means our sign-ups hit their highest total and then started to decline. This inflection point is almost impossible to spot accurately without a derivative graph.
• When the orange line is below zero: The blue line is going down. We are losing more sign-ups than we are gaining. The further below zero it is, the faster the decline.

Final Thoughts

By mapping the first derivative, you've transformed a simple Excel chart into a powerful analytical tool. You can now move beyond just observing trends and start to precisely identify when growth accelerates, slows down, peaks, and declines - giving you the insights needed to make smarter, more proactive decisions.

For one-off analyses, calculating rates of change in a spreadsheet is a fantastic skill to have. However, routinely pulling data from different systems like Google Analytics, Shopify, and your CRM to build these charts can quickly become a manual, time-consuming process. We built Graphed to solve exactly this problem. You can connect your marketing and sales tools in seconds and then simply ask in plain English, "show me the daily change in user sign-ups" to get an auto-updating dashboard instantly, no formulas or chart configurations required.