Percentage change: growth, decline, MoM and YoY

Sales increased by 200. Is that impressive? If they previously stood at 100, the change is enormous. If they stood at a million, the same additional 200 barely moves the result. That is why I calculate percentage change: I compare the difference with the starting value. Without that baseline, an absolute increase tells only part of the story.

The formula is short. Choosing the denominator, periods and source data deserves more attention. I will work through small synthetic examples, then look at situations where a correctly calculated percentage can still produce a misleading statement. My aim is for you to explain the result as well as calculate it, especially when someone asks the useful question: “compared with what?”.

The percentage change formula

For a positive starting value, I use this rule:

relative change = (new value - old value) / old value

The result is a fraction that can be displayed with percentage formatting. Outside a spreadsheet, multiply that fraction by 100 to obtain the number to accompany a percent sign. An equivalent expression is new / old - 1. Microsoft demonstrates the calculation for both increases and decreases in its percentage guide. Naming the old and new values first makes the calculation easier to follow.

Suppose a team closed 80 tickets in its first month and 100 in its second. The difference is 20. Dividing 20 by the original 80 gives 0.25, or 25%. A useful report sentence is: the number of closed tickets increased by 25% compared with the previous month. Include the levels of 80 and 100 as well, so the recipient can see the scale behind the percentage.

If the count falls from 100 to 80, the difference is -20 and the denominator is 100. The result is -0.20, or -20%. I describe that as a decrease of 20% or a change of -20%. The wording “a decrease of -20%” creates unnecessary confusion about the direction. Clear language helps preserve the meaning of the calculation when it leaves the spreadsheet and enters a presentation.

Why the denominator is the old value

The old value supplies the reference point. The question is how large the difference is relative to where the comparison began. Swap the two periods and you also change that reference point. This explains many apparently contradictory calculations: one person compares the current month with the previous month, while someone else reverses the comparison. Both may have entered their formulas correctly but asked different questions.

Moving from 80 to 100 gives a 25% increase. Returning from 100 to 80 gives a 20% decrease. Both results are correct because the bases differ. Likewise, a 20% increase after a 20% decrease does not restore the original value. Starting at 100, the decrease takes you to 80. Adding 20% of 80 adds 16, leaving a final value of 96.

I like to explain that asymmetry before filling a formula across an entire report. Percentages describe amounts relative to particular bases, so equal percentages do not necessarily represent equal quantities. Saying that a business “recovered the same percentage” does not establish that it returned to its starting level. Check the underlying values and the direction of each comparison before drawing that conclusion.

Calculate it in Excel

Put the old value in A2, the new value in B2 and enter this in C2:

=(B2-A2)/A2

Apply percentage formatting to C2. With 80 in A2 and 100 in B2, the displayed result is 25%. Do not also multiply the formula by 100 when using that format. Percentage formatting already displays 0.25 as 25%; including the extra multiplier would display 2500%. This mistake is easy to overlook once the number has been copied into a chart with an authoritative title.

Keep the calculation’s precision and choose the displayed decimal places for the audience. Showing only whole percentages can conceal a small change. Six decimal places for a dataset containing a handful of orders creates an unhelpful impression of precision. I usually begin with one or two decimal places, then check whether that display hides a distinction relevant to the decision. Rounding for display should not replace the underlying calculation.

For a longer set of comparisons, prepare an Excel table with clearly named columns. Keep the original levels, calculated change and any comparability note separately. Avoid typing 25% over a formula because you happen to know the answer for one row. New data should follow the same understandable rule. A manual exception makes the next update harder to trust and harder to explain.

MoM and YoY identify the comparison period

MoM means month over month: a month compared with the previous month. YoY means year over year: a period compared with the corresponding period a year earlier. The calculation itself stays the same. What changes is the pair of values supplied to it. I identify those periods before calculating the percentage, because a familiar abbreviation in the heading does not establish that the selected data matches it.

Consider these synthetic monthly order counts. They describe an illustrative business, rather than any actual company.

For September 2026, MoM change is (120-100)/100, or 20%. YoY change is (120-80)/80, or 50%. “Up 20% month over month” and “up 50% year over year” can therefore both be accurate descriptions of the same current month. They have different baselines. Label those baselines explicitly so that readers do not have to reconstruct them from another page of the report.

YoY comparisons can reduce some seasonal effects, but they do not guarantee full comparability. Different working-day patterns, moving holidays and one-off campaigns may still matter. The European Central Bank explains base effects in annual growth rates. In a practical report, I examine what happened during the reference period as well as the latest period. An unusual starting point can strongly influence the current growth figure.

Make partial-period cutoffs explicit

A report prepared on 12 October should not compare the first twelve days of October with the whole of September and label the result ordinary MoM growth. The exposure periods differ. One option is to compare days one to twelve in both months, but name that approach and check the completeness of both intervals. A technically valid division cannot correct an unsuitable selection of periods.

Equal numbers of calendar days do not solve every comparison either. A business operating Monday to Friday may care about working days, while an online service may have a distinctive weekend pattern. Choose a rule appropriate to the process: matching calendar dates or comparable operating days. Record that rule alongside the result. There is no universally suitable shortcut that can replace understanding how the measure is generated.

Check source delays too. Suppose the export contains complete figures for the previous year, while current orders arrive with a two-day delay. Matching the date boundaries alone would still create an uneven comparison. A possible response is to end both periods at the last complete day, after confirming that boundary with the source owner. A percentage cannot tell you that one system is still sending records.

Percentages and percentage points

Comparing two shares calls for two distinct descriptions. Suppose the share of tickets resolved on time rises from 20% to 30%. That is an increase of 10 percentage points. The relative increase in the share is (30%-20%)/20%, which equals 50%. The ONS guidance distinguishes percentages from percentage points, because confusing those units materially changes the claim being made.

I normally state the levels first: from 20% to 30%. Then I add the increase of 10 percentage points. If relative growth is relevant, I label it separately. Saying only “an improvement of 10%” could instead mean a move from 20% to 22%. The audience should not have to guess which interpretation the writer intended. Precise wording saves time in the discussion that follows.

Also inspect the counts behind the share. Two on-time tickets out of ten give 20%; three out of ten give 30%. Here the improvement represents one additional on-time case. At another scale, the same change in percentage points could represent hundreds of events. The share, numerator and denominator together provide a more useful picture than a large percentage displayed without its underlying population.

Zero, missing data and negative values

If the old value is zero, the standard formula requires division by zero. A move from 0 to 10 has no finite percentage change under that definition. Report the levels and the absolute increase instead: from 0 to 10, an increase of 10. Calling it 100% growth supplies a number that the stated calculation does not support. A clear exception is better than a convenient invented percentage.

Zero in both periods also needs an agreed reporting convention. You can describe an unchanged level, but the formula still involves division by zero. Use a clearly explained “not applicable” or another documented representation for an uncalculated rate. Avoid using the same label for a zero baseline and a failed data source. They explain different situations, even if neither produces a percentage in the final table.

A missing observation in the earlier period is not automatically zero. Perhaps collection had not started, or the export is incomplete. Replacing that absence with zero invents a baseline. In a simple report, I add a comparison status and explain why growth was not calculated. That allows the reader to distinguish genuinely new activity from a data-quality problem and choose an appropriate next step.

Negative values introduce another interpretation problem. Moving from -100 to -50 gives -50% under the ordinary formula, although the loss has become smaller. I prefer stating both levels and the improvement of 50 units. If an organisation uses a different convention for changes involving negative values, agree and document it explicitly. Quietly replacing the denominator with its absolute value changes the definition and makes comparisons harder to interpret.

Small bases and combining segments

Moving from one order to three gives 200% growth. Moving from 100 to 120 gives 20%. The first percentage is larger, while the second case adds more orders: 20 rather than 2. I show absolute change alongside growth to keep the scale visible. A small project can have meaningful progress, but the percentage should not obscure how many additional events actually occurred.

Do not average segment growth rates without checking what the resulting measure means. Suppose segment A grows from 10 to 20, and segment B from 100 to 110. Their rates are 100% and 10%. The arithmetic average is 55%, but the combined total rises from 110 to 130, approximately 18.18%. When the question concerns the whole business, calculate growth from the combined starting and ending values.

An average segment growth rate can be a separate useful measure, provided its weighting and purpose are explicit. Equal weighting gives the small segment as much influence as the large one. That may be intentional, but it does not represent the change in total orders. Readers need to know whether you are describing a typical segment or the aggregate. This choice belongs to the analytical question itself.

Combine successive changes through multipliers

Two consecutive increases of 10% produce 21% growth overall. Starting at 100, you reach 110 and then 121. The second percentage uses the larger base. The calculation corresponds to multiplying 1.10 × 1.10, rather than adding two rates. To describe the change between the first and last period, use the endpoints or compound the intervening growth factors consistently.

The same idea matters for an average annual growth rate. If a value rises from 100 to 121 across two years, a constant annual rate of 10% reproduces those endpoints. That does not establish that each actual year grew by 10%. The measure smooths the path between the beginning and end. Show individual years too when the path contains a substantial fall that an endpoint summary would conceal.

Distinguish annual growth from a shorter-period rate expressed at an annual pace. BEA explains annualisation through compounding, assuming the period’s pace continues. A monthly increase does not automatically become a prediction for the full year. If the report uses an annualised rate, the label should make that clear. Otherwise, two apparently comparable percentages may represent different constructions and lead to an avoidable misunderstanding.

Check that the measure stays the same

Order count can rise from 100 to 120 while total sales value stays unchanged. A smaller average order value makes that possible. The statement about order growth remains correct, but “sales grew by 20%” becomes ambiguous if the recipient understands sales as revenue. Name the measure precisely. Similarly, opening a new location can increase a network total even if existing locations remain unchanged. A whole-network comparison and a comparable-location comparison answer different questions.

For monetary values, also distinguish changes in prices from changes in units sold. The ordinary percentage formula does not select a business perspective for you. Define the measure, scope and unit before calculating it, then keep those definitions consistent across periods.

Reconstruct the ending value

A small example makes a useful reasoning check. With an old value of 80 and growth of 25%, the additional amount is one quarter of 80: 20. Adding it gives 100. This can expose a reversed denominator or a percentage entered as a whole number. Also distinguish increasing by 25% from reaching 25% of the starting level. The former ends at 125% of the original; the latter leaves just one quarter of it.

Check the statement before sharing it

Before passing a growth figure on, I check the measure definition, unit, periods, source completeness and baseline. I trace at least one row back to its underlying values. If the rate is unusually large, I inspect the base and any one-off events. I also ask whether growth represents improvement: more complaints may be a warning even when the percentage change is positive. Direction alone does not provide an evaluation.

For practice, calculate a move from 50 to 60 and then from 60 to 50. The first change is 20%; the second is approximately -16.67%. Then describe a share moving from 40% to 50%: up 10 percentage points, or a relative increase of 25%. Write one sentence for each result that names the period and reference value. If you can explain it without shortcuts, you have more than a formula to copy.

The original Polish article includes a video; this English explanation stands on its own with the same synthetic examples. As a next step, revisit the Excel table guide and build a small report with separate columns for original level, new level, absolute change and percentage change. Add a note wherever a comparison cannot be interpreted using the ordinary positive-baseline definition.