Hong Life CalculatorsUnderstanding the month-over-month (MoM) growth calculator — concept and principle
This calculator takes a series of monthly values, such as revenue, users or orders, and works out the change from each month to the next. It shows the latest month-over-month change, the compound monthly growth rate (CMGR), the annualized rate, the simple average, the best and worst months and the total change. Start-ups, marketers and analysts use it to track growth and report trends.
How it is calculated
- Month-over-month change = (this month − last month) ÷ last month × 100, for each pair of neighbouring months
- CMGR = (last value ÷ first value)^(1 ÷ (months − 1)) − 1
- Annualized growth = (1 + CMGR)^12 − 1
- Simple average = mean of the monthly changes
- Total change = (last ÷ first − 1) × 100
Enter values oldest first, separated by spaces or line breaks.
The principle
Single month-over-month changes are noisy: one strong or weak month can mislead. CMGR summarises the whole series as the steady monthly rate that would take the first value to the last, the geometric mean of the monthly growth factors. It is usually a little lower than the simple average of changes, because percentage ups and downs do not cancel out: +10% then −10% leaves you 1% lower. Annualizing compounds CMGR over twelve months, which assumes the pace continues.
Worked example
Defaults: 8,200, 8,650, 9,100, 8,900, 9,700, 10,400, 10,900, 11,800.
- Changes: 5.5%, 5.2%, −2.2%, 9.0%, 7.2%, 4.8%, 8.3%; latest = 8.3%.
- CMGR = (11,800 ÷ 8,200)^(1/7) − 1 = 5.34%.
- Annualized = 1.0534^12 − 1 = 86.6%.
- Simple average = 5.39%; best 9%, worst -2.2%.
- Total change = 43.9%; months with growth: 6 of 7 changes.
How to read the result
CMGR is the fairest single number for the period. An annualized rate of 86.6% is what a full year at this pace would give; it is a projection, not a forecast, and fast growth often slows. Look at the worst month and how often growth was positive to judge stability. For seasonal businesses, compare each month with the same month last year instead.
Common mistakes
- Averaging the monthly changes and calling it the growth rate.
- Annualizing a short burst of growth.
- Comparing months of different length without adjustment, such as February and March.
- Ignoring seasonality in retail, travel or education.
Frequently asked questions
What is CMGR?
The compound monthly growth rate: the constant monthly rate that turns the first value into the last over the period.
Why is the simple average higher than CMGR?
Because percentage gains and losses do not offset each other exactly; volatility pulls the compound rate below the average.
Is month-over-month or year-over-year better?
Month-over-month shows recent momentum; year-over-year removes seasonal effects. Use both.
Sources: Standard compound-growth arithmetic: geometric mean growth factor (last ÷ first)^(1/(n−1)) − 1 and annualization (1 + r)^12 − 1