How this calculator works
A month-over-month change compares one month with the month before it. The same calculation works for quarters and years; only the label changes. Because it compares adjacent periods, it reacts quickly to turning points, but it is noisy when the data has seasonal patterns. Many analysts therefore compare the same month a year earlier, which is the year-over-year change, or use a compound growth rate over several months. The compound monthly growth rate smooths the path and answers what constant monthly rate would take the first value to the last.
Formula
Month-over-month change = (value in month 2 - value in month 1) / value in month 1. Quarter-over-quarter and year-over-year use the same formula with the corresponding periods. Compound monthly growth rate = (last value / first value)^(1 / number of months) - 1.
Worked example
A value rising from 100 in one month to 120 the next has a month-over-month change of 20 per cent. The same 20 per cent over 12 months as a compound rate is (120 / 100)^(1/12) - 1 = 1.53 per cent a month, which compounds to 20 per cent over the year.
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Frequently asked questions
When should I use month-over-month rather than year-over-year?
Use month-over-month when you want to see the latest direction and there is little seasonality. Use year-over-year when the business has strong seasonal patterns, because it compares like with like and removes the seasonal effect.
Why is the compound monthly rate lower than the total change divided by months?
Compounding. A constant 1.53 per cent a month multiplies the starting value by 1.0153 twelve times, which gives about 1.20. Dividing 20 per cent by 12 gives 1.67 per cent, which would overshoot when compounded.
What if the first value is negative?
A percentage change from a negative base is hard to interpret: a move from -100 to -50 is mathematically a 50 per cent decrease in the raw number but an improvement in the business. The compound growth rate requires positive values, and this calculator rejects them otherwise.