Growth Rate Calculator
Start value, end value, and elapsed periods. Get simple growth, compound annual growth, months to double, and a forward projection.
Compound growth per month
–
The rate that actually compounds from start to end
- Total growth
- –
- End ÷ start − 1
- Growth multiple
- –
- End ÷ start
- Annualized rate
- –
- Doubling time
- –
- At the compound rate
- Simple average per period
- –
- Total ÷ periods. Shown for contrast.
- Projected value
- –
Projection at the compound rate
| Periods ahead | Multiple | Projected value |
|---|
Simple growth, compound growth, and the averaging mistake
Growth compounds, so the average of monthly percentages is not your growth rate. If a metric goes from 42,000 to 68,000 in a year, it grew 61.9%. Divide that by 12 and you get 5.2% a month, but a business that really grew 5.2% every month would have finished at about 76,800, not 68,000. The rate that actually gets you there is 4.1% a month, compounded. That is what this tool reports as the primary figure.
The same trap appears whenever someone averages a column of month-over-month percentages in a spreadsheet. Percentages taken off different bases cannot be averaged arithmetically; a 50% drop followed by a 50% rise leaves you down 25%, not flat. The compound rate, sometimes called CAGR when the periods are years, is the geometric mean of the period-over-period growth factors, and it is the only single number that reproduces the actual start and end.
Two habits keep growth reporting honest. First, state the unit and the rate together: 4.1% a month and 61.9% a year describe the same trajectory, and quoting the bigger one without the unit is how growth slides get inflated. Second, count elapsed periods, not data points. January to December is eleven monthly steps, not twelve.
Formulas
- Total growth
- = End ÷ Start − 1
- Compound rate per period (r)
- = (End ÷ Start)^(1 ÷ Periods) − 1
- Simple average per period
- = Total growth ÷ Periods
- Annualized rate
- = (1 + r)^(periods per year) − 1
- Doubling time
- = ln(2) ÷ ln(1 + r)
- Projected value
- = End × (1 + r)^N
Frequently asked questions
What is the difference between a simple and a compound growth rate?
Simple growth divides the total change by the number of periods. Compound growth finds the single rate that, applied every period and building on the previous period, takes you from start to end. Compound is the honest one: if revenue grows 5% a month for a year it is up 79.6%, not 60%, because each month grows off a larger base. Dividing 79.6% by 12 gives 6.6% a month, a rate the business never actually achieved.
How do I convert a monthly growth rate to an annual rate?
Raise one plus the monthly rate to the twelfth power and subtract one. A 4% monthly rate is (1.04)^12 − 1, about 60.1% a year, not 48%. The same logic applies to quarters with a power of four. This calculator does the conversion for you based on the period unit you select.
How is doubling time calculated?
Doubling time is ln(2) divided by ln(1 + rate), measured in the same periods as the rate. At 4.1% a month that is about 17 months. The rule of 72 (72 divided by the rate in percent) gives a quick mental approximation, roughly 17.6 months here, and is accurate enough for rates under about 10% a period. A rate of zero or below never doubles.
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