Growth rate is how much a quantity varies with interval of time expressed as percentage. In business and financial matters, rates of growth indicate the speed of an important indicator (sales, revenue, or an investment value, etc.) to rise or fall between periods. To illustrate, the revenue of Amazon increased by 12 percent temporarily between 2022 and 2023 due to the sustained growth of revenue to the tune of $514 billion in 2022 to $575 billion in 2023.
Growth rates are used to track the performance and give insights into the future and trends. A slowing-down represents growth – lower growth – if the rate of growth is positive, expansion – higher sales or profits for instance, as well as, negative rates, represent contraction. An example is the revenue growth rate, which is an immediate indication of the health of a company and its attractiveness to investors since it tells how much sales grew in a year. Raw values become percentage changes that are related to growth rates in data analysis making comparisons between time or comparisons between firms easier.
Basic Growth Rate (Percentage)
The simplest growth rate formula compares the change to the original value. In general:
- Absolute change = (New value) − (Original value).
- Growth rate = (Absolute change) ÷ (Original value).
- Percentage growth = (Growth rate) × 100%.
In other words:
Growth Rate (%) = [(Final Value – Initial Value) / Initial Value] × 100%.Steps to calculate basic growth rate:
- Find the difference: Subtract the original (starting) value from the new (ending) value. This gives the absolute change.
- Divide by original: Divide that difference by the original value. This yields the decimal growth (e.g. 0.2164).
- Convert to percentage: Multiply by 100 to get a percentage rate.
Example: Suppose a school had 402 students last year and 489 this year. The absolute change is 489 – 402 = 87 students. Dividing by 402 gives 0.2164, or 21.64% growth. (That is, (489–402)/402 ≈ 0.2164, then ×100.) This tells us the student population grew by 21.6%.
You can use this method for any one-period change: monthly, quarterly, annual, etc. For instance, if a product’s sales went from $50,000 in Q1 to $60,000 in Q2, the growth rate is (60,000–50,000)/50,000 × 100% = 20%. A negative result simply means a decline (e.g. if sales fell from 50,000 to 40,000, the growth rate is -20%).
Average Growth Rates (Arithmetic Mean)
Occasionally it is useful for you to have the average growth per period across numerous years (or months) without growing. The average growth rates according to the level of growth within each year is termed as the average annual growth rate (AAGR). The formula is:
AAGR = (g₁ + g₂ + … + gₙ) / nwhere each g is the year-over-year growth rate for that year.
Steps to calculate average growth rate:
- Step 1: Compute each period’s growth rate using the basic formula. For each year (or period) i, calculate (Value_i – Value_{i–1})/Value_{i–1} × 100%.
- Step 2: Add those percentage rates together.
- Step 3: Divide by the number of periods.
That arithmetic average gives a feel of growth that is average. It is easy and it does not take into account the compounding since it merely averages the percentages.
Example: A firm brings in revenue of 100 dollars in year one, 150 dollars in year two and 180 dollars in year three. The year-to-year growth rates are:
- Year1→2: (150–100)/100 × 100% = 50%
- Year2→3: (180–150)/150 × 100% = 20%
The AAGR = (50% + 20%) / 2 = 35% per year.
It is simple to calculate; yet, it is important to remember that AAGR is nothing more than the average of rates. Most applicable as a rough, and speedy indicator of multi-period growth. It is, however, misleading when there are wide fluctuations in growth as it will balance with a few large fluctuations as well as small changes. As we invest over long distances or long periods of time, the Compound Annual Growth Rate (CAGR) (below) is more often going to be more illuminating.
Compound Annual Growth Rate (CAGR)
The Compound Annual Growth Rate (CAGR) is the smoothing growth rate of a period, supposing that quantity increased at an unvarying compound rate of increase in every year of the period. The answer to this is: Assuming that an investment or measurement increased at a constant rate every year, what would be the constant rate to go from the initial value to the final value? The formula is:
CAGR = [(Ending Value / Beginning Value)^(1/years) – 1] × 100%.Steps to calculate CAGR:
- Divide the ending value by the beginning value.
- Raise the result to the power of (1/number of years).
- Subtract 1.
- Multiply by 100 to convert to a percentage.
This computes the geometric average growth per year. It “smooths out” volatile year-to-year changes by assuming reinvestment each period.
Example: Imagine investing $10,000 in a fund. After 3 years the account is $19,000. To find the CAGR:
- Beginning Value (BV) = 10000, Ending Value (EV) = 19000, n = 3 years.
- EV/BV = 1.9.
- Take the cube root: 1.9^(1/3) ≈ 1.2386.
- Subtract 1 and multiply by 100%: (1.2386 – 1) × 100% ≈ 23.86%.
Thus the investment’s CAGR was about 23.9% per year, even though the annual returns varied.
CAGR is widely used for comparing growth of investments or revenues over multiple years. For instance, if Amazon stock grew from a $64,900 investment to $176,000 in 3 years (as in the Investopedia example), the CAGR is [(176000/64900)^(1/3)-1]×100% ≈ 39.5%. CAGR is especially useful when you need a single annual growth figure to compare different investments or project long-term growth.
Monthly Growth Rate
This is the same with shorter cycles such as months. Compounder formula: in order to determine a monthly growth, an equivalent formula without exponents is used with n being months. In the case where you have values on a monthly basis the monthly compound rate is:
Monthly Growth Rate = [(End Value / Start Value)^(1/n) – 1] × 100%,where n is the number of months.
Alternatively, if you know an annual rate and want the equivalent per-month rate, use:
Monthly Rate = (1 + AnnualRate)^(1/12) – 1:contentReference[oaicite:22]{index=22}.For example, a 5% annual growth corresponds to (1.05)^(1/12)-1 ≈ 0.407% per month. Or conversely, if sales grew from $10,000 to $11,000 over 3 months, the growth rate is (11000/10000)^(1/3) – 1 ≈ 3.23% monthly.
Revenue Growth Rate
A revenue growth rate is simply the level of growth that has been multiplied in the revenue amount of a company. Take the exact same growth formula of percentage and apply that on sales or income values. For example, if a company’s quarterly revenue goes from $1,000,000 to $1,200,000, the revenue growth rate is (1,200,000 – 1,000,000)/1,000,000 × 100% = 20%. Tracking revenue growth is crucial: it indicates how fast a business is expanding its sales. Strong revenue growth (normally a percentage in the higher, possibly double-digit, numbers in the case of tech or startups) could be an indication of a healthy business, and declining or a negative revenue growth could be a red flag to prospective investors.
The rate of revenue growth is very frequently issued as a report by the firm. To give an illustration, Userpilot states that revenue growth illustrates the total increase of income during the given period, and, therefore, tracking the revenue growth will aid in strategic decision making and raise the company valuation. Practically one of the prominent practices of measurement is to calculate growth on a quarterly or year- to-year basis in revenue to determine its performance.
Comparison of Growth Rate Metrics
Formulas of growth rate are suited differently. The most important types along with formulas and the usage of them are summarized in the table below:
| Growth Rate Type | Formula (for percent) | When to Use / Notes |
| Basic / Percentage Growth | (New – Old) / Old × 100% (for one period) | Use for simple short-term change (e.g. YoY revenue or quarter-to-quarter). Straightforward and commonly used. |
| Average Growth Rate (AAGR) | (g₁ + g₂ + … + gₙ) / n where each g is year-over-year % change | Averages multiple period changes arithmetically. Good for rough long-term trends, but does not compound. Useful when you want a simple average of volatile annual growth. |
| Compound Annual Growth Rate (CAGR) | [(Ending / Beginning)^(1/years) – 1] × 100% | Smooths growth over many years into one rate. Ideal for investments or revenue streams with varying year-to-year growth, because it accounts for compounding. |
| Monthly Growth Rate (CMGR) | [(Ending / Beginning)^(1/n) – 1] × 100% (n = # of months) | Like CAGR but for monthly data. Use when computing consistent monthly growth from start/end of a multi-month span. |
| Revenue Growth Rate | (New Revenue – Old Revenue) / Old Revenue × 100% | Applies the basic formula to sales or revenue figures. Key KPI for businesses; used in financial reports and investor analyses. |
| Annual Growth Rate | (Value_end – Value_start) / Value_start × 100% (for one year) | Essentially the same as basic for yearly data. Use when comparing year-on-year values. |
Each of the methods are used in different instances. The simplest way to estimate is basic percent growth and it applies to one-period variation (e.g. this year compared to last year). AAGR does nothing more complex than averaging two or more annual rates, and this may prove misleading, when values are compound. Annual rate is usually sought through CAGR (compound growth) to get an effective rate to represent long term period (years) investments or projects. Month over month growth also uses the same methodology on shorter cycles. Leaders rate of revenue is merely the identical calculation that was utilized towards making the revenue. As a rule, company representatives state both the straightforward year-on-year increase and the compound rates to give a complete picture of their activities.
Apple’s Historical Revenue Graph
Figure: Apple’s historical revenue (blue line) and earnings (orange line) from 1981–2010 (in millions USD). This graph (Wikimedia Commons) indicates the more detailed progress of the Apple Company control over its revenues in decades. The blue curve’s steep rise in the late 2000s illustrates compounding growth. To give an example, the revenue of Apple in a single year, 1999 was approximately 6,134 million, which increased to 65225 million in the year 2010 – a compounded annual growth rate of approximately 24 percent over this 11year period. (You can compute this by plugging EV=65225, BV=6134, n=11 into the CAGR formula.)
By contrast, the early years are flatter: revenue was only $335 million in 1981 and $4,071 million in 1988, reflecting slower growth early on. This example shows how a high compound growth rate (over 20% annually) can dramatically expand a company’s sales over time. Visual charts like this help compare growth patterns and underscore why understanding the right growth-rate formula is important for business analysis.
Using a Growth Rate Calculator
The growth rate can be manually calculated by hand, but the online tools that can be used to make this considerably faster when the growth rate is complex. To provide an example, the Growth Rate Calculator that Databox has will only require you to put in a starting and ending price; this will automatically calculate the growth rate in percentages. Our calculators have the formulas of these above incorporated to allow you to get your calculator in a few seconds. Most analytics software and in-spreadsheet applications (Excel, Google Sheets, etc.) even include their own CAGR formula and percentage growth formula on the platform.
How to use a calculator? When all you have is data and you just want to give an answer. An example would be to enter a starting amount of revenue of 5000 and end amount of revenue of 8000 after 2 years, and this immediately displays the CAGR or the simple growth rate. Errors that are made in the application of the formula can also be prevented by the use of tools. Nevertheless, it can still be useful to know how the formulas are manually calculated as this will help explain the result and can be useful in diagnosing why something seems to be wrong. We also recommend that you make use of a growth rate calculator to practice these formulas but to double-check using the step-by-step method as above anytime you may have to.
Frequently Asked Questions
Q: How do I calculate a growth rate between two values?
A: Subtract the old value from the new to get the change, divide by the old value, then multiply by 100 to get a percentage. In formula form: ((New – Old)/Old)×100%. This works for any one-time change (year-over-year, month-over-month, etc.). For example, $120K vs $100K gives 20% growth.
Q: What’s the difference between CAGR and average growth rate?
A: CAGR assumes compounding and gives a smoothed annual rate over multiple years. The average (AAGR) is just the simple mean of each year’s growth rates. Use CAGR when valuing investments or smoothing volatile data, because it reflects compound growth. Use average growth for a quick, rough metric when compounding isn’t a concern.
Q: Can a growth rate be negative or over 100%?
A: Yes. A negative growth rate simply means a decrease (e.g. -10% means the value dropped 10%). A growth rate over 100% means the value more than doubled. For instance, going from 100 to 250 is a 150% growth. The formulas allow any result; the context determines interpretation.
Q: When should I use CAGR instead of simple growth?
A: Use CAGR when comparing performance over multiple periods or forecasting under compound conditions. It’s ideal if returns are reinvested or if growth builds on prior growth. Simple growth is fine for a single interval or when compounding isn’t assumed.
Q: How do I find monthly or annual growth from each other?
A: To convert an annual rate to a monthly equivalent, use (1+annual)^(1/12)-1. Conversely, monthly to annual is (1+monthly)^12 – 1. This accounts for compound effects. Simply dividing by 12 (or multiplying) is incorrect unless growth is extremely small.
Conclusion
Business analysis and investment require an understanding of how to determine growth rate. We have discussed the basic growth metrics: the percent interval growth formula for one-period and the average growth rate (AAGR), that is, simple multi-period trend and one-year average growth rate (AAGR) for smoothing out multi-year human performance. They all have applications but basic growth should be used to get a quick comparison, average growth can be used to do some general trending and CAGR should be used as a year-over-year comparison. We even learned how to deal with special cases such as monthly growth and growth specific to revenue.
Practically, it is always required to indicate which growth formula to be applied and why. As an example, one might mention a CAGR in which one desires to demonstrate smoothed historic long-run operation of revenue or investment. To not make errors, calculate step-by-step or use dice roll growth rate calculators. These formulas can save time by being applied instantly on many free online calculators, You may also like Our Growth Increase Decrease Calculator.
Through these formulas and concepts, business people and students will be able to make precise growth estimates and articulate them accurately, whether it is forecasting, investment, or trend-analysis. To practice more, insert your numbers in a growth rate calculator or a spreadsheet and see whether the above steps agree. The ease of growth rate use will make you make a decision that will lead to financial independence as well as interpret your findings based on information results.
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