What Is Growth Rate? Formula and How to Calculate Annual Growth

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A growth rate is the percentage change in a variable over a specific period. It shows how much something increased or decreased relative to where it started. The variable can be revenue, earnings, dividends, an investment balance, a country’s gross domestic product (GDP) or a population. The simplest growth rate formula divides the change in value by the starting value:

Growth rate = (Ending value - Beginning value) / Beginning value × 100

A positive result means the variable expanded. A negative result means it contracted. A growth rate always needs a period attached to it. “Revenue grew 12%” says little until you know whether that was over a quarter, a year or five years.

How Growth Rate Works

Growth rates began in biology, where researchers used them to track how fast populations of organisms expanded. Economists, corporate managers and investors later adopted the same arithmetic, because the question is the same in every field: how fast is this thing changing compared with its own size?

Measuring the change against the starting value is what makes growth rates comparable. A $50,000 increase means something very different for a company earning $100,000 than for one earning $50 million. Converting the change to a percentage puts both on the same scale.

Calculating a simple growth rate

Take a hypothetical company whose annual sales rose from $800,000 to $920,000.

1. Subtract the beginning value from the ending value: $920,000 - $800,000 = $120,000.
2. Divide the change by the beginning value: $120,000 / $800,000 = 0.15.
3. Multiply by 100 to express it as a percentage: 15%.

This is the standard sales growth formula, and the same steps work for revenue, net income, website visitors or any other quantity. If sales had fallen to $720,000 instead, the result would be ($720,000 - $800,000) / $800,000 = -10%, a contraction.

The denominator is always the starting value. Dividing by the ending value is a common mistake, and it understates growth and overstates declines.

Period-over-period comparisons

Public companies usually report growth in two ways when they release quarterly results:

• Quarter over quarter (QoQ): this quarter compared with the previous quarter.
• Year over year (YoY): this quarter compared with the same quarter a year earlier.

YoY comparisons remove seasonal patterns. A retailer’s fourth quarter includes the holiday season, so comparing it with the third quarter would show a spike that reflects the calendar, not the business. Comparing it with the prior year’s fourth quarter isolates the underlying change.

Annual growth over several years: CAGR

When a value changes over more than one year, the simple formula gives the total growth, not the yearly rate. To find the steady annual rate that would turn the beginning value into the ending value, use the compound annual growth rate (CAGR):

CAGR = (Ending value / Beginning value)^(1/n) - 1

where n is the number of years.

CAGR is not an actual return in any single year. It is a smoothed figure: the rate at which the value would have grown if it had grown at the same pace every year with gains reinvested. Companies often use it to report and project earnings growth because it compresses a multi-year record into one number.

How to calculate the annual growth rate of money (hypothetical example): an investment grows from $10,000 to $14,000 over five years.

• Total growth: ($14,000 - $10,000) / $10,000 = 40%.
• CAGR: (14,000 / 10,000)^(1/5) - 1 = 1.4^0.2 - 1 ≈ 6.96% per year.

Dividing the 40% total by five years gives 8%, which overstates the yearly rate because it ignores compounding. Each year’s growth builds on a larger base, so a lower annual rate is enough to reach the same endpoint.

The same formula answers a common question: if revenue doubles every year, what growth rate is that? Doubling means the ending value is twice the beginning value, so (2/1) - 1 = 100% per year. Over three years of doubling, revenue would be eight times its starting level, and the CAGR would still be 100%.

Arithmetic average vs. compound rate

When you have a series of yearly growth rates, there are two ways to summarize them, and they can give very different answers.

Hypothetical example: a value goes from 100 to 150 in year one (+50%) and then to 105 in year two (-30%).

• Arithmetic average: (50% + (-30%)) / 2 = 10% per year.
• Compound (geometric) rate: (105/100)^(1/2) - 1 ≈ 2.47% per year.

The value actually rose only 5% over two years, so the compound rate describes what happened. The arithmetic average overstates it. The more volatile the yearly rates, the wider the gap between the two. For growth over time, and especially for investment balances, the compound rate is the appropriate mean. The arithmetic average is still useful as a description of a typical single year.

A related shortcut is the Rule of 72: divide 72 by an annual growth rate in percent to estimate the years needed to double. At 6% a year, a value doubles in roughly 72 / 6 = 12 years (the exact figure is about 11.9). The rule is an approximation that works best for rates in the single digits.

Calculating growth rate in Excel

Spreadsheets handle these formulas easily:

• Simple growth: =(B2-A2)/A2, formatted as a percentage, with the starting value in A2 and the ending value in B2.
• CAGR: =(B2/A2)^(1/n)-1, replacing n with the number of years or a cell reference.
• RRI function: =RRI(nper, pv, fv) returns the equivalent compound rate in one step, using the number of periods, the starting value and the ending value.

Excel’s GROWTH function sometimes confuses people because of its name. It does not return a growth rate. It fits an exponential curve to existing data and returns predicted values along that trend. LOGEST returns the growth factor of that fitted curve. The base of the fitted trend is 1 + the growth rate, so subtracting 1 gives the rate.

Types of Growth Rates

The arithmetic stays the same across uses, but what is being measured, and why, changes.

Company growth rates

Analysts, investors and management teams track growth in revenue (sales), earnings, earnings per share and cash flow most often. Some also track growth in book value or in valuation measures such as the price-to-earnings ratio.

Two time orientations matter:

• Trailing growth rate: calculated from reported historical results, such as revenue growth over the past four quarters or the past five years.
• Expected (forward) growth rate: a projection of future growth, often drawn from company guidance or analyst consensus estimates. A near-term growth rate usually refers to the next one or two years, as opposed to a long-term rate covering several years.

To estimate a company’s expected annual earnings growth, investors commonly start from published analyst consensus estimates, compare them with the company’s trailing growth and guidance, and then test them against fundamentals such as the sustainable growth rate below. Projecting forward by applying a historical CAGR to current revenue is the simplest method, but it assumes the past pace continues.

Internal and sustainable growth rates

Two corporate finance measures estimate how fast a company can grow with its existing financing:

• Internal growth rate (IGR): the highest growth a company can achieve using only retained earnings, with no outside financing. IGR = (ROA × b) / (1 - ROA × b), where ROA is return on assets and b is the retention ratio (the share of earnings not paid out as dividends).
• Sustainable growth rate (SGR): the growth a company can fund while keeping its debt-to-equity ratio constant. SGR = ROE × b, where ROE is return on equity.

Hypothetical example: a company with an 8% ROA, a 15% ROE and a 60% retention ratio has an IGR of (0.08 × 0.6) / (1 - 0.048) ≈ 5.04% and an SGR of 0.15 × 0.6 = 9%. These rates differ from company to company because they depend on each firm’s profitability and payout policy. There is no standard figure, such as 10%, that applies to all companies.

Dividend growth and stock valuation

Under the dividend discount model, a share is worth the present value of all its future dividends. The Gordon Growth Model is the constant-growth version of that idea:

Price = D1 / (r - g)

where D1 is next year’s expected dividend, r is the investor’s required rate of return and g is the constant dividend growth rate. The model only works when g is below r.

Hypothetical example: with D1 of $2.00 and a required return of 8%, a 3% dividend growth rate gives a value of $2.00 / 0.05 = $40. Raise the growth assumption to 4% and the value becomes $2.00 / 0.04 = $50. One percentage point of assumed growth changes the estimate by 25%, which shows how heavily valuation depends on the growth input.

More broadly, because stock prices are thought to reflect the discounted value of future cash flows, rising prices imply that investors expect higher growth.

Investment growth rates

For a portfolio, the growth rate is essentially its rate of return, and the simple formula or CAGR applies. The figure investors usually care about is net growth after fees, transaction costs, taxes and inflation. Growth rate and return on investment (ROI) are calculated similarly, but ROI usually describes total gain relative to cost, while a growth rate is tied to a stated period. Neither accounts for the risk taken to get the result, which is what risk-adjusted measures like the Sharpe ratio address.

When money is added to or withdrawn from a portfolio, a simple start-to-end growth rate mixes investment performance with cash flows. A $10,000 account that becomes $15,000 because the owner deposited $5,000 did not grow 50% through investing.

Economic growth rates

The GDP growth rate uses the simple formula: (GDP this period - GDP prior period) / GDP prior period. Two refinements matter:

• Nominal vs. real: nominal GDP growth includes price increases. Real GDP growth strips out inflation. The exact adjustment is (1 + nominal growth) / (1 + inflation) - 1. With 5% nominal growth and 3% inflation, real growth is 1.05 / 1.03 - 1 ≈ 1.94%. Subtracting inflation from the nominal rate (5% - 3% = 2%) is a close approximation at low rates. Historical figures are on our U.S. inflation rate by year page.
• Quarterly vs. annualized: quarterly GDP growth is often reported at an annualized rate, which compounds the quarterly change over four quarters. A 1% quarterly change annualizes to about 4.06%.

Two consecutive quarters of declining real GDP is a widely used rule of thumb for a recession, although official recession dating in the U.S. considers a broader set of indicators. Retail sales growth is another closely watched economic growth rate, because it reflects consumer spending.

Industry and population growth rates

Industries have their own growth benchmarks. Technology sectors have historically grown faster than mature industries such as retail. Cyclical industries like autos tend to see sales grow in expansions and shrink in recessions, when households delay large purchases. A company’s growth is most meaningful when compared with its industry’s rate.

Population growth uses the same formula. Dividing total growth by the number of years gives a simple average annual rate. For long periods, the compound formula gives a more accurate yearly figure.

Example of Growth Rate: Two Hypothetical Companies

Company A is a large, established manufacturer. Company B is a young software firm. Their annual revenue over three years:

• Company A: $2.00 billion in year 1, $2.10 billion in year 2 (growth: 0.10 / 2.00 = 5.0%), $2.16 billion in year 3 (growth: 0.06 / 2.10 ≈ 2.9%).
• Company B: $40 million in year 1, $52 million in year 2 (growth: 12 / 40 = 30.0%), $70 million in year 3 (growth: 18 / 52 ≈ 34.6%).

Company A is growing modestly and slowing. Company B is growing fast and accelerating. Over the two years from year 1 to year 3:

• CAGR for A: (2.16 / 2.00)^(1/2) - 1 ≈ 3.92% per year.
• CAGR for B: (70 / 40)^(1/2) - 1 ≈ 32.29% per year.

In both cases the CAGR sits slightly below the arithmetic average of the two yearly rates (about 3.93% and 32.31%). The gap is small here because the yearly rates are close together.

The percentages favor Company B, but the dollars tell a different story. Company A added $160 million of revenue over the period, while Company B added $30 million. In year 3, Company A is still about 31 times larger. A high growth rate on a small base does not mean a larger absolute gain.

Limitations of Growth Rate

It ignores the path. A growth rate compares two points and says nothing about what happened between them. A stock at $50 today and $50 a year from now has a 0% growth rate whether it barely moved or swung between $30 and $70 in the meantime.

It is sensitive to the endpoints. Starting a measurement at a cyclical low makes growth look strong. Starting at a peak makes it look weak. Changing the start or end year by one period can change a CAGR substantially.

It ignores absolute size. As the example shows, 50% growth from $100,000 to $150,000 adds $50,000, while 5% growth at a large company can add millions.

Small or negative bases distort it. Growth from $1 to $5 is 400%, which sounds dramatic but may mean little. When the starting value is zero, the growth rate is undefined. When the starting value is negative, such as a move from a $2 million loss to a $1 million profit, the standard formula produces a misleading result. Analysts usually describe such changes in dollar terms or mark them “not meaningful.”

Gains and losses are asymmetric. A 50% decline followed by a 50% gain does not restore the starting value. One hundred falls to 50, then rises only to 75. Recovering from a 50% loss requires a 100% gain.

It is hard to compare across unlike variables. A 5% growth rate may be excellent for a consumer staples company and poor for a young technology firm. A 4% change in unemployment does not carry the same meaning as a 4% change in GDP.

Past growth does not guarantee future growth. Historical rates are the easiest basis for projections, but economic and industry conditions change, and fast-growing companies tend to slow as they get larger.

Growth Rate vs. Related Terms

• Growth rate vs. absolute growth: absolute growth is the raw change ($120,000). The growth rate is that change relative to the starting value (15%).
• Percent vs. percentage points: if a growth rate rises from 4% to 6%, it increased by 2 percentage points, which is a 50% increase in the rate itself. Mixing the two is a frequent source of confusion.
• Growth rate vs. CAGR: a growth rate can cover any single period. CAGR is a specific, annualized, compound version for multi-year periods.
• Growth rate vs. return: for an investment, they overlap, but total return includes income such as dividends and interest, while price growth alone does not.

FAQs

The Bottom Line

Investors, analysts and business owners use growth rates to compare change across companies, portfolios and economies of very different sizes. Always attach a period, divide by the starting value and use CAGR for multi-year figures. Then check the dollar change, the industry benchmark and the chosen endpoints, because a single percentage can hide volatility, small bases and slowing momentum.