Growth Rate Calculator

Find the growth rate between two values, project future growth, or measure population growth

What do you want to calculate?

Starting Value

Ending Value

Number of Periods

months

Period Length

Results

Monthly Growth Rate (compound)16.50%

Annualized Growth Rate525.00%

Total Percent Change150.00%

Total Change1,500.00

Average Change per Month (simple)25.00%

Time to Double (months)4.54

What is a Growth Rate?

A growth rate measures how fast something changes over time, expressed as a percentage per period. It works for anything you can count or measure: revenue, sales, users, subscribers, income, website traffic, prices or population. This growth rate calculator finds the steady rate of growth per period that takes your starting value to your ending value, for any period length from days to years. It can also project a value forward at a known rate, or measure a population growth rate and project it to a future year.

Most real growth compounds. When revenue grows 10% this month and 10% again next month, the second month's growth is 10% of a larger number. That is why the compound growth rate, not the simple average, is the right way to describe growth over several periods. For annual investment returns specifically, our CAGR Calculator gives the same answer with years as the period.

How to calculate growth rate

To calculate a growth rate by hand:

Divide the ending value by the starting value.
Raise the result to the power of 1 divided by the number of periods.
Subtract 1 and multiply by 100 to get a percentage.

Example: a newsletter grows from 1,000 to 2,500 subscribers in 6 months. 2,500 / 1,000 = 2.5. 2.5^(1/6) = 1.165. 1.165 - 1 = 0.165, so the monthly growth rate is 16.5%. Compounded over 12 months, that is an annualized growth rate of about 525%.

Growth rate formula

The compound growth rate per period is:

Growth Rate = (Ending Value / Starting Value)^(1/n) - 1

Where:

Ending Value = the value at the end of the period
Starting Value = the value at the beginning
n = the number of periods (days, weeks, months, quarters or years)

The other results use these formulas:

Percentage Growth = (Ending Value - Starting Value) / Starting Value × 100

Annualized Rate = (1 + Growth Rate)^(periods per year) - 1

Future Value = Starting Value × (1 + Growth Rate)^n

Time to Double = ln(2) / ln(1 + Growth Rate)

Periods per year are 365 for days, 52 for weeks, 12 for months, 4 for quarters and 1 for years.

Example: a salary rises from $50,000 to $65,000 over 5 years. (65,000 / 50,000)^(1/5) - 1 = 1.3^0.2 - 1 = 5.39% per year. Compare that with inflation over the same years to see your real raise.

Percentage growth vs. growth rate

Percentage growth is the total change from start to end, regardless of how long it took. The growth rate is the change per period. They answer different questions: "how much did it grow?" versus "how fast did it grow?"

Percentage Growth = (End - Start) / Start × 100

Growth Rate per Period = (End / Start)^(1/n) - 1

Example: sales grow from 100 to 150 units over 5 years. The percentage growth is (150 - 100) / 100 = 50%. The annual growth rate is 1.5^(1/5) - 1 = 8.45%. Dividing 50% by 5 years gives 10%, the simple average, which overstates the real rate because it ignores compounding.

Population growth rate

A population growth rate is the yearly percentage change in the number of people in a city, region or country. Choose "Population growth rate" above, enter two counts and the years between them, and pick a future year to project to.

Annual Growth Rate = (P₁ / P₀)^(1/t) - 1

Exponential Growth Rate = ln(P₁ / P₀) / t

Projected Population = P₁ × (1 + Annual Growth Rate)^(years ahead)

P₀ is the starting population, P₁ the ending population and t the years between them. The World Bank and many demographers report the exponential rate; it is slightly lower than the annual compound rate for a growing population, and the two are almost identical for small rates.

Example: a town grows from 50,000 people in 2015 to 62,000 in 2025. The annual population growth rate is (62,000 / 50,000)^(1/10) - 1 = 2.17% (2.15% as an exponential rate). If that pace continues, the town reaches about 76,880 people in 2035 and doubles in about 32 years.

When to Use This Calculator

Use it whenever you know where something started and where it ended and want the rate in between: month-over-month startup growth, year-over-year sales, subscriber growth, salary history, traffic growth after a launch, or a city's population between two censuses. Switch to the future value mode to see where a known rate leads. For detailed revenue plans, use the Revenue Growth Calculator, and for savings and investments, the Compound Interest Calculator.

Tips for Best Results

Count periods, not data points: January to July is 6 months of growth, not 7.
Compare like with like: Seasonal businesses should compare the same month or quarter across years.
Prefer the compound rate: The simple average overstates growth; use it only as a rough comparison.
Watch short windows: A high monthly rate over two or three months rarely holds for a whole year, so treat large annualized figures and long projections with care.
Separate price from volume: For sales growth, check whether the change came from more customers or higher prices. The Sales Growth Calculator breaks this down.

Frequently Asked Questions

How do you calculate growth percentage between two numbers?

Subtract the starting number from the ending number, divide by the starting number and multiply by 100. Growing from 1,000 to 2,500 is (2,500 - 1,000) / 1,000 × 100 = 150% growth. If the change happened over several periods, the growth rate per period is (2,500 / 1,000)^(1/n) - 1, which over 6 months is 16.5% a month.

What is the formula for rate of growth?

The rate of growth per period is (Ending Value / Starting Value)^(1/n) - 1, where n is the number of periods. This is the compound growth rate: the steady rate that turns the starting value into the ending value. When the periods are years, it is the same as CAGR (compound annual growth rate).

How do you calculate annual growth rate over multiple years?

Divide the final value by the first value, raise the result to the power of 1 divided by the number of years, and subtract 1. A salary that rose from $50,000 to $65,000 over 5 years grew 30% in total, which is an annual growth rate of (65,000 / 50,000)^(1/5) - 1 = 5.39%. Dividing 30% by 5 gives 6%, which overstates it because it ignores compounding.

How do you calculate population growth rate?

Use the same compound formula with years as the period: (Ending Population / Starting Population)^(1/years) - 1. A town that grew from 50,000 to 62,000 people in 10 years has an annual population growth rate of 2.17%. Demographers and the World Bank often use the exponential rate ln(P₁ / P₀) / t instead, which gives 2.15% for the same town.

Can a growth rate be negative?

Yes. A negative growth rate means the value shrank. Revenue that fell from $200,000 to $150,000 over 2 quarters is a 25% decline, or a growth rate of -13.4% per quarter. A population that fell from 50,000 to 42,000 over 10 years has an annual growth rate of -1.73%. Growth rates from a starting value of zero are undefined.