Growth Rate Calculator

Growth that builds on itself

Plenty of things grow by a percent of what is already there: a following on social media, a population of bacteria, the number of customers telling their friends. That kind of growth starts slow and then speeds up, because each step adds a share of a bigger total. It is called exponential growth.

This calculator does two things with it. Project exponential growth takes a starting value, a rate and a number of periods and tells you where you end up, plus how long it takes to double. Growth between two values works backwards from real numbers to the rate per period, in months, weeks or any other step you like.

How to use it

1. Pick Project exponential growth or Growth between two values.
2. To project, enter the starting value, the growth rate per period as a percent, and the number of periods. Choose Once per period for growth that happens in steps, or Continuous for growth that happens all the time.
3. To measure, enter the start and end values and how many periods passed between them.
4. Read the answer, then look at the extra lines: total growth, doubling time, or the per-period rate in a few different forms.

The exponential growth formula

x(t) = x₀ × (1 + r)^t          growth once per period
x(t) = x₀ × e^(r × t)          continuous growth
r = (end ÷ start)^(1 ÷ t) − 1    growth rate from two values
doubling time = ln 2 ÷ ln(1 + r)

Here x₀ is the starting value, r is the rate as a decimal (8% is 0.08), and t is the number of periods. The letter e is a constant, about 2.718, that appears whenever growth happens continuously instead of in steps.

The two versions give close answers when the rate is small. At 8% for 12 periods, stepwise growth gives about 1,259 from 500 and continuous growth gives about 1,306.

Worked example: 500 followers growing 8% a month

An account has 500 followers and grows by 8% a month. Where will it be in a year?

• Growth factor: 1.08^12 = 2.5182
• End value: 500 × 2.5182 = 1,259.09
• Total growth: 151.82%
• Doubling time: ln 2 ÷ ln 1.08 = 9.01 periods

After 12 months the account has about 1,259 followers, and it doubles roughly every 9.01 months. Notice that 8% for 12 months is far more than 12 × 8% = 96%, because every month adds 8% of a larger number.

The rule of 70

A handy shortcut for doubling time is to divide 70 by the growth rate in percent. At 7% a period, something doubles in about 10 periods. The rule is close for small rates and drifts as rates get bigger.

Common mix-ups

• Multiplying the rate by the number of periods. That is linear growth, which is only right when the same fixed amount is added each time.
• Mixing period lengths. A monthly rate of 2% is not a yearly rate of 24%. Keep the rate and the number of periods in the same unit.
• Expecting it to last. Real growth slows down as markets fill up and resources run out. Use projections for a sense of scale, not as a forecast.
• Measuring yearly growth here when a single figure is all you need. For growth across years, the CAGR calculator gives the standard yearly rate.

Frequently asked questions

Related calculators

• CAGR CalculatorThe compound annual growth rate between two values, or where a growth rate leads.
• Percentage Change CalculatorPercent increase or decrease from an old value to a new one, or raise and lower a number by a percent.
• ROI CalculatorReturn on investment in percent, plus the yearly rate when you know how long it took.
• Percentage CalculatorFind a percent of a number, what percent one number is of another, or the whole from a part.

See all free calculators