Exponential growth calculator
Enter a starting value, the growth per period in percent and the number of periods. You get the end value, the growth factor, the doubling time and the value after every period.
Fill in the fields; the answer appears here straight away.
How it's worked out
How it works
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Enter the values
Type the numbers or the formula. Decimals may use a point or a comma. No idea? Click Fill in an example.
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Instant answer
The answer appears as you type, with the most important intermediate values.
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See the working
Under "How it's worked out" you see the steps, handy for checking your own calculation.
The formula
N(t) = N₀ · gᵗ, where the growth factor g = 1 + percentage ÷ 100. With 5% growth per year, g = 1.05, and 1,000 grows to 1,000 × 1.05¹⁰ ≈ 1,628.89 after 10 years.
Doubling time
The doubling time is how many periods it takes to double: log(2) ÷ log(g). At 5% that is about 14.2 periods. A rough rule is the rule of 72: 72 ÷ 5 ≈ 14.4.
Where you see it
Compound interest, population growth, bacteria and viral spread all grow exponentially, at least for a while. For something that shrinks by a percentage, use the exponential decay calculator.
Doubling time by growth rate
| Growth per period | Doubling time |
|---|---|
| 1% | 69.7 periods |
| 2% | 35.0 periods |
| 3% | 23.4 periods |
| 5% | 14.2 periods |
| 7% | 10.2 periods |
| 10% | 7.3 periods |
Exponential versus linear
1,000 that grows by 50 every period reaches 1,500 after ten periods. 1,000 that grows by 5% per period reaches 1,628.89, because each period's growth is added to the base that the next period grows on. The longer the period, the larger the difference.
Reading the list of values
The calculator also lists the value after every period, so you can see when the number crosses a target. For 5% on 1,000, it passes 1,500 in the 9th period (1,551.33). Use the exponent calculator to check a single factor such as 1.05⁹.
Frequently asked questions
How do I find the growth rate from two values?
Divide the end value by the start value, take the t-th root and subtract 1. From 1,000 to 1,628.89 in 10 periods: (1.62889)^(1/10) = 1.05, so 5% per period.
What counts as a period?
Anything you like, as long as you are consistent: years, months, days or hours. The growth percentage must be per that period.
How is this different from compound interest?
The maths is the same. The [compound interest calculator](/en/math/compound-interest-calculator) adds monthly deposits and works with yearly rates, while this one is for anything that grows by a percentage per period, such as a population.
How accurate is the rule of 72?
Good between about 4% and 10%. At 5% it gives 14.4 periods against the true 14.2. At very low or very high rates it drifts further off, so use the doubling time shown by the calculator.