What this calculator does
Exponential growth is what happens when something increases by the same percentage, rather than the same fixed amount, in every period: a population growing 2% a year, an investment compounding at 7%, or a number of infections doubling on a fixed schedule. This calculator projects a starting value forward under exactly that pattern.
The exponential growth formula here is framed the way most people actually think about growth, as a percentage rate per period, rather than as a raw multiplier. Enter a starting value, a growth rate and a number of periods, and it works out the value at the end, the total change, and how long it takes to double at that rate.
The formula
The value after each period is multiplied by (1 + rate ÷ 100). Repeating that multiplication for the number of periods entered is the same as raising (1 + rate ÷ 100) to the power of the period count, which is what value = starting value × (1 + rate/100)^periods computes directly. Doubling time comes from solving that same equation for the number of periods where the value exactly doubles.
| Term | Meaning |
|---|---|
| Growth rate | The percentage increase applied in each period, compounding on the value from the previous period rather than the original starting value. |
| Periods | The number of times the growth rate is applied. Periods can be years, months, days or any other consistent interval, as long as the rate matches it. |
| Doubling time | The number of periods it takes the value to reach twice its starting size at a given growth rate, found from ln(2) ÷ ln(1 + rate/100). |
The inputs explained
| Field | What to enter |
|---|---|
| Starting value | The value you are starting from, before any growth is applied. |
| Growth rate per period (%) | The percentage growth rate applied in every period, compounding on the previous period’s value. |
| Number of periods | The number of periods the growth rate is applied over. |
When to use it
Projecting population or user growth
A population, customer base or user count growing at a roughly steady percentage rate per year is a textbook exponential growth curve; this projects it forward a chosen number of years.
Modelling an investment or savings balance
Compound growth at a fixed annual rate is exactly this calculation, with the starting value as the initial deposit and periods as years (or another compounding interval, provided the rate matches it).
Comparing two growth rates over the same horizon
Running the same starting value and period count at two different rates shows exactly how much a small difference in growth rate compounds into over time, which flat percentage comparisons alone do not make obvious.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Value after 10 periods at different exponential growth rates
A fixed starting value of 1,000 over 10 periods, at a range of growth rates.
| Growth rate per period | Value after 10.00 periods | Doubling time at this rate |
|---|---|---|
| 1% | 1,104.62 | 69.66 periods to double |
| 2% | 1,218.99 | 35.00 periods to double |
| 5% | 1,628.89 | 14.21 periods to double |
| 10% | 2,593.74 | 7.27 periods to double |
| 15% | 4,045.56 | 4.96 periods to double |
| 20% | 6,191.74 | 3.80 periods to double |
How a fixed 5% growth rate compounds over more periods
A fixed 5% growth rate, projected over a range of period counts.
| Number of periods | Value after N periods | Overall growth over the full period |
|---|---|---|
| 5 | 1,276.28 | 27.6% |
| 10 | 1,628.89 | 62.9% |
| 15 | 2,078.93 | 107.9% |
| 20 | 2,653.30 | 165.3% |
| 25 | 3,386.35 | 238.6% |
| 30 | 4,321.94 | 332.2% |
Questions
What is the exponential growth formula used here?
Value = starting value × (1 + rate/100)^periods. It is the same relationship as compound interest, just applied to any quantity that grows by a fixed percentage each period rather than a currency amount specifically.
How is this different from a raw base-and-exponent exponential calculation?
The underlying maths is identical, but this calculator takes a percentage growth rate as the input (such as "grows 5% per year") rather than a raw base multiplier like 1.05, which is closer to how growth rates are usually reported or discussed.
What does the exponential growth curve look like?
It starts relatively flat and curves sharply upward as periods increase, because each period’s growth is calculated on an already-larger value than the period before. That accelerating shape is the defining feature of exponential, as opposed to straight-line, growth.
Can this calculator model decline instead of growth?
Yes, by entering a negative growth rate. A rate of -100% is the lower limit, since a rate at or below that would reduce the value to zero or below in a single period, which the calculator rejects with a message rather than showing an invalid result.
To evaluate a raw y = a × bˣ exponential function directly from its base rather than a percentage rate, see the exponential function calculator.