Exponential Growth Calculator
Project a value forward at a constant growth rate and see the final amount, the multiplier and the doubling time.
How to use it
- Enter the starting value, the growth rate per period and how many periods.
- Use a negative rate for exponential decay.
- Doubling time tells you how many periods it takes to grow 2×.
Examples
| 1000 at 5% for 10 periods | 1628.89 |
| Growth 7% | Doubles in about 10.2 periods |
Exponential growth compounds a fixed percentage rate onto an ever-larger base, so the absolute increase gets bigger every period even though the rate stays constant: x(t) = x₀ × (1 + r)^t. It's the model behind population growth, investment returns, viral spread and — with a negative rate — radioactive decay and depreciation.
Worked example — user base growth
An app starts with 1,000 users and grows 5% a month. After 10 months: 1,000 × 1.05¹⁰ ≈ 1,629 users. Linear thinking (adding 50 users a month, the month-1 increase) would predict only 1,500 — exponential growth pulls ahead because each month's 5% is calculated on the larger, already-grown total, not the original 1,000.
Doubling time and the rule of 72
Doubling time — how many periods until the value doubles — is ln 2 ÷ ln(1 + r). At 7% a year, that's ln 2 ÷ ln 1.07 ≈ 10.24 years. The rule of 72 (72 ÷ rate) is the classic mental shortcut: 72 ÷ 7 ≈ 10.3, close enough for a back-of-envelope estimate at typical growth rates.
Questions people ask
What is the rule of 72?
A shortcut: divide 72 by the percentage growth rate to estimate the doubling time. At 8% that predicts 9 periods, against an exact 9.006.
Is anything sent to a server?
No. Every calculation runs in your browser, so nothing you type is uploaded and the page keeps working offline once it has loaded.
Last updated 17 August 2026