Population Growth Calculator
Population after a number of years at a continuous growth rate, with the doubling time.
Results
What this tool does
Continuous exponential growth is the model behind population projections, and the same equation describes compound interest, bacterial cultures and the early phase of an epidemic. A negative rate works too and gives decline. The catch is that nothing grows exponentially forever — food, space or energy always intervenes.
Formula
P = P₀ e^(rt) ; doubling time = ln2 ÷ r
Variables
| Symbol | Meaning | Unit |
|---|---|---|
p0 | Initial population | — |
r | Growth rate | %/a |
t | Years | — |
P | Final population | — |
DB | Doubling time | a |
CH | Difference | — |
R7 | Doubling time | a |
PC | Percentage | % |
Worked example
- Initial population10,500,000
- Growth rate1.2 %/a
- Years25
- Final population14,173,517
- Doubling time57.76 a
- Difference3,673,517
- Doubling time58.33 a
- Percentage34.986 %
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
Frequently asked questions
What is the rule of 70?
A shortcut for doubling time: divide 70 by the percentage growth rate and you get the years to double, close enough for mental arithmetic. It works because the natural logarithm of two is about 0.693, and multiplying by a hundred gives 69.3, which rounds conveniently. The fourth result shows the shortcut beside the exact answer so you can see how close it stays.