Doubling Time Calculator
The doubling time calculator is a tool that tells you how much time it takes for something double, assuming that it grows at a constant rate.
Doubling time by growth rate
| Rate | Exact periods | Rule of 72 |
|---|---|---|
| 1% | 69.66 | 72 |
| 2% | 35 | 36 |
| 3% | 23.45 | 24 |
| 5% | 14.21 | 14.4 |
| 7% | 10.24 | 10.29 |
| 10% | 7.27 | 7.2 |
| 12% | 6.12 | 6 |
| 15% | 4.96 | 4.8 |
| 20% | 3.8 | 3.6 |
| 25% | 3.11 | 2.88 |
The formula
time = ln(2) ÷ ln(1 + rate ÷ 100)
The rule of 72
Dividing 72 by the growth rate gives a quick doubling time that is remarkably good between about 5% and 12%. It works because ln(2) ≈ 0.693 and, over that range, the compounding correction happens to push the useful numerator up towards 72. Outside that band the rule drifts, which is why the exact figure is given above too.
What a percentage is
"Per cent" means "per hundred", so a percentage is just a fraction with 100 on the bottom. 15% is 15/100, which is 0.15 as a decimal. Every percentage calculation is therefore multiplication or division by a decimal — the percent sign is bookkeeping, not a new operation.
The three questions
Almost every percentage problem is one of three:
- What is P% of N? Multiply:
N × P/100 - A is what percent of B? Divide:
A/B × 100 - A is P% of what? Divide the other way:
A ÷ (P/100)
Recognising which one you have is most of the work; the arithmetic is straightforward once you do.