Growth Rate Calculator
Calculate simple growth rate, CAGR (compound annual growth rate), or continuous growth rate — plus doubling time using the Rule of 72.
Growth Rate Formulas
There are three main ways to measure growth, depending on your data and purpose.
1. Simple Growth Rate
Simple Growth Rate (%) = (New Value − Old Value) / Old Value × 100
Best for: single-period comparisons (one year, one quarter, one month).
2. CAGR — Compound Annual Growth Rate
CAGR = (Ending Value / Beginning Value)^(1 / Years) − 1
CAGR smooths out volatility and gives the steady annual rate that would produce the same ending value. It’s the preferred metric for multi-year investment and revenue analysis.
Example: A company grows revenue from $2M to $10M over 5 years. CAGR = (10 / 2)^(1/5) − 1 = 5^0.2 − 1 = 1.3797 − 1 = 37.97% per year
The simple 5-year growth rate would be 400%, which is accurate but doesn’t communicate the annual story.
3. Continuous Growth Rate
Continuous Growth Rate = ln(New Value / Old Value) / Years
This is used in advanced financial modeling, physics, and biology. It assumes growth happens at every instant (not at discrete intervals). It’s always slightly lower than the equivalent CAGR.
The Rule of 72 — Doubling Time
Doubling Time (years) = 72 / Growth Rate (%)
This mental math shortcut tells you approximately how long it takes to double an investment or quantity.
| Growth Rate | Doubling Time |
|---|---|
| 2% | 36 years |
| 4% | 18 years |
| 6% | 12 years |
| 8% | 9 years |
| 10% | 7.2 years |
| 12% | 6 years |
| 18% | 4 years |
| 24% | 3 years |
| 36% | 2 years |
| 72% | 1 year |
CAGR vs. Simple Growth — Why It Matters
If a $100 investment falls 50% in year 1 (to $50), then rises 100% in year 2 (back to $100), the average annual return by simple averaging is 25% — but the actual return is 0%. CAGR correctly shows 0%.
Always use CAGR for multi-year analysis. Simple averages of percentage changes are misleading.
Applications
- Revenue growth: SaaS companies often report CAGR over 3–5 years
- Population growth: Countries use annual % change (simple or continuous)
- Investment returns: Index funds report 10-year CAGR
- Inflation: CPI growth is typically expressed as year-over-year simple %
- Biology: Bacterial colony growth uses continuous (exponential) rate
Worked Example — All Three Methods
Revenue grew from $500,000 to $1,200,000 over 4 years.
- Simple Growth = ($1,200,000 − $500,000) / $500,000 × 100 = 140%
- CAGR = (1,200,000 / 500,000)^(1/4) − 1 = 2.4^0.25 − 1 = 24.4% per year
- Continuous = ln(1,200,000 / 500,000) / 4 = ln(2.4) / 4 = 21.9% per year
- Doubling Time (at 24.4% CAGR) = 72 / 24.4 = 2.95 years
Pro Tips
- CAGR is always lower than the arithmetic average return when returns vary year to year.
- For continuous processes (biology, physics), use the continuous rate.
- For business and finance, CAGR is the gold standard for multi-year comparisons.