Growth Rate Calculator

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, the 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 and 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.

Read the bottom of that table with some suspicion. The rule is a shortcut for the real answer, ln(2) / ln(1 + r), and it is tuned to be accurate around 8%. At 8% the rule says 9 years and the truth is 9.01. At 36% the rule says 2 years and the truth is 2.25. At 72% the rule says 1 year and the truth is 1.28, so it is out by 28%. For the single-digit rates that savings accounts and index funds actually produce, the rule is excellent. For the growth rates a startup quotes, use the exact formula, which the calculator prints alongside it.

The rule also assumes annual compounding. Its continuous-growth cousin is the Rule of 69.3, since ln(2) ≈ 0.693, and that one is exact rather than approximate.

CAGR vs. Simple Growth, and 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%, while 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 = 24.47% per year
• Continuous = ln(1,200,000 / 500,000) / 4 = ln(2.4) / 4 = 21.89% per year
• Doubling Time at that CAGR = ln(2) / ln(1.2447) = 3.17 years, which the Rule of 72 estimates as 72 / 24.47 = 2.94

Note what the 140% is and is not. It is the total change across the whole four years, not a yearly rate, and dividing it by 4 to get 35% a year would be wrong: compounding 35% for four years turns $500,000 into $1.66M, not $1.2M. That is the trap the CAGR line exists to avoid, and it is why the calculator only offers a doubling time for the annualised methods.

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.