Compound Growth Calculator Formula

Understand the math behind the compound growth calculator. Each variable explained with a worked example.

Use the Compound Growth Calculator

Formulas Used

CAGR (%)

cagr = (pow(final_val / initial, 1 / periods) - 1) * 100

Total Growth Factor

growth_factor = final_val / initial

Total Return (%)

total_return = ((final_val - initial) / initial) * 100

Variables

VariableDescriptionDefault
initialInitial Value1000
final_valFinal Value2000
periodsNumber of Periods5

How It Works

How to Calculate Compound Annual Growth Rate

Formula

CAGR = (Final / Initial)^(1/n) - 1

CAGR is the constant annual growth rate that would take the initial value to the final value over n periods. It smooths out volatility and gives a single rate that represents the equivalent steady growth. Multiply by 100 to express as a percentage.

Worked Example

An investment grows from $1,000 to $2,000 over 5 years.

initial = 1000final_val = 2000periods = 5
  1. 01Growth factor = 2000 / 1000 = 2.0
  2. 02CAGR = 2.0^(1/5) - 1 = 2.0^0.2 - 1
  3. 03= 1.14870 - 1 = 0.14870
  4. 04CAGR = 14.87% per year
  5. 05Total return = 100%

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