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Miraç Özdemir
Investment Profitability

CAGR Calculator (Compound Annual Growth Rate)

Calculate the compound annual growth rate (CAGR) from a start and end value, the total growth and a projection at the same rate.

Version 1

Things to keep in mind:

  • CAGR is a smoothed rate of a past period; it does not guarantee future returns and the projection is only an assumption.
  • Interim cash flows (extra contributions, dividends, rent) are ignored; use the internal rate of return (IRR) for those.
  • The rate is nominal, not adjusted for inflation; use the Fisher equation for real growth.

Calculator

Values and period

Initial value of the investment, sales or price (greater than 0). Any unit, but use the same unit as the end value.

Value at the end of the period (greater than 0).

Time between the two values in years; decimals allowed (e.g. 18 months = 1.5).

Number of further years to project the end value at the same growth rate. 0 returns the end value.

After the first calculation, the result updates automatically when you change a value.

Result

Enter the values and press Calculate to see the result here.

About this tool

CAGR (Compound Annual Growth Rate) is the constant yearly rate at which a value would have had to grow to get from its starting point to its end point. It reduces volatile series such as investment returns, sales, subscribers or property prices to one comparable annual rate.

Formulas

  • CAGR = (End / Start)^(1 / Years) − 1
  • Total growth = (End − Start) / Start
  • Growth multiple = End / Start
  • Projection = End × (1 + CAGR)^(extra years)
  • Equivalent monthly rate = (1 + CAGR)^(1/12) − 1

Example 1

A value rising from 100,000 to 250,000 in 5 years: 250,000 / 100,000 = 2.5; 2.5^(1/5) − 1 = 20.11% CAGR. Total growth is 150%, the growth multiple 2.5000 and the equivalent monthly rate 1.5389%. If the same rate continues for 3 more years the value reaches about 433,215.53.

Example 2 — a decimal period

1,000,000 rising to 3,500,000 in 7.29 years: CAGR 18.75%; total growth 250.00%; absolute change 2,500,000.00. If the rate continues for 2 more years the value is 4,935,512.48.

Example 3 — a loss in value

200 falling to 150 in 2.5 years: CAGR −10.87%, total growth −25.00%, absolute change −50.00; after 1 more year at the same rate the value is 133.70.

CAGR hides the ups and downs in between; it only gives the smoothed rate between the two end points. The period may be decimal, so months or days can be converted to years. Percentages are rounded HALF_UP to 2 decimals (monthly rate 4).

How to read the result

CAGR is the rate you would have needed each year to get from the start to the end value; it puts investments or series of different lengths on the same annual basis so you can compare them. Total growth and the growth multiple summarize the whole period in one figure; negative values indicate a loss in value. The projection is an assumption that the past rate continues and does not guarantee future returns. The rate is nominal, not adjusted for inflation.

How to use

  1. Enter the start value.
  2. Enter the end value (same unit).
  3. Enter the period between them in years (decimals allowed).
  4. Optionally enter the projection years.
  5. Press Calculate.

Notes

Results use HALF_UP rounding: percentages to 2 decimals (monthly rate 4), amounts to 2 decimals. The projection uses the unrounded CAGR. CAGR is negative when the end value is below the start value.

Sources

Frequently asked questions

4 questions

  1. No. The arithmetic average is a simple mean of yearly returns and overstates growth when returns are volatile. CAGR includes compounding and matches the real growth between the end points.

Next step

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