Compound Annual Growth Rate · Total return · Doubling time · Year-by-year projection.
| Year | Value at CAGR | Gain This Year | % of Final Value |
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CAGR is the compound annual growth rate: the single annual rate that would take a beginning value to an ending value if growth were steady and reinvested every year. It matters because total return alone hides the pace of growth.
Two investments can both gain 50%, but one may take three years and another may take twelve. CAGR puts them on the same annual scale. That makes it useful for comparing funds, business revenue, savings products, property, and any series with a start and end point. CAGR is not the actual path of returns. It smooths volatility into one representative rate.
Select a currency so every monetary result uses the symbol you expect.
Choose whether you know your beginning and ending values or your CAGR percentage.
Enter the beginning value for the starting point of the period.
Enter the ending value when using value mode, or type a CAGR when using rate mode.
Set the number of years. The field accepts 0.1 to 100.
Click a quick example if you want to load a common growth pattern.
Press Calculate to refresh CAGR, total return, gain, doubling time, and the projection table.
Use Copy, Share, or Embed when you want to save or reuse the result.
The calculator finds the steady annual rate that connects a beginning value to an ending value over a set number of years, assuming compounding.
Formula: CAGR = (Ending Value ÷ Beginning Value)^(1 ÷ Years) − 1
Formula: Ending Value = Beginning Value × (1 + CAGR)^Years
Formula: Total Return = (Ending Value − Beginning Value) ÷ Beginning Value
Formula: Absolute Gain = Ending Value − Beginning Value
Formula: Multiple = Ending Value ÷ Beginning Value
Formula: Doubling Time = ln(2) ÷ ln(1 + CAGR)
Formula: Rule of 72 estimate = 72 ÷ CAGR%
Formula: Year value at CAGR = Beginning Value × (1 + CAGR)^t
The mode toggle changes which side of the equation is solved. In value mode, beginning and ending values produce CAGR. In rate mode, beginning value and CAGR produce an ending value. Years must be at least 0.1 and no more than 100. Beginning and ending values accept zero or positive numbers. CAGR input accepts −100% to 200%. If beginning value is positive and ending value is zero, CAGR becomes −1, representing a complete loss. If beginning value is zero or negative, or ending value is negative, the interpretation asks for values greater than zero. The growth table projects up to 50 yearly rows using the computed CAGR. Currency selection changes the displayed symbol only; it does not convert between currencies.
An investor puts $18,000 into a fund. After 6 years, the account is worth $31,000. What was the compound annual growth rate?
Step 1: Divide ending value by beginning value. $31,000 ÷ $18,000 = 1.7222.
Step 2: Raise that ratio to the power of 1 ÷ 6. 1.7222^(0.1667) ≈ 1.09485.
Step 3: Subtract 1 to get the CAGR. 1.09485 − 1 = 0.09485, or about 9.49%.
Step 4: Calculate total return. ($31,000 − $18,000) ÷ $18,000 = $13,000 ÷ $18,000 = 72.22%.
Step 5: Find the absolute gain. $31,000 − $18,000 = $13,000.
Step 6: Estimate doubling time. ln(2) ÷ ln(1.0949) ≈ 7.65 years. The Rule of 72 gives 72 ÷ 9.49 ≈ 7.59 years.
Step 7: Review the year-by-year table. The calculator shows the value compounding from $18,000 toward $31,000, with each year’s gain and the percentage of the final value reached.
The takeaway: a 9.49% CAGR turns $18,000 into $31,000 over six years. That rate sits in the “Good” range on the calculator’s badge scale and is close to long-run stock market averages.
CAGR measures the steady annual rate that connects a beginning value to an ending value over a period, assuming gains are reinvested. It smooths out year-to-year volatility into one comparable growth figure.
Average annual return adds yearly returns and divides by the number of years. CAGR uses compounding and a geometric path, so it reflects the actual end value more accurately when returns vary.
Yes. Switch to CAGR mode, enter a beginning value, a CAGR percentage, and a number of years. The calculator computes the ending value and fills it into the ending value field.
If the beginning value is positive and the ending value is zero, the calculator sets CAGR to −100%. That represents a complete loss over the period.
The years field accepts decimals so you can model holding periods such as 2.5 years or 18 months. The growth table rounds up to the next full year for display, capped at 50 rows.
No. Total return measures the overall percentage change from beginning to ending value. CAGR converts that total change into an equivalent annual compounded rate.
Doubling time estimates how long an investment would take to double at the computed CAGR. It uses the natural logarithm formula and also shows the Rule of 72 approximation.
No. Currency selection changes the symbol shown beside monetary values. It does not convert amounts or alter the percentage-based CAGR.
Yes. A negative CAGR means the ending value is lower than the beginning value. The calculator labels this as a loss and still reports total return, gain, and the projected decline.
The Rule of 72 is a quick estimate for doubling time: divide 72 by the annual growth rate percentage. The calculator displays it alongside the more precise logarithmic doubling time.
Yes. Revenue, profit, user counts, portfolio values, and other financial series can be compared with CAGR as long as you have a beginning value, ending value, and time period.
The badge uses fixed ranges: Loss below 0%, Modest from 0% to 5%, Good from 5% to 10%, and Excellent at 10% or higher. These are general guides, not personalized investment ratings.
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