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    Performance / Average return

    Average Return Calculator

    The arithmetic average return and the compound annual growth rate for the same investment. They differ, and the difference is why a fund can report a positive average and still lose money.

    Average return15.00%CAGR9.60%Total gain$15,000
    Average return
    15.00%
    Per year, simple
    CAGR
    9.60%
    Compounded
    Total gain
    $15,000
    Start to end
    Multiple
    2.50×
    End over start
    Two averages
    Same investment, two definitions.
    Two averages
    MeasureValue
    Arithmetic average15.00%
    CAGR9.60%
    Total return150.00%
    Gap5.40 pp

    The gap widens with volatility; with a single start and end it is just the difference between linear and geometric growth.

    Inspect the model
    Choose a quick result view, a scaled comparison, or the complete diagnostic set.
    Linear against compound growth
    The arithmetic average draws a straight line; CAGR draws the curve that actually arrives.
    Linear against compound growth$0$35.0k$70.0k$105.0k$140.0k$175.0kY1Y1Y2Y2Y3Y3Y5Y5Y7Y7Y10Y10Y15Y15Y20Y20Y30Y30LinearCAGR
    Canonical equations
    The exact relationships implemented by this engine.

    (end − start) / start / years · Linear.

    (end/start)^(1/years) − 1 · Geometric.

    finance methodology

    A clear path from inputs to results.

    The arithmetic average return and the compound annual growth rate for the same investment. They differ, and the difference is why a fund can report a positive average and still lose money.

    Step-by-step methodWorked exampleAssumptions explained

    How to use

    1. Set starting value ($).
    2. Set ending value ($).
    3. Set years held.
    4. Read the headline metrics, then check the table for the detail.

    The formula

    (end−start)/start/years(end − start) / start / years

    Reference: CAGR is the geometric mean and the arithmetic average is linear (Broverman, Mathematics of Investment and Credit).

    Worked example

    At the default inputs

    Inputs
    • Starting value ($): 10000; Ending value ($): 25000; Years held: 10
    Calculation path
    1. 1

      Total gain → $15,000 CAGR → 9.60%

    Result

    Average return: 15.00% · CAGR: 9.60% · Total gain: $15,000

    Interpreting the result

    $10,000 growing to $25,000 over 10.0 years is 15.00% a year simple, or 9.60% compounded.

    Assumptions & limitations

    • Only the start and end values are known.
    • No intermediate cash flows.
    • Both figures ignore volatility along the path.

    Frequently asked questions

    Which number should I quote?

    CAGR, if you are describing what the investment actually did; the arithmetic average overstates it.

    Does this account for dividends?

    Only if the ending value includes reinvested dividends.

    When do they differ most?

    When returns are volatile — the gap is roughly half the variance.

    Methodology last reviewed 2026-10-22. Results are informational and not financial or engineering advice — see our disclaimer.