Skip to content
MasterMath

Dollar Cost Averaging Calculator

Investing 100 at prices of 10, 8, 12, 9 and 11 gives an average paid of 9.80, below the 10.00 average of the prices themselves. Buying a fixed amount buys more units when it is cheap.

Currency and number format for

Average price you paid

—

Average price you paid—
Average of the prices—
Advantage of the method—
Units accumulated—
Total invested—
Current value—

How this was worked out

    The formula

    average paid = total invested ÷ total units bought

    Where it comes from

    Investing a fixed sum each period buys more units when prices are low and fewer when they are high, entirely automatically. The result is a harmonic mean rather than an arithmetic one, and it is always at or below the simple average of the prices.

    How to work it out by hand

    1. Divide each period's investment by that period's price to get the units bought
    2. Add up all the units
    3. Divide the total invested by the total units
    4. Compare it with the plain average of the prices

    What is worth knowing

    The mathematical advantage is real but small, and it is not the main reason the method works. Its real value is behavioural: it removes the decision of when to buy, which is the decision people get most consistently wrong. Two honest caveats. If you already have a lump sum, investing it all at once has historically beaten spreading it out about two thirds of the time, simply because markets rise more often than they fall — spreading it out buys peace of mind, not returns. And the advantage over the arithmetic average grows with volatility, so in a steadily rising market it amounts to almost nothing.

    Frequently asked questions

    Does dollar cost averaging beat investing a lump sum?

    Usually not, if you already have the lump sum. Markets rise more often than they fall, so waiting costs more than it saves about two thirds of the time. It buys emotional comfort, not return.

    Why is the average paid lower than the average price?

    Because a fixed sum buys more units at low prices. That skews the weighted average downwards; it is a harmonic mean, and it can never exceed the arithmetic one.

    Does it protect me from losses?

    No. It spreads the entry point, which reduces the impact of buying at a single bad moment. If the asset falls permanently, you still lose.

    How big is the advantage?

    It grows with volatility and vanishes in a smoothly rising market. In the example here it is about 2%, which is typical.