Dollar-Cost Averaging (DCA) Calculator
Dollar-cost averaging (DCA) is the practice of investing a fixed amount on a regular schedule (monthly, weekly, quarterly) regardless of price. You automatically buy more shares when prices dip and fewer when they spike. The resulting average cost equals the harmonic mean of all prices — mathematically always ≤ the arithmetic mean. Enter your amount per period, the actual price paid at each period and an optional current price to see DCA results alongside a lump-sum comparison at the first period’s price.
Please enter a valid number
Average cost / share
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Total invested ÷ total shares (the harmonic mean of prices, always ≤ their arithmetic mean).
Total shares
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Current value
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Versus lump-sum at the first price
- Lump-sum shares
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- Lump-sum value
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- Lump-sum return
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Excludes fees, taxes, dividend reinvestment and intra-period drift. The "average cost = harmonic mean" identity is a mathematical fact about DCA, not a claim that DCA beats lump-sum — in a steadily rising market lump-sum usually wins.
Formula
Total invested = amount × N Total shares = Σ (amount ÷ priceᵢ) Average cost = Total invested ÷ Total shares (= harmonic mean of prices) Current value = Total shares × current price Lump-sum shares = Total invested ÷ price₁
- · Average cost = the harmonic mean of all buy prices. By the AM-GM-HM inequality, this is always ≤ the simple arithmetic mean of those prices.
- · DCA does not guarantee beating lump-sum investing. Vanguard research (2012, 2023) found lump-sum outperformed DCA roughly two-thirds of the time across global stock and bond markets — DCA’s advantage is psychological and reduces sequence-of-returns risk near entry.
- · Calculations assume frictionless execution. Brokerage fees, bid-ask spreads, stamp duties and taxes are not included.
- · Dividends, dividend reinvestment, fresh contributions and FX moves are excluded — this is purely a buy-price averaging tool.
- · When the current price field is blank, the tool defaults to using the last entered price (mark-to-market at the most recent buy).
- · To model "fixed shares" rather than "fixed amount", record each period’s amount as (target shares × price that day) and use the tool to inspect the realised average cost.
Frequently asked
Does DCA mathematically guarantee beating lump-sum?
No. The only mathematical guarantee DCA provides is that your average cost ≤ the arithmetic mean of prices over the period (because the harmonic mean ≤ the arithmetic mean). But average cost is not the same as total return — if prices generally rise, having more money invested earlier wins, so lump-sum usually wins. Vanguard data across global markets shows lump-sum outperforms about ⅔ of the time. DCA’s real value is risk reduction near entry, smoother emotions and matching the cadence of a regular paycheque.
Can I use this for monthly index-fund or ETF contributions?
Yes — this is the canonical DCA use case. Put your monthly contribution (e.g. $500) in the amount field, and list the unit NAV / ETF price at each contribution date in time order. For broker "monthly stock plans" that execute at a volume-weighted average price within the month, use the price your broker reports on each month-end statement.
Does the order of the prices matter?
For the average cost itself, no — Σ(amount / priceᵢ) is commutative, so reordering the prices doesn’t change average cost or total shares. But it does affect the lump-sum comparison: the lump-sum baseline uses the *first* price in the list, so moving the highest price from start to end (or vice versa) flips who wins the lump-sum vs DCA verdict.
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