How it works
Two things about this calculator are easy to get wrong, and both matter more than the headline numbers. The first is that it is deterministic, not a simulation. The price path is a straight line from the starting price to the ending price, split evenly across the months you enter — month one is the start price, the last month is the end price, everything in between is the line between them. The second is the consequence of that: the volatility input does nothing. The field is there, with a help note about Bitcoin’s 60–80% historical range, but the engine never reads it, so dialling volatility from 10% to 150% returns the identical result. If you came here to model a bumpy ride, this tool cannot do it; it models a smooth glide from A to B and therefore can never show you the "lump sum beats DCA about two-thirds of the time" finding from Vanguard’s historical-market work, because there is no randomness in it to produce that statistic. What it does compute is exact. Each month it buys total-invested ÷ that month’s price worth of the asset, and the average buy price is the total invested divided by the total tokens — which is a weighted harmonic mean of the path prices, so it sits below the simple midpoint. Worked example on the defaults: $500 a month, a start price of $40,000, an end price of $80,000, over 24 months. Total invested = $500 × 24 = $12,000. The path runs $40,000 to $80,000; buying $500 along it accumulates tokens whose average cost is $56,845, so the holding is worth 0.211 × $80,000 = $16,888, a 40.7% return. A lump sum of the same $12,000 at the $40,000 start would be 0.3 tokens, worth $24,000 at the end — a 100% return. In a rising market the lump sum wins, because DCA deploys the money slowly and so misses part of the climb; it buys cheap early but also buys expensive late, and the average cost ends up above the start price. Now flip it. End price $40,000 with the same $80,000 start: DCA finishes at $8,194 (−31.7%) and the lump sum at $6,000 (−50%), so DCA loses less, because averaging in during the fall keeps the average cost down. End prices equal (a flat $50,000): both finish at $12,000, 0%, average cost $50,000. That pair of outcomes is the real lesson. DCA’s edge is not a higher return in rising markets — lump sum usually wins those — it is lower risk and a lower average cost when prices fall or chop, plus the behavioural advantage of never having to pick the bottom. The SEC’s investor bulletin on virtual currencies (at sec.gov) is the place to read the same caution from the regulator: crypto is volatile, the tax treatment is that of property, and only invested amounts you can lose should be used. None of that changes the arithmetic above, but it is the arithmetic that decides whether DCA was the right frame in the first place.
Formula
price in month i = start + (end − start) × (i ÷ months), for i = 0 … months − 1
(a straight line — the volatility input is NOT used)
total invested = monthly investment × months
total tokens = Σ (monthly investment ÷ price in month i)
average buy price = total invested ÷ total tokens
DCA value = total tokens × end price
DCA return % = (DCA value − total invested) ÷ total invested × 100
lump sum value = (total invested ÷ start price) × end price
Worked example — $500/mo, $40,000 → $80,000, 24 months
total invested = 500 × 24 = $12,000
average buy price = $56,845
DCA value = 0.211 × 80,000 = $16,888 (40.7%)
lump sum value = (12,000 ÷ 40,000) × 80,000 = $24,000 (100%)
→ in a rising market lump sum wins; DCA deploys too slowly
Falling market — $80,000 → $40,000
DCA value $8,194 (−31.7%) vs lump sum $6,000 (−50%)
→ DCA loses less, because averaging in lowers the cost basis
Flat market — $50,000 → $50,000: both $12,000, 0%, avg cost $50,000
Tips
- Ignore the volatility slider on this tool — the engine interpolates a straight line and never reads the value, so it is decorative. If you want to reason about a volatile path, do it in your head: more volatility is exactly where DCA’s average-cost advantage shows up, and this calculator cannot show it.
- Read the rising-market result as a warning, not an endorsement of DCA. When the end price is above the start, lump sum almost always finishes ahead because DCA commits the money gradually and misses part of the climb. DCA earns its keep when prices fall or chop, not when they rise.
- Treat each monthly buy as its own tax lot. DCA creates two dozen small positions instead of one, which is fine but means more bookkeeping, and in a rising market you owe gains on every lot you ever sell — the same property/capital-gains treatment the IRS applies to crypto under Notice 2014-21.
- Size the monthly amount so a 70% drawdown mid-plan does not derail you. The DCA mechanic smooths the entry price but does nothing to the asset’s risk; the SEC bulletin on virtual currencies is the regulator’s view on how much of a portfolio this kind of volatility deserves.
Frequently asked questions
- What does the volatility input actually do?
- Nothing. The engine builds a straight-line price path from the starting price to the ending price and never references the volatility field, so changing it from 10% to 150% returns the identical numbers. The field and its help text about Bitcoin’s historical range are left over from a description that promised a random walk the calculator does not perform. Use the start and end prices to set the trend you want to test, and treat volatility as not implemented rather than as a risk dial.
- Why does lump sum beat DCA here when prices rise?
- Because DCA commits the money month by month, so during a climb it is only partially invested while the price is rising — it buys some at the low start price but also keeps buying as the price approaches the high end, and its average cost lands above the start. A lump sum at the start owns the whole position from day one and captures the entire move. On the defaults that is $24,000 from lump sum versus $16,888 from DCA. The flip side is that this only helps when the end price is above the start; when prices fall, the slower deployment is what protects you, which is the next question.
- When does DCA actually win?
- When the end price is at or below the start, or when the path is choppy rather than smooth. In the falling case the tool shows — $80,000 down to $40,000 — DCA ends at $8,194 and lump sum at $6,000, so averaging in during the decline keeps the average cost down and DCA loses less. More generally, DCA’s value is risk reduction and behaviour: you never have to pick the bottom, and you avoid the real risk of dumping everything at a local top. Vanguard’s historical-market work finds lump sum ahead roughly two-thirds of the time in trending-up markets, which is exactly why DCA is the more defensive, not the higher-return, choice.
- Is the average buy price the simple average of the start and end?
- No — it is a weighted harmonic mean of every monthly price along the path, which always sits below the simple arithmetic average. On the defaults the start is $40,000 and the end is $80,000, whose simple average is $60,000, but the tool reports an average buy price of $56,845 because you buy more tokens when the price is low and fewer when it is high. That below-midpoint average is the mechanical reason DCA can show a gain even when the end price is only modestly above the start, and the reason it softens a fall.
- How is this taxed?
- The same as any crypto: the IRS treats virtual currency as property, so each monthly buy is a separate tax lot and selling or exchanging it later is a capital gain or loss measured from that lot’s cost. Holding more than a year gets long-term rates; under a year gets ordinary rates; and US brokers report spot disposals on Form 1099-DA from the 2025 tax year. DCA therefore creates more lots to track than a single lump sum, which is manageable but is real bookkeeping. The engine models none of this, so the returns shown are pre-tax.
- Can I model a flat or falling market to stress-test?
- Yes, and it is the most useful thing to do with this tool given that it cannot model volatility. Set the end price equal to the start to see the break-even case (both finish at the total invested, 0%), or below the start to see DCA limit the damage. Those two scenarios, plus the rising one, cover the range the calculator can actually represent; anything involving a bumpy path has to be reasoned about separately, because the straight-line engine cannot produce it.