Compound growth calculator
“If an account grows at some rate per period, where does it end up — and what does the same account look like once returns arrive unevenly?”
Two modes, and the second is the interesting one. Ideal compounds a fixed return each period: the smooth curve everyone draws. Realistic draws each period from a win rate and average win and loss, runs it thousands of times, and reports the gap — which is always in one direction.
Free to use, nothing to sign up for, and nothing you type here is sent anywhere — the arithmetic runs in your browser.
What it computes
Ideal: balance = balance x (1 + net return) + contribution - withdrawal (each period)
Realistic: the typical (geometric) and ideal (arithmetic) paths are computed
deterministically; a seeded Monte Carlo supplies the 10th-90th
percentile band, the probability of profit and the median worst drawdown.What you type in
| Field | What it means | Example |
|---|---|---|
| Starting balance | The account. | $10,000 |
| Return per period % | Ideal mode's fixed rate. | 5 |
| Periods / unit | How many, and whether they are days, weeks, months or years. | 24 months |
| Contribution / withdrawal | Added or removed each period, after growth. | 0 |
| Fee % | Drag subtracted from each period's return. | 0 |
| Realistic mode: win rate, average win %, average loss % | The distribution of period outcomes. | 60% / 8% / 6% |
Reading the result
- The ideal path — what the arithmetic average implies.
- The typical (geometric) path — what the same edge produces when the sequence varies.
- The volatility tax: the gap between the two. It is always positive when returns vary, because losses compound against you.
- A 10th–90th percentile band, the share of runs ending above what was contributed, and the median worst drawdown along the way.
Worked example
$10,000 over 24 periods. Ideal at 5%; realistic at a 60% win rate with +8% wins and -6% losses.
- Ideal at a flat 5% per period: $32,251
- Realistic, ideal path: $17,668 — what the arithmetic average implies
- Realistic, typical (geometric) path: $16,724
- Volatility tax 5.3%, lost to nothing but the unevenness of the sequence
- 10th-90th percentile range $10,431 to $27,567; median worst drawdown 16.9%
Those two figures are the most useful comparison in the whole set: 5% over 24 periods should be $32,251, and a realistic path with a genuine edge lands at $16,724. The percentile band is wider than the median itself.
What trips people up
- The ideal curve is not a forecast and neither is the realistic band. Both are arithmetic on assumptions typed into the fields.
- The percentile band comes from a seeded simulation: identical inputs always give identical output.
- Contributions are added after growth each period, which is why they appear in the contributed line separately from returns.
Questions
- What is the volatility tax?
- The gap between the arithmetic average of a series of returns and the geometric one. A +10% period followed by a -10% period averages zero and leaves the balance down 1%. Over a long run that gap compounds, and it is always in the same direction.
- Why is the realistic path so much lower than the ideal one?
- Because a fixed return per period is not the same thing as an average return per period. The realistic mode is what the same average looks like when it arrives as wins and losses instead of a constant.
Related calculators
These are the same calculators built into Ledger of Alpha, where they read your own trade history instead of numbers you re-type. See the full product
Keep the record these numbers come from
A free account logs the trades you size here, so the win rate and averages you type into these calculators come from your own history rather than a guess.