Binary Options Compounding Calculator

Why this isn’t a compound-interest calculator

A savings calculator assumes every period pays the same rate. A binary options account has two outcomes per trade and no rate at all — which is why the textbook formula gives an answer that never arrives.

Put $1,000 into an account paying 5% a year and the third year is simply $1,157.63. The rate never varies and the balance only ever moves one way. That is what A = P(1 + r)ⁿ describes, and it is why it works for savings.

A binary trade has no rate. It has two outcomes. A win returns a fixed percentage of what you staked — the payout, typically between 65% and 98% depending on broker, asset and session. A loss returns nothing: the whole stake is gone. There is no partial loss, no “down 2% on the position”, no stop-loss distance that limits the damage. The CFTC and SEC put the structure plainly in their joint investor alert: the holder “will receive either a pre-determined amount of cash or nothing at all.”

That asymmetry is what breaks the compound-interest formula. It needs one r that applies every period. A real trading sequence has two multipliers that alternate unpredictably, and averaging them into a single rate throws away the only thing that matters — which one lands, and how often.

So two very different tools both get called a “compounding calculator”, and traders reach for the wrong one constantly. A lump-sum compounding calculator projects a balance forward at a fixed rate — correct for a savings account, useless here. A per-trade win/loss calculator, which is what this page runs, steps through discrete outcomes at your payout and stake fraction and reports what the balance actually did along the way.

Run the same $1,000 through both at what looks like the same return and the savings formula produces a number a real sequence will essentially never reach, because it has quietly assumed you never lose. Everything below is about what the second calculator shows once you stop assuming that.

Every input, and where the real number comes from

Two of these five are usually guessed rather than looked up, and both guesses push the answer the same way — toward optimism.

Fixed fraction versus full reinvestment

The stake input is where two philosophies split, and the difference is not one of degree.

Fixed-fraction reinvestment stakes the same percentage every trade. The dollar stake rises with the balance and falls with it, so a drawdown automatically reduces exposure. Full reinvestment stakes the entire balance every trade. It draws the steepest curve on paper, and it is the mode nearly every competing calculator defaults to.

Those calculators model only the second, print the resulting number as the headline, and never show what it costs. It costs everything, on the next loss — whenever that loss happens to arrive. The worked examples below prove it on a real sequence, and it is why this calculator asks for a stake fraction at all instead of quietly assuming 100%.

The real formula, and why “5% a day” is a trap

The arithmetic most traders do in their head is addition. The arithmetic the account does is multiplication, and the gap between them is about thirteen times.

The plan sounds disciplined. Risk 2% per trade, take five trades a day, twenty trading days in the month — a hundred trades. Two percent times a hundred is 200%, so the month should roughly triple the account. This is wrong in a way that is genuinely hard to see, because nothing about it looks reckless. It is just addition applied to something that does not add.

What actually happens per trade is an expected multiplier. With win rate W, payout p and stake fraction s, each trade multiplies the balance by 1 + s·p on a win and 1 − s on a loss, so the honest per-trade figure is:

That is +0.146% per trade. Compounded over the same hundred trades it comes to +15.71% for the month. A good month — but not 200%, and not within a factor of ten of it.

Now the part that costs accounts. Drop the win rate to 53%, a rate that still feels comfortably better than a coin flip and that most traders would describe as winning most of the time. Same payout, same stake:

The trader wins 53 of every 100 trades and the account still bleeds — slowly, with no dramatic loss to point at. Nothing about the experience feels like failure. The month simply ends lower than it started.

The reason is the payout. At 85%, a win returns 85 cents per dollar risked while a loss takes the whole dollar, so wins have to outnumber losses by enough to cover that 15-cent gap. The exact break-even is 54.1%. At 53% the trader is 1.1 points under water, and 1.1 points is invisible day to day and decisive over a hundred trades.

When compounding works, and the three conditions where it quietly wipes you out

Compounding is neither good nor bad. It is a multiplier on whatever edge you already have, including a negative one. Three conditions decide which.

1. The win rate has to clear the payout’s break-even

   Break-even is 1 / (1 + p). It depends only on the payout — not the stake size, not the balance, not how many trades you take. At an 85% payout that is 54.1%; at 70% it is 58.8%. Above the line, compounding accelerates a gain. Below it, compounding accelerates a loss.

   Nothing else in this section matters if this condition fails, because a larger stake on a losing edge only loses faster. If your own number sits under the line, the fix is the strategy or the payout you trade at — never a bigger stake.

2. The stake has to shrink when the balance does

   Losses and gains are not symmetric, and the asymmetry widens the deeper the hole gets. Down 10%, you need +11.1% to get back. Down 30%, +42.9%. Down 50%, you have to double the account just to return to where you started.

   Percent of balance lost Percent gain needed to recover

   Fixed-fraction staking handles this on its own: because the stake is a percentage of the current balance, a shrinking balance means a shrinking dollar stake. Fixed dollar staking does the opposite — the same $50 that was 2% of a $2,500 account is 5% of it after a 60% drawdown, so risk rises exactly when the account can least carry it.

3. Sequence risk, and the surprising thing about it

   The intuition is that a bad run early is worse than a bad run late. At a fixed stake fraction that intuition is wrong about the destination and right about the journey, and the distinction matters more than it sounds.

   Take a real 20-trade record: 12 wins, 8 losses, 2% stake, 85% payout, starting at $1,000. Deal it in the order it happened and it ends at $1,041.50. Reorder it so all twelve wins come first and the eight losses follow — it still ends at $1,041.50. Put all eight losses first instead. Still $1,041.50.

   That is not a coincidence or an approximation. The ending balance is the product of the same twenty multipliers, and multiplication does not care about order. Where the losses fall cannot change where you finish.

   What it changes is how far down you go on the way. The wins-first ordering never dips below the $1,000 it started with. The losses-first ordering of that identical record bottoms out at $850.76 — a 14.9% drawdown — before climbing back to the same ending number.

   Where the real risk sits

   Sequence risk is not a risk to the arithmetic. It is a risk to the trader. Both paths pay identically, but only one asks you to sit through being down 15% first. The account that fails is usually not the one whose math was wrong — it is the one whose owner changed the plan at $850.76.

Compounding is not martingale

These two get conflated constantly, and they are opposites. Martingale raises the stake after a loss, trying to win back what just went — so risk climbs exactly when the evidence says the edge is not working. Compounding raises the stake after a win, because the balance the percentage is drawn from got bigger — so risk climbs only after the account can carry it. Fixed-fraction compounding is self-limiting by construction; martingale is self-destructive by construction.

The payout is the term that sets the bar

Break-even moves by nearly ten points across the payouts a binary trader actually meets. The same strategy compounds at one and bleeds at another.

The payout is not a detail of the platform — it is the term that decides whether there is anything to compound at all. Because break-even is 1 / (1 + p), every payout implies one exact win rate you have to beat, and nothing about your strategy changes it. Find the payout you actually trade at and read across.

The third column is the part worth sitting with. A trader holding a steady 55% win rate is profitable at a 90% payout and losing money at 75% — same trader, same strategy, same skill. Which side of the line they land on was decided by the asset and session they happened to trade, not by anything they did.

Why no page can tell you your payout

A payout is not a property of a firm. It is a property of the exact contract in front of you, and the asset, the expiry, the session and the account tier each move it independently — two rows on the same screen at the same moment can differ by twenty points. That is why any figure printed beside a platform’s name is a headline rather than a rate, and why this calculator asks you for the number instead of assuming one.

Read every advertised ceiling literally: “up to 95%” describes the best asset in the best session, not the rate a sequence of twenty ordinary trades will earn. Plan against the ceiling and trade at the ordinary rate and you have planned against the wrong break-even — on this page’s arithmetic, a few points is the whole difference between an edge and a bleed. Read the figure off your own ticket, not the platform’s headline — the common mistake is entering a payout a hundred points too high.

What a fifteen-point payout gap does to the same run

Take Example A below — the same twelve wins, eight losses and 2% stake — and change nothing but the payout, from 85% to 70%:

Identical trading. Identical decisions. Nearly eight times less profit, purely because of where the payout sat — and at 70% the break-even is 58.8%, so the same 60% win rate that was comfortable at 85% is now 1.2 points from being underwater. Check the payout on the specific asset and session you actually trade, not the platform’s headline.

Log the payout, then plan on your own median

One number solves this permanently, and it is not one anybody can publish for you: the median payout you were actually filled at over your last fifty trades. Record it beside every entry for two weeks and the distribution appears — usually a tight cluster with a thin tail toward the advertised ceiling, and often a second cluster ten or more points lower for the sessions or assets you assumed were the same.

Plan on the median rather than the best fill, and size against the lower cluster if you trade both. Log payout, outcome, and stake for every trade, and split a week into segments to judge each against its own bar. A blended average across two payout regimes is the most common way a losing segment hides inside a winning month.

Two worked examples, trade by trade

Same account, same payout, same twenty outcomes in the same order. The only difference is the stake fraction, and it decides everything.

Both examples run $1,000 at an 85% payout through this record: W L W W L W L W L L W W L W W L W W L W — twelve wins and eight losses, a 60% win rate that comfortably clears the 54.1% break-even.

Example A — 2% of the balance per trade

The stake resets to 2% of the current balance each trade, so it drifts between roughly $19.67 and $20.90 as the balance moves. The account never travels far from where it started.

The hero calculator runs the same twelve wins and eight losses but spreads them evenly rather than in this order, so for identical inputs it reports a shallower trough. Both orderings end at $1,041.50: the order changes the path, never the destination — which is the sequence-risk point above, met a second time.

Two things are worth noticing. The account spends most of the run slightly below where it started — the back-to-back losses at trades 9 and 10 pull it to a trough of $983.41, and it does not clear $1,000 again until trade 11. And the final figure, $1,041.50, is a 4.2% return from a 60% win rate over twenty trades. That is what a genuine edge looks like at a sane stake size: unglamorous, and intact.

Example B — the whole balance, every trade

Identical record. Identical payout. The stake fraction goes to 100%.

Trade 1 wins and the balance jumps 85% to $1,850 — a result that would look outstanding in any screenshot. Trade 2 loses, and because the stake was the entire balance, the account is at zero. The eleven wins still remaining in the sequence are worth nothing, because there is nothing left to stake.

This is the comparison every competing calculator omits. They model Example B, print $1,850 as the headline after one trade, and never run trade 2.

The mathematical ceiling on your stake

“Pick a stake you can sit through” is good advice but not a number. There is a number, and once you have a win rate and a payout you can read it.

It comes from the Kelly criterion — the stake fraction that maximises long-run growth for a known edge. For a fixed-odds bet like a binary option it is:

Two things make that number useful rather than academic. The first is that it collapses to exactly zero at the break-even win rate — at an 85% payout and a 54.1% win rate, Kelly says stake nothing at all. That is Condition 1 arrived at from a completely different direction, which is a good sign that the line is real.

The second is that full Kelly is famously punishing to sit through: it maximises growth while accepting drawdowns most people abandon the plan during. The common practitioner adjustment is half Kelly, which gives up a little growth for a far smoother path.

What half Kelly looks like across the range

The ceiling is far more sensitive to the win rate than to the payout, which is the opposite of most traders’ intuition. Two points of win rate move it further than ten points of payout do.

Read the “stake nothing” cells literally — they are not a rounding artefact. At a 54% win rate and a 75% payout the edge is negative, so no stake size turns the sequence profitable; there are only sizes that lose the money faster or slower. That is the same conclusion the break-even win rate and the per-trade expectancy reach from their own side of the math.

Treat the ceiling as a ceiling and not a target. Kelly assumes you know your true win rate, and the whole problem with a win rate is that you do not: you have an estimate from a limited sample. Every point by which you have overestimated it pushes the “optimal” stake further above what is actually safe, which is why most traders sizing this way sit well below half Kelly rather than at it. If your sample is under a few hundred trades, the honest reading of that table is that your true ceiling could be any of three adjacent rows.

What to do with the number

A projection is only worth the decision it changes. Three of those are worth making before the next trade.

Run it at three stake sizes, not one. Try 2%, then 5%, then 10%, with your own win rate and payout unchanged. The ending balances will differ less than you expect and the troughs will differ far more. Pick the stake by the trough you could actually sit through, because that is the number that decides whether you stay with the plan.

Check where your win rate really came from. If it was an estimate rather than a count, the output is an estimate too. A documented win rate is the difference between planning and hoping, and it has to come from recorded entries and exits rather than recollection.

If the drawdown is more than you could absorb, cut the reinvestment fraction. Not the payout you demand, and not the win rate you assume. The stake fraction is the only input here you fully control.

Which of these are you?

The projection changes a different decision depending on where you are standing when you read it.

You have just had a winning week and want to let it ride. Three good sessions, the balance up sharply, and full reinvestment starting to look reasonable for next week. The number that should stop you is not the size of a losing streak — it is that Example B dies on trade 2. A bounded fraction inside the half-Kelly ceiling captures most of the growth and none of the ruin.

You are deciding whether to pay for a signal service. Someone is advertising a 78% win rate. Check your broker’s payout, read the break-even off the table above — 54.1% at 85% — and the gap between the two is how much the claim can degrade in live conditions before it stops being profitable. That is a concrete diligence step rather than trusting a marketing figure.

You are running a larger account and keep not taking profit out. The withdrawal checkpoint below is the answer: a rule with a trigger, tested against a real sequence, instead of an open-ended intention to bank something eventually.

You are down and deciding how hard to rebuild. Put your actual drawdown into the recovery formula before you touch the stake size. Down 35% needs +53.8% to get level — and the instinct to double the stake to get there faster is the single most reliable way to turn a recoverable drawdown into a terminal one.

Withdrawal checkpoints

Compounding indefinitely means every dollar you have ever made stays exposed to the next sequence. A checkpoint rule is how that stops.

The rule is one line: every ten trades, withdraw whatever sits above the starting balance. Run it against Example A and it behaves like this.

1. Checkpoint at trade 10

   Balance is $983.41 — below the $1,000 the run started from. There is no profit to skim, so nothing is withdrawn and the working balance carries forward. The rule never forces a withdrawal that would eat into capital.

2. Checkpoint at trade 20

   Balance is $1,041.50. The $41.50 above the starting balance is withdrawn and the working balance resets to $1,000.00 for the next block of twenty.

3. The alternative

   Full reinvestment carries the whole $1,041.50 into the next sequence. More compounding base — and every dollar of it, including profit already earned, still exposed to the next run.

The checkpoint trades a little forgone growth for a hard ceiling on how much of any bad stretch can reach money that has already been banked. Whether that trade is worth making depends on whether you are compounding a balance you can afford to lose or one you cannot.

Run the rule on your own numbers

The interval is the variable worth testing, because it decides both how much gets banked and how much growth you give up. This runs the rule against the balance, payout, win rate and stake set in the calculator at the top of the page — change any of them and this follows.

Two patterns show up immediately. A shorter interval banks slightly less in total, because each block starts from the smaller reset balance and compounds from a lower base. And the gap between the two columns stays small at a sane stake fraction and widens sharply as the stake climbs — the protection is cheap exactly where you need it least, and expensive where the account is already fragile.

How a withdrawal is taxed depends entirely on where you live, and is a question for a licensed tax adviser rather than this page.

What this calculator does not answer

Compounding answers what a sequence is worth. It does not answer whether you survive the sequence, and those are different questions with different arithmetic.

Every figure on this page assumes the run completes. The ending balance is the product of the same multipliers whatever order they arrive in, so the calculator can report it without knowing anything about streaks. A trader cannot: the account has to still be there at trade fifty, and the balance has to still be large enough to place a stake the platform will accept. Three adjacent questions sit outside this page, and each has a calculator of its own.

1. Will a losing streak end the account before the edge pays?

   That is a ruin probability, not a growth projection, and it comes from an exact binomial rather than from anything on this page. A 5% stake through seven consecutive losses removes about 30% of the balance; whether seven in a row is a remote possibility or a monthly event depends on your win rate and the number of trades. The risk of ruin calculator answers it directly.

2. How far back does a drawdown put you?

   Losses and recoveries are not symmetric, and the asymmetry is the reason a stake fraction chosen for growth can still be the wrong one. Down 35% needs +53.8% to get level. The drawdown recovery calculator turns any drawdown into the gain it demands, and it is the number to look at before deciding how hard to rebuild.

3. Is raising the stake after a loss ever the answer?

   It is the opposite of what this page models, and it fails for a reason worth understanding rather than being warned about. The martingale calculator shows how quickly a doubling ladder outruns any account, and the money management calculator sets the fixed rules that keep a stake bounded in the first place.

Run this page for what a plan is worth and those three for whether the plan survives. A stake fraction that looks good here and fails there is the single most common way a mathematically sound edge still ends in a closed account.

Risk and disclosures