Probability of Profit Calculator

Probability of profit (POP) is the model-implied likelihood that an options trade will have a positive P&L at expiration — meaning the underlying price finishes on the profitable side of the trade's breakeven. It is derived from the Black-Scholes lognormal model: POP = N(d2) for strategies that profit when the underlying rises above the breakeven, or N(-d2) for strategies that profit when it falls below. A POP of 70% means the model expects the trade to be profitable at expiration in about 70 out of 100 scenarios with the given inputs — it is not a guarantee.

Delta approximates the probability the option expires in-the-money (above the strike for a call, below for a put) under the risk-neutral measure — it is N(d1) in Black-Scholes. POP uses N(d2) and is evaluated at the trade's breakeven price (strike plus or minus the net premium paid or received), not the strike itself. Because the breakeven of a long call is higher than the strike (it includes the premium cost), POP is lower than the call delta. For a short put, the breakeven is below the strike, so POP is higher than the absolute delta. Delta and POP converge when the premium is negligible relative to price.

Not necessarily. POP measures the probability of any profit at expiration, not the expected dollar value of the trade. Many high-POP strategies are credit spreads or short premium positions that collect a small premium most of the time but face a large loss on the infrequent losers — a risk profile called negative skew. A 70% POP strategy with a max loss 3x the max profit has a negative expected value if the losses are not managed. Always evaluate POP alongside the max profit, max loss and expected value when assessing a trade.

The breakeven is the underlying price at which the trade neither gains nor loses money at expiration. For a long call it is strike + premium paid. For a long put it is strike - premium paid. For a short call or short put (credit positions), the breakeven shifts in the seller’s favour by the premium received. For multi-leg spreads, compute each leg’s contribution to the net premium and use the resulting net breakeven(s) as inputs to this calculator.

Enter the current implied volatility (IV) of the option or the average IV of the legs in a spread, expressed as an annualized percentage. You can read it from your broker’s option chain. Implied volatility is forward-looking — it represents the market’s consensus expectation of future realized volatility — and it directly determines the width of the lognormal distribution used to compute POP. Higher IV produces a wider distribution, so OTM breakevens become more reachable: POP for a profit-above trade rises as IV rises (and falls for a profit-below trade).

Option pricing — and by convention, broker-reported probability ITM and POP figures — use the risk-neutral measure in which the expected return of the underlying equals the risk-free rate minus the dividend yield. This is the same framework used to price options (Black-Scholes-Merton) and ensures POP is internally consistent with option greeks and market prices. A real-world POP based on the trader’s personal expected return for the underlying would be unobservable and would differ for each trader. If you believe the underlying will drift faster than the risk-free rate, the model-implied POP understates your personal expectation of profit.

Profit-between applies to strategies that profit when the underlying finishes between two breakeven prices at expiration — such as iron condors, short strangles, short straddles or butterfly spreads. Enter the lower breakeven and the upper breakeven and the calculator returns the lognormal probability the underlying expires in that range. POP = N(d2_low) - N(d2_high) where d2 is computed separately for each breakeven. This directly reflects the probability both sides of the trade expire worthless (for an iron condor, for example).

Time to expiration (T) enters the formula as sigma*sqrt(T), which is the standard deviation of log-returns over the option’s life. Shorter time compresses the distribution, making it less likely the underlying travels far from its current price. For an out-of-the-money breakeven above spot, shorter time reduces POP. For a near-the-money short-premium strategy with a breakeven close to spot, shorter time increases POP as there is less time for the underlying to breach the breakeven. Theta decay and POP are related: as time passes and IV is stable, the distribution narrows and POP typically rises for credit strategies.

No. The standard normal CDF N(d2) is strictly between 0 and 1 for any finite d2, so POP is always in the range (0%, 100%) exclusive, never exactly 0 or 100 for finite inputs. In the profit-above case, as the breakeven moves far above spot or time collapses to zero, POP approaches 0% asymptotically. As the breakeven moves far below spot, POP approaches 100%. The engine enforces these bounds.

This is a quick approximation used by some traders for defined-risk vertical credit spreads: POP ≈ 1 - (net credit received / spread width). For example, a $0.30 credit on a $1.00-wide spread gives POP ≈ 70%. It does not require volatility or time as inputs. The heuristic equals the lognormal POP only approximately — it can diverge significantly for deep ITM or OTM strikes or near expiry. This calculator uses the rigorous lognormal formula; the heuristic is a useful sanity check but should not replace the model-based figure for planning a trade.

There is no single threshold, because the right POP depends on the strategy and the accompanying risk-reward profile. As a practical guide: credit strategies (short puts, iron condors, credit spreads) typically target 65–80% POP — the trade collects premium most of the time but faces a large loss on the minority of losses, so the POP must be high enough that winners outweigh the occasional big loser in expected-value terms. Debit strategies (long calls, long puts, debit spreads) typically carry a POP below 50%, because the potential gain if the underlying moves far enough can more than compensate for the higher loss frequency. The decisive test is not the POP alone but the combination: (POP × average win) − ((1 − POP) × average loss) should be positive. A 70% POP strategy with a $0.30 average win and a $1.00 average loss has a negative expected value of −$0.02 per trade. Always compute expected value alongside POP before committing capital.

No. The probability of profit computed here is a single-point at-expiration probability under the European-exercise lognormal model. It does not account for early assignment (relevant for American-style options), mid-trade stop-losses, barriers, or any active management that closes the trade before expiration. If you plan to manage the trade at a profit target or stop-loss level before expiration, the realized POP will differ from the at-expiration figure shown here.