About the Option Probability Calculator
Implied volatility tells you how much movement the options market is pricing in, and that can be turned into odds. This option probability calculator uses the lognormal model behind Black-Scholes to estimate the probability that a call or put finishes in the money at expiration, the probability it expires worthless, the probability the stock touches the strike at any point before expiry, and the probability a long option is profitable after paying its premium.
Option sellers use these numbers to choose strikes with a target probability of expiring worthless, buyers use them to judge how far the stock must move, and anyone can use the expected-move range to see the one-standard-deviation band the market is implying. The chart shows the probability of finishing above each price around the current one.
Probabilities are risk-neutral (the drift is the risk-free rate minus the dividend yield), assume constant volatility and continuous trading, and ignore volatility skew and jumps around earnings. Real-world odds can differ; treat them as the market’s implied estimate, not a forecast.
With the default inputs, the probability of expiring in the money is 13.39%. Change any value above to recalculate instantly.
How to use the option probability calculator
- 1Choose call or put and enter the stock price and strike.
- 2Enter days to expiration and the option’s implied volatility from your broker’s chain.
- 3Adjust the risk-free rate and dividend yield if needed.
- 4Optionally enter the premium to see break-even and probability of profit.
- 5Compare the in-the-money, worthless and touch probabilities to choose a strike.
Formula and method
Under the Black-Scholes assumptions the stock price at expiry is lognormal, so the probability of finishing above the strike is N(d₂), the standard normal CDF of d₂. A call is in the money above the strike and a put below it, so the put probability is N(−d₂). The drift μ = r − q − σ²/2 is the risk-neutral log drift. Probability of profit uses the same formula with the break-even price (strike ± premium) in place of the strike.
The probability of touching uses the reflection-principle formula for Brownian motion with drift, where b = ln(K/S); for strikes below the stock price the signs flip. With little drift it is close to twice the in-the-money probability. The expected move is S × σ × √T, the one-standard-deviation price change implied by volatility.
- S
- Current stock price
- K
- Strike price
- T
- Time to expiry in years (days ÷ 365)
- σ
- Implied volatility (annual)
- r, q
- Risk-free rate and dividend yield
- N()
- Standard normal cumulative distribution function
Worked examples
30-day $110 call, stock $100, IV 30%
With 30 days left and 30% volatility, d₂ = −1.108, so the call has about a 13.4% chance of finishing above $110 and an 86.6% chance of expiring worthless. The odds of the stock touching $110 at some point are about 26.8%, and the one-standard-deviation move is ±$8.60.
45-day $90 put bought for $1.50, IV 35%
The put is in the money if the stock ends below $90, which the model puts at about 20%. Because you paid $1.50, it only makes money below $88.50, which drops the probability of profit to about 16.4%. There is roughly a 39.7% chance the stock dips to $90 at some point.
60-day $260 call on a $250 dividend stock
A strike 4% out of the money with 60 days and 25% volatility has about a 34.9% chance of finishing in the money. After the $6 premium the break-even is $266, reached with about 27% probability, while the stock has roughly a 70% chance of touching $260 before expiry.
Frequently asked questions
Is delta the probability of an option expiring in the money?+
Delta is often used as a shortcut, but it is N(d₁), not N(d₂). The true risk-neutral probability of finishing in the money is N(d₂), which is a little lower than call delta; the gap grows with volatility and time to expiry.
What is the probability of touch?+
It is the chance the stock trades at the strike at least once before expiration. For low-drift cases it is roughly twice the probability of finishing in the money, because a stock that reaches the strike has about even odds of ending beyond it.
Are these real-world probabilities?+
They are risk-neutral probabilities implied by option prices, using the risk-free rate as drift. They do not include your own forecast, volatility skew, or the expected return of the stock, so treat them as the market’s implied odds.
What is probability of profit (POP)?+
For a long option it is the probability the stock ends beyond break-even — strike plus premium for calls, strike minus premium for puts — at expiration. It is always lower than the in-the-money probability because the premium must be recovered first.
What does the expected move mean?+
It is the one-standard-deviation price change implied by volatility: price × IV × √(days/365). Under the model there is roughly a 68% chance the stock finishes within that range at expiration.
Results are estimates for educational purposes and are not financial advice. Rates, fees and terms vary — confirm with your lender or a licensed advisor before making decisions.