Calculators · free, no signup

Options probability calculator: chance of finishing above, below or touching a strike

Short answer: With the Black-Scholes model (no interest or dividends), the chance a stock finishes above a strike at expiry is N(d2), where d2 = [ln(price / strike) - IV^2 x t / 2] / (IV x sqrt t). At $100 with 20% IV and 30 days, the chance of finishing above $110 is about 4.5%, and the chance of touching $110 before expiry is roughly double, about 9%.

Showing a worked example. Enter your own numbers above; the result's link can be shared.

How it's calculated

Under Black-Scholes with no interest rate or dividends, the chance the price finishes above the strike K at expiry is N(d2), with d2 = [ln(S ÷ K) − σ²t ÷ 2] ÷ (σ√t), where S is the price, σ the implied volatility and t the years to expiry. The chance of finishing below is 1 − N(d2). The chance of touching a strike at any point before expiry is close to twice the chance of finishing beyond it (the reflection principle), which is why "probability of touch" is roughly double "probability ITM".

Delta is not the same thing

An option's delta is often quoted as its chance of expiring in the money. It is close, but delta is N(d1), not N(d2), and the gap grows with volatility and time. For a 30-day option at 20% IV the two differ by about 1 to 2 points.

Limits

These are model probabilities from the market's implied volatility, not forecasts. Real prices have fatter tails and jumps (earnings, macro news), and implied volatility tends to overstate the volatility that follows, so outcomes far from the price are usually less likely than the model says and sudden jumps more likely. Use it to compare strikes, not to predict.

Other calculators: Expected move calculator: price, implied volatility and days · Options breakeven and profit calculator for calls and puts. Explainers: Learn.

Arithmetic and model estimates, not investment advice. Options involve substantial risk.