How it works
The calculator applies the Black-Scholes formula for European options on an underlying that pays no dividends. It first computes d1 = [ln(S/K) + (r + σ²/2) × T] / (σ × √T) and d2 = d1 − σ × √T, where T is the number of days to expiration divided by 365, σ the annual volatility and r the annual interest rate. The call price is S × N(d1) − K × e−rT × N(d2), the put price K × e−rT × N(−d2) − S × N(−d1), with N as the standard normal distribution.
Delta shows roughly how much the option price changes when the underlying moves by 1; gamma shows how quickly delta itself changes. Theta is the change in value per calendar day if nothing else moves, and vega the change for a one-point rise in volatility. Break-even is the strike plus the premium for a call, or minus the premium for a put, at expiration. The chart shows the profit or loss of a bought option at expiration between 50% and 150% of the strike; the dashed line marks the current underlying price.
The result is a model value, not a market quote. Real prices also depend on the volatility the market implies, dividends, early exercise for American options, bid-ask spreads and fees, and the model assumes that volatility and interest rates stay constant.