Calculate the theoretical price of a European call and put option using the Black-Scholes model.
Call option price—USD
Put option price—USD
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About the Black-Scholes Option Pricing Calculator
The Black-Scholes model is the classic formula for pricing European-style options — ones that can only be exercised at expiration — based on the stock price, strike price, volatility, time to expiration and the risk-free rate.
Formula: Call = SN(d1) − Ke−rTN(d2), where d1 = [ln(S/K) + (r + σ²/2)T] ÷ (σ√T), d2 = d1 − σ√T, and N(x) is the standard normal cumulative distribution function.
Put price follows from put-call parity. This calculator uses a self-contained polynomial approximation of N(x), accurate to roughly 7 decimal places, so no external statistical library is needed. Real-world option prices can diverge from Black-Scholes due to factors like dividends, early exercise and changing volatility.