The concept
What the Black-Scholes model estimates, and what it assumes
The Black-Scholes model is a formula for estimating the theoretical fair value of a European-style option based on five inputs: the current stock price, the strike price, time remaining to expiration, a risk-free interest rate and an assumed (implied) volatility. It's the foundation most options pricing tools build on, including how implied volatility itself is typically inferred from a market price.
The model rests on simplifying assumptions that don't perfectly hold in real markets: constant volatility over the option's life, no dividends (unless separately adjusted for), frictionless trading with no bid-ask spreads or commissions, and European-style exercise only (no early exercise, which American-style options technically permit). Real option prices can and do deviate from the model's output, especially around dividends, earnings events, and volatility skew.
The method
How the calculation works
d1 and d2 are calculated from the stock price, strike, time to expiration, risk-free rate and volatility. The call price applies the cumulative standard normal distribution to d1 and d2 to weight the stock price and the present value of the strike price. The put price is derived from the same d1 and d2 using put-call parity, so both prices come from one consistent set of inputs.
d1 and d2 combine the stock price, strike, time, rate and volatility into two standardized values whose normal-distribution probabilities (N) determine the price.
Worked example
A neutral example
For a $100 stock price, $100 strike, 3 months to expiration, a 4.5% risk-free rate and 30% implied volatility, the calculator estimates both the call and put price the Black-Scholes model would assign under those exact assumptions.
This example explains the method. It does not recommend a financial action or predict an outcome.
Frequently asked
Option Price Calculator questions
Is the Black-Scholes price the same as the real market price?+
Not necessarily. Black-Scholes produces a theoretical estimate based on the inputs you provide, especially the assumed volatility. Real market prices reflect actual supply and demand, and can diverge from the model due to dividends, early-exercise value on American-style options, volatility skew, and market frictions like bid-ask spreads.
Where do I get an implied volatility number to enter?+
Implied volatility is usually quoted by your broker or options data platform for a specific option, back-calculated from that option's current market price. If you don't have a specific IV figure, you can enter historical volatility as an approximation, understanding that it's a different (though related) measure.
Does this account for dividends?+
No. This calculator uses the standard Black-Scholes formula without a dividend adjustment. For dividend-paying stocks, especially with a dividend date before expiration, actual option prices — particularly for calls — will typically be lower than this model suggests, since the model doesn't reduce the stock price for expected dividend payments.