Black-Scholes Option Pricing Calculator

The Black-Scholes model is the standard formula for pricing European-style options. It takes five inputs (the underlying price, strike, time to expiration, volatility, and the risk-free rate) and derives a theoretical fair value for a call or put, along with the Greeks that describe how that value moves as each input changes.

This calculator uses the classic no-dividend Black-Scholes formula, the version most free options tools and textbooks implement, and shows the price alongside all five standard Greeks: Delta, Gamma, Theta, Vega, and Rho.

How does this calculator work?

Enter the underlying price, strike price, days to expiration, an annualized volatility assumption, and the risk-free rate (typically a Treasury yield near the option's expiration).

The calculator computes the theoretical price and the Greeks at those inputs, and charts how the option's value changes as the underlying price moves, useful for seeing how sensitive the position is before you're in it.

Don't know the volatility to use? Enter a real quoted option price into the Implied Volatility Calculator instead, and it'll back out the volatility the market is pricing in.

The model rests on strong simplifying assumptions, constant volatility, no dividends, and exercise only at expiration, so a live option rarely trades exactly at its Black-Scholes value. The price and Greeks are most useful as a baseline: drop a set of strikes into a full position payoff to see how they combine, or estimate a trade's probability of finishing profitable under the same volatility assumption.