How Is Implied Volatility Derived from the Black-Scholes Model?

Implied volatility (IV) is not an input to the Black-Scholes model, but rather a value derived from it. The Black-Scholes model uses five inputs: the underlying asset price, strike price, time to expiration, risk-free interest rate, and volatility.

To find IV, traders use the model in reverse: they input the current market price of the option and solve for the one unknown variable, volatility. IV is the market's collective forecast of the underlying asset's future price volatility.