The Black-Scholes formula is a formula and market model for explaining or determining the price of European-style options. It was developed in 1973 by two world-renowned economists, Fischer Black and Myron Scholes, and it led to a Nobel Prize in 1997.
As opposed to the American-style of options, which can be exercised at any time, European-style options can only be exercised on their expiration date, they are not exposed to dividends, and they have no commission structure to consider. Some are content to use Black-Scholes for quick applications to American-style, but It is not as accurate as it should be.
There are adaptations of the formula which can make it useful for American style options, incorporating dividends and other differences, but these formulas are not easily accessible or widely known. If you assume that American call options are rarely exercised early, and if the call is on an asset which doesn’t pay dividends, the Black-Scholes Formula should work fine.
The variables that must be input to the Black-Scholes Formula are: the strike price, the current price of the underlying, time until expiration, volatility of the asset, and the risk-free rate.