An option's price is never a guess -- it is the output of a formula that won its creators a Nobel Prize. The Black-Scholes model values a European option from five inputs: the stock price, the strike price, time to expiry, the risk-free rate, and volatility. Change any one and the price moves; volatility moves it most, which is why options traders speak of buying and selling volatility rather than buying and selling options.

This calculator prices both sides of the contract. Enter a $100 stock, a $100 strike, one year to expiry, a 5 percent risk-free rate, and 20 percent volatility, and it returns the call price, the put price, and the d1 and d2 terms from the formula's guts. It also reports each option's delta -- how much the option price moves per dollar of stock movement -- the number that tells hedgers how many shares offset their position.

Respect the model's boundaries. It assumes constant volatility and no early exercise, so it fits European options and liquid US equity options reasonably but not perfectly; American puts and dividend-paying stocks need adjustments. Use it to check whether a quoted option price implies sane volatility, to size hedges with delta, and to learn the intuition that time and volatility are what you are truly trading.

With the pre-filled defaults — Current Stock Price $100, Strike Price $100, Time to Expiry (Years) 1yr, Risk-Free Rate 5%, Implied Volatility 20% — the Black-Scholes Option Pricing returns d1 0.3500, d2 0.1500, Call Option Price $10.86, Put Option Price $5.98, Call Delta 0.6445, Put Delta -0.3555. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.