Black-Scholes Option Pricing Calculator
Estimate the fair value of a European call or put option using the Black-Scholes model. Enter the spot price, strike, time to expiration, interest rate and volatility to see the option price and its Greeks.
How to use the Black-Scholes calculator
- Enter the current spot price and the option's strike price.
- Set the time to expiration in years, the risk-free rate and the volatility.
- Pick call or put to read the fair value and the Greeks (delta, gamma, theta, vega, rho).
Examples
At-the-money one-year call
Spot 100, Strike 100, Time 1 year, Rate 5%, Volatility 20%, Call
Price 10.4506, Delta 0.6368, Gamma 0.0188
Same inputs, put option
Spot 100, Strike 100, Time 1 year, Rate 5%, Volatility 20%, Put
Price 5.5735, Delta -0.3632
Frequently asked questions
What is the Black-Scholes model?
It is a formula for the theoretical price of a European option, using the spot price, strike, time to expiration, risk-free rate and volatility. It assumes no dividends and that the option can only be exercised at expiry.
What do the Greeks mean?
Delta is how much the price moves per $1 change in the underlying. Gamma is how fast delta changes. Theta is time decay (shown here per day). Vega is sensitivity to a 1 point change in volatility, and rho is sensitivity to a 1 point change in the interest rate.
Is this financial advice?
No. This tool is for education and illustration only. Model prices rely on assumptions like constant volatility that real markets do not follow, so do not use the output as a recommendation to trade. Consult a licensed professional before investing.
Why does my result differ from a broker quote?
Real quotes reflect supply and demand, dividends, early-exercise value for American options, and implied volatility that shifts by strike and expiry. Black-Scholes gives a clean theoretical value, not a live market price.
Do you store my inputs?
No. Everything runs in your browser. Your spot price, strike, rate and other figures are never sent to a server or saved.
What volatility should I enter?
Use an annualized volatility for the underlying as a percent. Many people start from the implied volatility quoted by their broker, or a historical estimate, and adjust from there.
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