Black-Scholes Calculator
This calculator prices European-style call and put options using the Black-Schol
This calculator prices European-style call and put options using the Black-Schol
How to use Black-Scholes Calculator
- Choose call or put, then enter the spot price, strike price, and days to expiration.
- Enter the annual volatility, the risk-free interest rate, and any dividend yield.
- Read the theoretical option price and the delta, gamma, vega, theta, and rho below.
About Black-Scholes Calculator
This calculator prices European-style call and put options using the Black-Scholes-Merton formula. You enter the spot price, strike price, days to expiration, annual volatility, the risk-free interest rate, and an optional continuous dividend yield, and it returns the theoretical option price along with the main Greeks: delta, gamma, vega, theta, and rho.
The math is the standard closed-form Black-Scholes-Merton model. Time to expiration is measured as days divided by 365. Vega is reported per 1 percentage-point change in volatility, theta as the value lost per calendar day, and rho per 1 percentage-point change in the interest rate. The normal distribution is evaluated with a high-accuracy approximation, so results match typical textbook and broker figures closely.
Everything runs in your browser with plain JavaScript. Nothing you type is uploaded or stored, and there is no sign-up. Keep in mind this is a theoretical model for European options that assumes constant volatility and no early exercise, so it is an estimate for study and planning, not a live market quote or trading advice. American options and real-world quotes can differ.
Frequently asked questions
- What is the Black-Scholes model?
- Black-Scholes-Merton is a closed-form formula for the theoretical price of a European option. It uses the spot price, strike, time to expiration, volatility, the risk-free rate, and dividend yield to estimate what an option should be worth today.
- Does it price American options?
- No. The formula is for European options, which can only be exercised at expiration. American options allow early exercise and can be worth slightly more, especially for puts or dividend-paying stocks, so treat this as a close approximation for those.
- What are the Greeks it shows?
- Delta is the price sensitivity to the underlying, gamma is how delta itself changes, vega is sensitivity to volatility (per 1% here), theta is daily time decay, and rho is sensitivity to interest rates (per 1% here). They help you understand how the option value moves.
- What volatility should I enter?
- Enter an annualized volatility as a percent. Traders often use implied volatility from the option chain, or historical volatility of the underlying. There is no single correct number, so the output changes with your assumption.
- How accurate are the results?
- The formula is exact for its assumptions, and the normal distribution is computed to about seven decimal places, so prices are accurate to the cent. Real market prices differ because the model assumes constant volatility, no fees, and continuous trading.
- Is my data private?
- Yes. All calculations happen locally in your browser. No inputs are sent to a server, nothing is saved, and there is no sign-up.