Black-Scholes option calculator
Price an option with Black-Scholes and see all of its Greeks.
Runs 100% in your browser- Option price
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- Delta
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- Gamma
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- Theta / day
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- Vega / 1%
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- Rho / 1%
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How to use the Black-Scholes calculator
- Enter the contract. Set stock price, strike, days to expiry and option type.
- Add rate and volatility. Enter the risk-free rate and volatility (and dividend yield if any).
- Read price and Greeks. The fair value and all five Greeks update as you type.
What the Black-Scholes-Merton model prices
Black-Scholes is the closed-form solution for the fair value of a European option — one that can only be exercised at expiry. It takes six inputs: the spot price, the strike, time to expiry, the risk-free rate, the option's volatility, and a continuous dividend yield. From those it computes two intermediate terms, d1 and d2, runs each through the standard-normal cumulative distribution, and discounts the result back to today. The output splits cleanly into intrinsic value (how far in-the-money the option already is) and time value (everything the market is paying for the chance the stock moves further before expiry). This calculator implements the Merton extension that subtracts a continuous dividend yield, which is why a high-yield stock prices a call lower and a put higher than the dividend-free version.
Reading the five Greeks
The Greeks are partial derivatives of that price, each isolating one risk. Delta is the change in option value per $1 move in the stock — and doubles as a rough probability of finishing in-the-money. Gamma is how fast delta itself moves, peaking at-the-money and near expiry. Theta is time decay, shown here per calendar day, and is the price a long holder pays for every day that passes. Vega is sensitivity to volatility, quoted per one percentage point of IV, and is largest on longer-dated at-the-money contracts. Rho, the rate sensitivity, is the least important for short-dated trades but matters on LEAPS. Sizing and hedging a position is mostly about keeping these exposures where you want them.
Where its assumptions break
The formula assumes constant volatility, frictionless trading, and a lognormal price path — none of which hold exactly. Real markets show a volatility "smile," so a single IV rarely fits every strike, and American options (most US single-stock options) carry a small early-exercise premium this model ignores. Treat the price as a disciplined benchmark, not a live quote. To go the other way and back out the volatility the market is implying for a given price, use the implied-volatility calculator; to turn that IV into an expected range, the expected-move calculator.
Educational tool only — not financial advice. Prices are model estimates for European options and will differ from live market quotes. Options trading carries a high level of risk.
Frequently asked questions
- Black-Scholes is the classic formula for the fair value of a European option from five inputs: the stock price, strike, time to expiry, risk-free rate and volatility (plus dividend yield). It also yields the Greeks — the option’s sensitivities to each input.
- Delta is sensitivity to the stock price, gamma the rate of change of delta, theta the daily time decay, vega the sensitivity to a 1% change in volatility, and rho to a 1% change in interest rates.
- Black-Scholes prices European options on non-dividend or continuously-paying stocks. Real US equity options are American style and dividends are discrete, so live prices differ a little. The model is still the standard reference for value and Greeks.
- Use the option’s implied volatility for a market-consistent price, or your own forecast to see what an option “should” be worth. The implied-volatility calculator backs IV out from a market price.
- No — the pricing runs entirely in your browser.