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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

  1. Enter the contract. Set stock price, strike, days to expiry and option type.
  2. Add rate and volatility. Enter the risk-free rate and volatility (and dividend yield if any).
  3. Read price and Greeks. The fair value and all five Greeks update as you type.

About Black-Scholes and the Greeks

The model separates an option's value into intrinsic value and time value, and the Greeks tell you how that value reacts as the world changes — the stock moves (delta/gamma), time passes (theta), volatility shifts (vega) or rates change (rho). Traders use them to size and hedge positions. To find the volatility the market is implying for a quoted option, use the implied-volatility 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

What is the Black-Scholes model?
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.
What are the Greeks?
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.
Why does my broker’s price differ slightly?
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.
What volatility should I enter?
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.
Is anything sent to a server?
No — the pricing runs entirely in your browser.

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