About the Black-Scholes Calculator
The Black-Scholes model gives a theoretical price for a European call or put from five inputs: the current price, the strike, the time left, the interest rate and the volatility. This calculator also takes an optional dividend yield and reports the five common Greeks, which describe how the price should react when each input changes. It is useful for learning, for sanity-checking a quoted price and for seeing how time decay and volatility work. Real markets differ from the model, so treat the output as an estimate. All the maths runs in your browser and nothing is sent anywhere.
Updated October 2026
How to use the Black-Scholes Calculator
- 1Enter the price of the underlying and the strike price.
- 2Type the days until expiry, the risk-free interest rate and the volatility, each as a yearly percentage.
- 3Add a dividend yield if the asset pays one.
- 4Read the call and put prices at the top.
- 5Check delta, gamma, vega, theta and rho below to see how the price should react.
The five inputs
The spot price and the strike set how deep in or out of the money the option is. The time to expiry is entered in days and converted to years by dividing by 365. The interest rate is the yearly risk-free rate, such as a government bill yield, because holding the option instead of the share frees up cash.
Volatility is the least certain input. It is the yearly standard deviation of the asset's returns, so 20 means a one-year move of about 20 percent either way is roughly a one-sigma event. Doubling it makes a near-the-money option roughly twice as expensive.
Reading the Greeks
- Delta: a call delta of 0.64 means the call gains about 0.64 for each 1 the share rises.
- Gamma: highest near the strike and close to expiry, so delta changes fast there.
- Vega: per 1 point of volatility, so a vega of 0.38 adds 0.38 to the price if volatility rises from 20 to 21.
- Theta: the daily loss from time passing, usually negative for long options.
- Rho: the price change for a 1 point rise in interest rates, small for short-dated options.
Where to go next
To see what an option position earns at expiry across many prices, use the Options Payoff Calculator. To size a trade against your savings, the Kelly Criterion Calculator shows the maths of risking a fraction of your money. If you want to explore chances rather than prices, the Normal Distribution Calculator and the Z-Score Calculator give the probabilities behind the model. The page is for learning and is not financial advice.
Features
- Call and put prices together
- Delta, gamma, vega, theta and rho
- Dividend yield supported
- Theta per day, vega and rho per 1 point
- d1 and d2 shown for checking by hand
- Clear errors for impossible inputs
- Runs offline in the browser
Frequently asked questions
What is the Black-Scholes model?
It is a formula from 1973 that prices European options by assuming the underlying follows a random walk with constant volatility and that you can hedge continuously. It remains the common starting point for option pricing.
What volatility should I use?
Use the implied volatility quoted by your broker for that option, or an estimate of how much the asset typically moves in a year. Small changes here move the price a lot.
What do the Greeks mean?
Delta is the price change for a 1 unit move in the asset, gamma is how fast delta changes, vega is the change for 1 percentage point of volatility, theta is the loss per day from time passing and rho is the change for 1 percentage point of interest.
Does it work for American options?
Not exactly. American options can be exercised early, and the model here assumes exercise only at expiry. For calls on assets with no dividends the two are the same, but for puts and dividend payers they differ.
Why is my broker's price different?
Brokers show market prices set by supply and demand, which also include bid and ask spreads and a view on volatility that changes every second. The model gives a theoretical value.
What does put-call parity mean?
For the same strike and expiry, call minus put equals the share price minus the discounted strike. The numbers on this page obey that rule, which is a handy way to check them.
Can I use it for crypto or currencies?
You can enter any positive price, but the model assumes a lognormal price and a steady volatility, which are rough fits for crypto. Treat the result with extra caution.