Black-Scholes Option Pricing Calculator
Price a European call or put with the Black-Scholes model and see every Greek. Enter the inputs below - the theoretical value, delta, gamma, theta, vega and rho update instantly. You can also solve for implied volatility from a market price. Free, no sign-up.
Prices are per share (an equity option contract covers 100 shares). See the options profit calculator to build a full multi-leg strategy.
Greeks
| Greek | Call | Put |
|---|---|---|
| Deltaper $1 in the underlying | 0.5324 | -0.4676 |
| Gammadelta change per $1 | 0.0462 | 0.0462 |
| Thetavalue lost per day | -0.0624 | -0.0515 |
| Vegaper +1% volatility | 0.1140 | 0.1140 |
| Rhoper +1% interest rate | 0.0408 | -0.0411 |
Option value vs underlying price
Implied volatility
Implied volatility: 24.8% - the volatility that makes the Black-Scholes call price equal $3.00.
About the Black-Scholes model
The Black-Scholes formula prices a European option from six inputs: the underlying price, the strike, the time to expiration, the volatility, the risk-free rate, and the dividend yield. A call is worth S e-qT N(d1) - K e-rT N(d2), where d1 and d2 are shown above and N() is the standard normal distribution. The Greeks are the partial derivatives of that price: delta (sensitivity to the stock), gamma (how delta changes), theta (time decay), vega (sensitivity to volatility) and rho (sensitivity to rates). This calculator is for education, not investment advice, and prices European-style options; American options can be worth slightly more.
Want to see the payoff of a whole strategy - covered calls, spreads, iron condors - with breakeven, max profit and loss? Use the free options profit calculator and strategy builder.
Black-Scholes calculator questions, answered
What is the Black-Scholes model?
Black-Scholes is the classic formula for pricing European call and put options. Given the stock price, strike, time to expiration, volatility, and the risk-free rate, it returns a theoretical fair value for the option plus its sensitivities (the Greeks). It assumes the stock follows a lognormal random walk with constant volatility and that the option is exercised only at expiration.
How do I use this Black-Scholes calculator?
Enter the underlying price, the strike, days to expiration, the implied volatility, the risk-free rate, and any dividend yield. The calculator instantly shows the theoretical call and put price and every Greek (delta, gamma, theta, vega, rho). Change any input to see the option value and Greeks update live.
What are d1 and d2?
d1 and d2 are the two intermediate terms in the Black-Scholes formula. N(d1) is the option's delta-like probability factor and N(d2) is the risk-neutral probability the call finishes in the money. The calculator shows both so you can follow the math.
How is implied volatility calculated?
Implied volatility is the volatility that makes the Black-Scholes price equal the option's actual market price. There is no closed-form solution, so it is solved numerically - this tool searches for the volatility that reproduces the price you enter. Type a market option price into the implied-volatility box to back out its IV.
Does Black-Scholes work for American options?
Black-Scholes prices European options (exercisable only at expiration). Most US equity options are American (exercisable any time), but for non-dividend-paying stocks the values are nearly identical, and for typical dividend yields the difference is small. Treat the result as a close theoretical estimate.