Black-Scholes Option Pricing Calculator + Greeks
Calculate theoretical European option prices and all five Greeks: delta, gamma, theta, vega, rho. Includes implied volatility input.
European-style options, no dividends. Real-world prices differ due to demand, skew, and early-exercise premium (American options).
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What Black-Scholes gives you
Given a spot price, strike, days to expiry, risk-free rate and implied volatility, the Black-Scholes formula returns the theoretical fair value of a European-style option — plus the Greeks that tell you how that value will change as inputs move.
The five Greeks
Delta: change in option price per $1 move in the underlying. A 0.5 delta call gains $0.50 if the stock rises $1. Gamma: rate of change of delta — high gamma means delta swings quickly. Theta: $ lost per day to time decay (always working against you if you're long). Vega: $ change per 1% move in implied volatility. Rho: $ change per 1% move in interest rates — usually the least relevant Greek.
What this does not model
Black-Scholes assumes European exercise (no early), no dividends, lognormal returns, and constant volatility. Real markets violate all four. For US single-name equity options that are American-style, use this as an approximation. Real broker prices include skew, demand pressure, and early-exercise premium.
A theoretical value is one question; what the position actually pays at expiry is another, and the two diverge as time and volatility move. The options profit calculator covers the payoff.
How to use the Black-Scholes Calculator
Takes about a minute. No signup, no download, your data stays in your browser.
- 1Open the tool. Scroll up to the Black-Scholes Calculator above — it loads instantly in your browser, no install needed.
- 2Enter your values. The fields come pre-filled with realistic defaults so you can see how it works — replace them with your own numbers.
- 3Read the result. The output updates instantly. Copy or share it — nothing is uploaded to a server, everything stays on your device.
Frequently asked questions
Common questions about the Black-Scholes Calculator.
What is the Black-Scholes model?
Black-Scholes is a mathematical model that estimates the theoretical fair price of an option from the spot price, strike, time to expiry, volatility, and the risk-free rate.
Which option Greeks does this calculator show?
It returns the full set — delta, gamma, theta, vega, and rho — alongside the theoretical option price.
Does Black-Scholes work for American options?
The standard Black-Scholes formula prices European-style options (exercisable only at expiry). American options, which can be exercised early, need adjusted models, though the estimate is still a useful reference.
What is implied volatility?
Implied volatility is the volatility figure that, put into the model, makes the theoretical price match the market price — the market’s expectation of future movement.
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