Home › Calculators › Black Scholes Calculator

Black Scholes Calculator

Price a call or put with the Black-Scholes-Merton model and see all five Greeks.

Updated November 4, 2026. Free, no sign-up; everything runs in your browser and nothing you type is stored.

Black Scholes calculator

Stock price ($)Strike price ($)Days to expirationRisk-free rate (%)Implied volatility (%)Dividend yield (%)

Call value

–

–Put value

–Delta

–Gamma

–Vega

–Theta

–Rho

The Black-Scholes formula

The Black-Scholes-Merton model (1973) prices a European option (exercisable only at expiration) from five inputs plus dividends: stock price S, strike K, time to expiration T in years, risk-free rate r, volatility σ and dividend yield q.

d₁ = [ln(S/K) + (r − q + σ²/2)T] ÷ (σ√T), d₂ = d₁ − σ√T
Call = S e^−qT N(d₁) − K e^−rT N(d₂)
Put = K e^−rT N(−d₂) − S e^−qT N(−d₁)

N() is the standard normal distribution. Volatility is the only input you can't look up: use the option's implied volatility from your broker's chain.

The Greeks

Delta: option price change per $1 move in the stock (call 0 to 1, put −1 to 0).
Gamma: how fast delta changes.
Theta: time decay per day.
Vega: change per 1 point of volatility.
Rho: change per 1 point of interest rates.

Worked example

A $100 stock, a $105 strike, 30 days, 4% rate and 30% volatility: d₁ = -0.4861, d₂ = -0.5721, giving a call worth $1.66 and a put worth $6.32. American options on dividend stocks can be worth slightly more than the model says because of early exercise. Plan trades with the covered call calculator, cash-secured put calculator and Kelly criterion calculator.

Common questions

What is the Black-Scholes formula?

Call = S e^(−qT) N(d1) − K e^(−rT) N(d2), with d1 and d2 from price, strike, time, rate and volatility.

What volatility should I use?

The option's implied volatility from your broker.

Does Black-Scholes work for American options?

It's for European options; American calls on non-dividend stocks match it, others can be worth a little more.

Sources

More investing and trading calculators: Tax Loss Harvesting · Unrelated Business Taxable Income

General information, not financial, tax or legal advice. Check important numbers with the official source before acting on them.