Black Scholes Calculator

You can use this Black-Scholes Calculator to determine the fair market value (price) of a European put or call option based on the Black-Scholes pricing model. It also calculates and plots the Greeks – Delta, Gamma, Theta, Vega, Rho.

Enter your own values in the form below and press the "Calculate" button to see the results.

Black-Scholes Option Calculator




Option Type: Call Put Values
?x? Variable Symbol Input Value From To
Spot Price SP
Strike Price ST
Expiry Time (Y) t
Volatility (%) v
Rate (%) r
Div. Yield (%) d

Option Type: Call Option

y Axis Symbol Result

The Black-Scholes Option Pricing Formula

You can compare the prices of your options by using the Black-Scholes formula. It's a well-regarded formula that calculates theoretical values of an investment based on current financial metrics such as stock prices, interest rates, expiration time, and more. The Black-Scholes formula helps investors and lenders to determine the best possible option for pricing.

The Black Scholes Calculator uses the following formulas:

C = SP?e-dt?N(d1) - ST?e-rt?N(d2)

P = ST?e-rt?N(-d2) - SP?e-dt?N(-d1)

d1 = ( ln(SP/ST) + (r - d + (σ2/2))?t ) / σ?√t

d2 = ( ln(SP/ST) + (r - d - (σ2/2))?t ) / σ?√t = d1 - σ?√t


C? is the value of the call option,

P? is the value of the put option,

N (.)? is the cumulative standard normal distribution function,

SP? is the current stock price (spot price),

ST? is the strike price (exercise price),

e? is the exponential constant (2.7182818),

ln? is the natural logarithm,

r? is the current risk-free interest rate (as a decimal),

t? is the time to expiration in years,

σ? is the annualized volatility of the stock (as a decimal),

d? is the dividend yield (as a decimal).

You may also be interested in our EPS Calculator or RSI Calculator

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