Options Greeks Calculator

Calculate Black–Scholes option Greeks (Delta, Gamma, Theta, Vega, Rho) for European calls and puts with optional dividend yield.

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%

Annualized implied volatility as a percent (e.g., 20).

%

Annual rate as a percent (e.g., 5).

%

Optional — dividend yield as a percent (e.g., 2).

Enter underlying price, strike, implied volatility, risk-free rate, and time to expiration, then click Calculate Greeks to see Delta, Gamma, Theta, Vega, and Rho.

Options Greeks Formulas

d1 = [ln(S/K) + (r - q + 0.5σ²)T] / (σ√T)

d2 = d1 - σ√T

n(x) = exp(-0.5x²) / √(2π)

Call Δ = e^(-qT) N(d1)

Put Δ = e^(-qT) [N(d1) - 1]

Γ = e^(-qT) n(d1) / (Sσ√T)

ν = Se^(-qT) n(d1)√T  (÷100 for per 1%)

Call ρ = KTe^(-rT) N(d2)  (÷100 for per 1%)

Put ρ = -KTe^(-rT) N(-d2)  (÷100 for per 1%)

Θ per day = Θ annual / 365