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