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.
For educational purposes only. Not financial advice. Read full disclaimer
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Not sure whether to use Greeks or P/L? Compare Options Greeks vs Options P/L →
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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
Worked Examples
Example 1: At-the-Money Call with 30 DTE
SPY is trading at $450. You look at the 450 call with 30 days to expiration, implied volatility of 18%, and a risk-free rate of 5%.
- Delta ≈ 0.50 — the option moves ~$0.50 for every $1 move in SPY
- Gamma ≈ 0.05 — delta will increase by ~0.05 if SPY rises $1
- Theta ≈ −$0.03/day — the option loses ~$3 per day per contract
- Vega ≈ $0.15 — a 1% rise in IV adds ~$15 of value per contract
Example 2: Deep OTM Put with 60 DTE
SPY is at $450 and you examine the 420 put (deep OTM) with 60 days to expiration and IV of 22%.
- Delta ≈ −0.10 — low directional sensitivity given the OTM strike
- Gamma ≈ 0.01 — small gamma; delta changes slowly
- Theta ≈ −$0.01/day — slower time decay than an ATM option
- Vega ≈ $0.18 — moderate vega; longer duration boosts volatility sensitivity even at low delta
How to Use This Calculator
- Enter the stock price — the current market price of the underlying asset.
- Enter the strike price — the option's exercise price. Use the same strike you see on the options chain.
- Set time to expiry — enter the number of days until expiration. The calculator converts this to a fraction of a year (T = days / 365).
- Enter implied volatility — use the IV shown on your broker's options chain, expressed as a percentage (e.g., enter 20 for 20% IV).
- Set the risk-free rate — typically the current 3-month T-bill rate (e.g., 5.0%). This has a small effect on most short-dated options.
- Select call or put — choose the option type you want to analyze.
- Click Calculate — the calculator returns Delta, Gamma, Theta, Vega, and Rho using the Black–Scholes model.
Frequently Asked Questions
- What are the options Greeks?
- The Greeks are sensitivity measures that describe how an option's price changes in response to different variables. Delta measures price sensitivity, Gamma measures the rate of change in delta, Theta measures time decay, Vega measures volatility sensitivity, and Rho measures interest rate sensitivity.
- What does Delta tell you?
- Delta approximates how much the option's price will move for a $1 change in the underlying. A delta of 0.50 means the option gains or loses roughly $0.50 for every $1 move. Delta also approximates the probability that the option expires in-the-money.
- Why does Theta accelerate near expiration?
- Time value erodes faster as expiration approaches because there is less time for the underlying to move in your favor. The relationship is nonlinear — an ATM option loses more value per day in the final 30 days than in the first 30 days of its life.
- What is Gamma risk?
- Gamma measures how quickly your delta changes as the underlying moves. High gamma means your position's directional exposure is unstable and can shift rapidly — which is especially dangerous for short options near expiration when gamma spikes dramatically.
- How does Vega affect options during earnings?
- Before an earnings announcement, implied volatility typically rises, inflating option premiums. After the event, IV collapses — a phenomenon called a "vol crush." High vega means your option is more sensitive to this IV change, which can cause significant losses even if the stock moves in your direction.