What are the option Greeks?

The Greeks measure how an option's price changes relative to various factors: Delta (sensitivity to stock price), Gamma (rate of change of Delta), Theta (time decay per day), Vega (sensitivity to volatility), and Rho (sensitivity to interest rates).

What does Delta tell you?

Delta ranges from 0 to 1 for calls and -1 to 0 for puts. A call Delta of 0.6 means the option price increases by ~$0.60 for every $1 increase in the stock price. Delta also approximates the probability the option expires in-the-money.

Theta measures how much value an option loses per day due to the passage of time. An option with Theta of -0.05 loses $0.05 per day (or $5 per contract of 100 shares). Theta accelerates as expiration approaches.

What does Vega measure?

Vega measures the change in option price for a 1% change in implied volatility. A Vega of 0.10 means the option price increases $0.10 for each 1% rise in IV. Longer-dated options have higher Vega.

What are second-order Greeks?

Vanna measures the rate of change of Delta with respect to volatility (or Vega with respect to stock price). Volga (Vomma) measures the rate of change of Vega with respect to volatility. These matter most for complex options strategies.

Option Greeks Calculator

Calculate all 5 option Greeks: Delta, Gamma, Theta, Vega, and Rho for call and put options. Includes portfolio Greeks, dollar values per contract, and second-order Greeks (Vanna, Volga).

Stock Price (S)

Strike Price (K)

Time to Expiry (Years)

Risk-Free Rate (%)

Volatility (%)

Call Delta (Δ)

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Put Delta (Δ) —

Gamma (Γ) —

Call Theta (Θ/day) —

Vega (ν per 1% vol) —

Call Rho (ρ per 1%) —

Extended More scenarios, charts & detailed breakdown ▾

Stock Price

Strike Price

Time (Years)

Risk-Free Rate (%)

Volatility (%)

Delta

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Gamma —

Theta (per day) —

Vega (per 1% vol) —

Rho (per 1% rate) —

Professional Full parameters & maximum detail ▾

Stock Price (S)

Strike Price (K)

Time to Expiry (Years)

Risk-Free Rate (%)

Volatility (%)

Number of Contracts (100 shares each)

First-Order Greeks

Call Delta (Δ) —

Put Delta (Δ) —

Gamma (Γ) —

Call Theta (Θ/day) —

Put Theta (Θ/day) —

Vega per 1% vol —

Call Rho per 1% —

Second-Order Greeks

Vanna (2nd order) —

Volga (2nd order) —

Dollar P&L Impact (per contract)

Dollar Delta (per contract) —

Dollar Vega (per contract) —

Daily Theta $ (per contract) —

How to Use This Calculator

Enter Stock Price, Strike Price, Time to Expiry, Risk-Free Rate, and Volatility.
The Simple tier shows all 5 Greeks for a call option instantly.
Switch to Call Greeks or Put Greeks tabs to compare.
Use Portfolio Greeks to net 3 positions and see your delta-neutral hedge requirement.
Switch to Professional for dollar P&L impact per contract, Vanna, and Volga.

Formula

Delta (call) = N(d1), Delta (put) = N(d1) − 1

Gamma = N'(d1) / (S·σ·√T)

Theta (call) = [−S·N'(d1)·σ / (2√T) − r·K·e^(−rT)·N(d2)] / 365

Vega = S·N'(d1)·√T × 0.01

Rho (call) = K·T·e^(−rT)·N(d2) × 0.01

Example

Example: S=$100, K=$100, T=0.5yr, r=4.5%, σ=25%. Call Delta=0.618, Gamma=0.0312, Theta=−$0.054/day, Vega=$0.197 per 1% vol, Rho=$0.228 per 1%.

Frequently Asked Questions

The Greeks measure how an option's price changes relative to various factors: Delta (sensitivity to stock price), Gamma (rate of change of Delta), Theta (time decay per day), Vega (sensitivity to volatility), and Rho (sensitivity to interest rates).
Delta ranges from 0 to 1 for calls and -1 to 0 for puts. A call Delta of 0.6 means the option price increases by ~$0.60 for every $1 increase in the stock price. Delta also approximates the probability the option expires in-the-money.
Theta measures how much value an option loses per day due to the passage of time. An option with Theta of -0.05 loses $0.05 per day (or $5 per contract of 100 shares). Theta accelerates as expiration approaches.
Vega measures the change in option price for a 1% change in implied volatility. A Vega of 0.10 means the option price increases $0.10 for each 1% rise in IV. Longer-dated options have higher Vega.
Vanna measures the rate of change of Delta with respect to volatility (or Vega with respect to stock price). Volga (Vomma) measures the rate of change of Vega with respect to volatility. These matter most for complex options strategies.

Related Calculators

Sources & References (5) ▾

Options, Futures, and Other Derivatives — John C. Hull — Pearson Education
CBOE Greeks Guide — Chicago Board Options Exchange
Understanding the Greeks — Investopedia
Option Volatility and Pricing — Sheldon Natenberg — McGraw-Hill Education
NASDAQ Options Education — Greeks — NASDAQ