Options Greeks Calculator

Compute Delta, Gamma, Theta, Vega, and Rho instantly for any call or put. Free, no signup required.

Calculate Your Greeks

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Live Greeks — coming with Premium tier

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Right now IV is a manual entry — these are theoretical Greeks, not market Greeks. Premium auto-populates IV from the live option chain so every number reflects actual current pricing, and updates as the stock moves.

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Live IV from Option Chain
IV auto-filled from the real ATM option — no guessing what to enter, no stale numbers
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Greeks Across the Full Chain
Delta, Gamma, Theta, Vega for every strike and expiry — not just one contract at a time
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Real-Time Greek Updates
Greeks refresh as the stock ticks — watch Delta shift live on a fast-moving name
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Scenario Stress Tests
Pre-built shocks: "IV spikes +20pts", "stock gaps −8%", "rate hike" — instant Greek impact
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IV Rank & Percentile
Know if the IV you're pricing is cheap or rich vs. its own 52-week history before you trade
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Greeks P&L Simulator
Drag stock price and IV simultaneously — see combined P&L impact across all five Greeks

What Are the Options Greeks?

The Greeks are sensitivity measures — they tell you how much an option's price will change when one market variable moves while all others stay constant. Together they give you a complete risk profile of any option position.

Delta (Δ) — Directional Risk

How much the option price moves per $1 move in the stock. A delta of 0.50 means the option gains $0.50 if the stock rises $1. Call deltas range 0 to 1; put deltas range −1 to 0.

Gamma (Γ) — Delta Rate of Change

How fast delta changes as the stock moves. High gamma means your delta shifts quickly — great for directional bets, risky for short options. Gamma peaks at-the-money near expiration.

Theta (Θ) — Time Decay

How much value the option loses per calendar day, all else equal. Always negative for long options. An at-the-money option with 30 DTE loses value faster each day as expiry approaches.

Vega (V) — Volatility Sensitivity

How much the option price changes per 1% change in implied volatility. Long options have positive vega — they benefit when IV rises (like before earnings). Short options have negative vega.

Rho (ρ) — Interest Rate Sensitivity

How much the option price changes per 1% change in the risk-free interest rate. Rho matters most for long-dated options (LEAPS) and is usually the least impactful Greek for short-term trades.

How the Greeks Are Calculated

All five Greeks are derived from the Black-Scholes model. The core inputs are: stock price (S), strike price (K), time to expiry (T in years), implied volatility (σ), and risk-free rate (r).

d₁ and d₂ (intermediate values) d₁ = [ ln(S/K) + (r + σ²/2) × T ] / (σ × √T)
d₂ = d₁ − σ × √T
Delta Call: N(d₁)  |  Put: N(d₁) − 1
where N(x) is the cumulative standard normal distribution
Gamma N′(d₁) / (S × σ × √T)   — same for calls and puts
Theta (per day) Call: [ −S × N′(d₁) × σ / (2√T) − r × K × e^(−rT) × N(d₂) ] / 365
Put: [ −S × N′(d₁) × σ / (2√T) + r × K × e^(−rT) × N(−d₂) ] / 365
Vega (per 1% IV change) S × N′(d₁) × √T / 100
Rho (per 1% rate change) Call: K × T × e^(−rT) × N(d₂) / 100  |  Put: −K × T × e^(−rT) × N(−d₂) / 100

Reading Your Greeks in Practice

Example: 30-day ATM call on a $100 stock, 30% IV, 5% rate
  • Delta ≈ 0.52 — option gains ~$0.52 per $1 stock rise
  • Gamma ≈ 0.065 — if stock rises $1, delta becomes ~0.585
  • Theta ≈ −$0.055/day — option loses ~$5.50/week from decay alone
  • Vega ≈ $0.115 — if IV rises from 30% → 31%, option gains ~$0.115
  • Rho ≈ $0.013 — minimal impact for 30-day options

Key insight: Greeks aren't static. Delta and gamma change as the stock price moves; theta and vega change as time passes. Re-check your Greeks after any significant stock move or IV shift.

Using Greeks for Position Sizing

Delta tells you your effective share exposure — a 0.50 delta option on 1 contract (100 shares) behaves like holding 50 shares. If you want the P&L sensitivity of 200 shares, you need 4 contracts at 0.50 delta.

Greek Relationships to Watch

  • Long gamma, short theta: Buying options gives you positive gamma (delta accelerates in your favor) but costs theta every day.
  • Short gamma, long theta: Selling options (iron condors, covered calls) collects daily theta but exposes you to fast delta shifts.
  • Long vega before earnings: If you expect an IV spike before a catalyst, long vega positions benefit. Post-event IV crush hits long vega hard.

For a full P&L analysis with live stock data, try the OptionsVault options calculator.