See how an option's value responds to the stock price, time, volatility and interest rates. Enter your call or put and position size to get the five main Greeks per share and for your whole position, second-order Greeks, and charts of each Greek against stock price, days to expiration or implied volatility.
Last updated:
Option position
Option type
Position
Market inputs
$
$
Calendar days (÷ 365)
%
%
%
Sensitivity chart
Enter your values to see the result.
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How to use the Option Greeks Calculator
Choose call or put, long or short, and the number of contracts.
Enter the stock price, strike and days to expiration.
Enter implied volatility, the risk-free rate and dividend yield as percentages.
Pick a Greek to chart and whether to chart it against stock price, days left or volatility.
Press Calculate Greeks to see per-share and position Greeks, the formulas and the sensitivity chart.
Option Greeks at a glance
Greek
Measures
Long call
Long put
Largest when
Delta (Δ)
Price change per $1 in the stock
0 to +1
−1 to 0
Deep in the money
Gamma (Γ)
Delta change per $1
Positive
Positive
At the money, near expiry
Theta (Θ)
Value change per day
Usually negative
Usually negative
At the money, near expiry
Vega (ν)
Change per 1 point of IV
Positive
Positive
At the money, long-dated
Rho (ρ)
Change per 1 point of rates
Positive
Negative
Deep in the money, long-dated
Short positions flip every sign: a short option has negative gamma and vega and usually positive theta.
Formulas (Black-Scholes-Merton)
With d1 = [ln(S/K) + (r − q + σ²/2)T] ÷ (σ√T), d2 = d1 − σ√T, N() the normal CDF and φ() the normal density:
Delta: call e−qTN(d1); put −e−qTN(−d1)
Gamma: e−qTφ(d1) ÷ (Sσ√T), the same for calls and puts
Vega: S·e−qTφ(d1)√T, divided by 100 for a 1-point IV change
Theta (call): −S·e−qTφ(d1)σ ÷ (2√T) − rK·e−rTN(d2) + qS·e−qTN(d1), divided by 365 for one day
Rho: call K·T·e−rTN(d2); put −K·T·e−rTN(−d2), divided by 100
Example: S = $100, K = $105, 45 days, IV 25%, r = 4.25%, no dividend. The call has d1 ≈ −0.452, delta 0.326, gamma 0.041, theta −$0.039 a day and vega $0.127 per IV point. One long contract therefore acts like about 33 shares and loses about $3.87 a day to time decay.
Using Greeks to manage a position
Delta hedging: to make a position roughly neutral to small moves, offset its position delta with shares (for example, sell 33 shares against one long call with delta 0.33).
Gamma risk: short options near expiration can change delta very fast; a short at-the-money weekly can go from 0.5 to 0.9 delta in one move.
Theta vs. gamma: sellers collect theta but carry negative gamma; buyers pay theta for positive gamma. You cannot have both for free.
Volatility events: before earnings, high vega means a drop in IV after the announcement can hurt long options even if the stock moves.
Rescale theta: this calculator uses calendar days; some platforms show theta per trading day (÷ 252), which is about 45% larger.
Frequently asked questions
What do the option Greeks mean?
Delta is the change in option price per $1 move in the stock. Gamma is how much delta changes per $1 move. Theta is the value lost per day as time passes. Vega is the change per 1 percentage point of implied volatility, and rho is the change per 1 point of interest rates.
How is option delta calculated?
In the Black-Scholes-Merton model, call delta = e^(−qT)·N(d1) and put delta = −e^(−qT)·N(−d1), where d1 = [ln(S/K) + (r − q + σ²/2)T] ÷ (σ√T). Call deltas run from 0 to 1 and put deltas from −1 to 0; an at-the-money option is near ±0.5.
What are position Greeks?
Position Greeks scale the per-share Greeks by contracts × 100 shares and flip the sign for short positions. Long 2 calls with delta 0.40 behave like +80 shares; short 2 puts with delta −0.40 also behave like +80 shares, but with negative gamma and positive theta.
Why does theta get larger near expiration?
Time value decays faster as expiration approaches, especially for at-the-money options. Theta is roughly proportional to 1 ÷ √T, so an at-the-money option with 9 days left loses about twice as much per day as one with 36 days left, all else equal.
Why is gamma highest for at-the-money options near expiry?
Near expiration, a small move decides whether an at-the-money option finishes in or out of the money, so delta can swing from near 0 to near 1 quickly. Gamma measures that swing and peaks at the strike as time runs out.
What are vanna, charm and vomma?
They are second-order Greeks. Vanna is the change in delta per 1 point of implied volatility, charm is the daily change in delta from time passing (delta decay), and vomma is the change in vega per 1 point of implied volatility.
Are these Greeks exact for American options?
They come from the Black-Scholes-Merton model for European options. For most stock options without imminent dividends the values are close, but American puts and calls near ex-dividend dates can differ. Broker platforms may also scale theta by trading days.
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