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Options Greeks: every number a trader looks up
Greeks are sensitivity measures. Each one tells you how much an option's price changes when a single input moves by one unit: the stock price, time, implied volatility, or interest rates. Five Greeks cover virtually every position you will manage.

:TABLE [title:The five Greeks at a glance, links:https://www.optionseducation.org/advancedconcepts/delta]
Greek | Measures | Per unit change | Long call sign | Long put sign
Delta | Option price vs stock price | $1 move in underlying | +0.00 to +1.00 | -1.00 to 0.00
Gamma | Delta vs stock price | $1 move in underlying | Positive | Positive
Theta | Option price vs time | 1 calendar day passes | Negative | Negative
Vega | Option price vs implied vol | 1% IV move | Positive | Positive
Rho | Option price vs interest rates | 1% rate move | Positive | Negative

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Delta: how much the option moves with the stock
Delta is the most-watched Greek. A call with 0.50 delta gains roughly $0.50 when the underlying rises $1, and loses $0.50 when it falls $1. At-the-money options typically sit near 0.50. Deep in-the-money calls approach 1.00 as expiration nears; far out-of-the-money calls approach 0. Some traders treat delta as an approximate probability that the option expires in the money. Example from OIC: a $20 call trading at $2.00 with 0.50 delta rises to $2.50 when the stock gains $1, and falls to $1.50 when the stock drops $1.

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Gamma: the rate of change of delta
Gamma tells you how quickly delta shifts. A call with 0.40 delta and 0.10 gamma has a delta of 0.50 after the stock rises $1. A gamma above 0.05 is often considered relatively high. Gamma is highest for at-the-money options close to expiration and lowest for deep in-the-money or far out-of-the-money options, where delta is already near its limits and cannot accelerate further. Front-month ATM options carry substantially more gamma than long-dated options at the same strike. Short gamma positions benefit from quiet markets; long gamma positions benefit from large moves in either direction.

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Theta: time decay, the seller's income
Theta is almost always negative for option buyers and positive for sellers. An option with theta -0.05 loses five cents per day in extrinsic value, all else equal. Decay is non-linear: it accelerates sharply inside the last 30 days before expiration. At-the-money options have the most extrinsic value and therefore the highest absolute theta. Deep in-the-money and far out-of-the-money options hold little time premium and decay more slowly. Pricing models account for weekends, so an option decays seven days' worth of theta over five trading days.

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Vega: sensitivity to implied volatility
Vega is not a Greek letter, but it behaves like one. It measures how much an option's price changes for a 1% (100 basis point) shift in implied volatility. An option with vega 0.15 and 30% IV gains $0.30 if IV rises 2 percentage points to 32%. Long options (calls and puts) always carry positive vega: they benefit from rising volatility. Short options carry negative vega. Longer-dated options have higher vega than near-term ones, because there is more time for volatility to move the price. At-the-money options typically have higher vega than out-of-the-money options at the same expiration.

:LINK
https://www.tastylive.com/concepts-strategies/option-greeks
tastylive: Options Greeks overview

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Rho: interest rate sensitivity
Rho measures the change in an option's value for a 1% move in interest rates. Calls have positive rho (rising rates increase call premiums); puts have negative rho (rising rates reduce put premiums). A $100 call with rho +0.45 gains $0.45 per share if rates rise from 3% to 4%. Rho is larger for longer expirations and higher-priced stocks, because the cost of carrying the position is greater. Most short-term traders treat rho as a minor Greek: interest rates rarely move sharply within a single option cycle.

:TABLE [title:How Greeks behave across moneyness levels, links:https://www.optionseducation.org/advancedconcepts/gamma]
Greek | Deep in the money | At the money | Deep out of the money
Delta (call) | Near +1.00 | Near +0.50 | Near 0.00
Delta (put) | Near -1.00 | Near -0.50 | Near 0.00
Gamma | Low (delta near its limit) | Highest (delta most reactive) | Low (delta near its limit)
Theta | Lower (less extrinsic value) | Highest (most extrinsic value) | Lower (less extrinsic value)
Vega | Lower | Highest | Lower
Rho | Highest (most intrinsic to carry) | Moderate | Near zero

:TABLE [title:Practical DTE reference rules, links:https://www.optionseducation.org/advancedconcepts/theta]
Scenario | Practical rule of thumb
Selling premium for income | Enter around 30 to 45 DTE, where theta is healthy \
and gamma risk is still manageable | 
Theta acceleration | Decay accelerates noticeably inside the last 30 days. \
Sellers who want to avoid gamma spikes often close by 21 DTE | 
Gamma spike risk | Inside 14 DTE, ATM gamma rises sharply. A small stock move \
can produce a large delta change. Most income traders close well before this. | 
Long options timing | Buying 60 to 90 DTE or longer keeps vega exposure high \
and theta decay relatively slow per day | 
Weekend theta | Models price in Friday-to-Monday decay. Options lose roughly \
3 days of theta over each 2-day weekend, not 2. | 

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Greeks are theoretical estimates, not guarantees. They assume all other inputs stay constant, which they never do. Delta, gamma, theta and vega all change simultaneously as the stock moves, time passes and volatility shifts. Treat them as a directional guide rather than a precise prediction.

:LINK
https://www.optionseducation.org/advancedconcepts/delta
Options Industry Council: Greeks reference