Option Greeks Calculator
Delta, Gamma, Theta, Vega and Rho from the Black-Scholes model
Put the option's details in
Free. No sign-up. Every figure below updates while you type, so there is no button to press.
Are you looking at a call or a put?
What one share trades at now, for example 100. For an option on an index, type the index level.
The price at which the option lets you buy, for a call, or sell, for a put. For example 100.
Calendar days from today to the expiry date, for example 30. A year is 365.
The IV figure beside the option quote: the yearly swing the market expects. Type 20 for 20%.
The yield on a government bill or bond maturing around the same time as the option. Type 5 for 5%.
Leave it at 0 if the share pays nothing. Type 2 for a 2% annual yield.
Use any currency, as long as the share price and the strike are in the same one.
What comes back in that currency
Use whatever currency the option is quoted in. Nothing here is converted, so the only rule is that the share price and the strike are in the same one. The option price, Theta, Vega and Rho then come back in that currency too. Delta carries no currency at all: it is a ratio, how far the option moves for each unit the share moves.
This call gains about 0.6368 when the share rises by 1, and loses about 0.0176 a day
By the model it is worth 10.4506 today, with the share at 100.00, the strike at 100.00 and 365 days left. Both figures hold for small steps only. The lines below give all five changes, each with the price the model gives afterwards. All figures are for one option on one share.
What moves that figure, one change at a time
Click a line to jump to the field it depends on.
Every figure here is for one option on one share. Check your contract size before scaling them up to a position.
What these figures assume
Conventions: Theta is per calendar day (the yearly figure divided by 365). Vega is the price change for a move of 1 percentage point in volatility. Rho is the price change for a move of 1 percentage point in the interest rate. Switching between call and put changes the price, Delta, Theta and Rho. Gamma and Vega stay the same.Each line changes one thing and holds the rest still, and it describes a small step. After a large move, or when several things change together, type the new numbers above instead of adding the lines up. The model prices an option that can only be used on its expiry date, and it assumes the volatility and the interest rate stay the same until then.
Insight: The Greeks describe how an option position reacts to each market variable. Traders combine them to build delta-neutral hedges, manage time decay, and size exposure to volatility, but every value here assumes the Black-Scholes world of constant volatility and continuous trading, which real markets only approximate.
What happens if the share price moves further
Same strike, same days left, same volatility, interest rate and dividend. Only the share price changes. Your own price is the highlighted row.
| If the share price were | What the option is worth | Delta | Gamma | Theta per day |
|---|---|---|---|---|
| 80.00 | 1.8594 | 0.2219 | 0.018598 | -0.0087 |
| 90.00 | 5.0912 | 0.4298 | 0.021820 | -0.0143 |
| 100.00yours | 10.4506 | 0.6368 | 0.018762 | -0.0176 |
| 110.00 | 17.6630 | 0.7958 | 0.012887 | -0.0181 |
| 120.00 | 26.1690 | 0.8965 | 0.007500 | -0.0171 |
Reading down the Delta column shows the thing a single Delta cannot: it is not a fixed property of the option but a number that slides as the share moves, and Gamma is the speed of that slide.
This calculator derives the option Greeks analytically from the Black-Scholes-Merton model. Each Greek is a partial derivative of the option price with respect to one input, so they tell you precisely how a small change in the share price, time, volatility, or interest rate is expected to move the option value.
d₁ = [ln(S/K) + (r − q + σ²/2)T] / (σ√T)
Step 1: Choose whether you are looking at a call or a put, then type the share price today and the strike price written on the contract.
Step 2: Type the calendar days left until expiry, and the volatility shown beside the option quote.
Step 3: Type the interest rate you want the model to assume, and the dividend yield of the share if it pays one.
Step 4: Read the sentence at the top of the result, then the five lines under it and the table of nearby prices. It all recalculates while you type, so there is no button to press.
Delta (Δ): The change in the option price for a change of one in the share price. A call Delta normally sits between 0 and 1, and a put Delta between -1 and 0. The dividend factor multiplies Delta, so a negative dividend yield can push a call Delta above 1, and this calculator shows that rather than hiding it. Traders also read Delta as the number of shares that would move by the same amount, which is how it is used for hedging.
Gamma (Γ): The rate of change of Delta for a change of one in the share price. Gamma is identical for calls and puts at the same strike and peaks for at-the-money options near expiration, where Delta is most unstable. High Gamma means a hedge needs frequent rebalancing.
Theta (Θ): Time decay, the change in option value as one calendar day passes with nothing else changing. It is usually negative for a bought option, because extrinsic value erodes as expiry approaches, and positive for the seller who collects that decay. Usually, not always: a deep in the money European put, and a call on a share paying a large dividend, can both carry a positive Theta, because waiting brings the payout closer. This tool reports Theta per calendar day and captions it according to the sign it actually computes.
Vega (ν): Sensitivity to implied volatility, reported here per 1 percentage point change. Vega is identical for calls and puts at the same strike and is largest for at-the-money options with plenty of time left. Long options are long Vega; they gain when volatility rises.
Rho (ρ): Sensitivity to the risk-free interest rate, reported per 1 percentage point change. Rho is positive for calls and negative for puts, and it matters most for long-dated options. For short-dated contracts it is usually the least significant Greek.
What Are the Option Greeks?
The option Greeks are a family of risk measures, each named after a Greek letter, that quantify how the theoretical value of an option responds to a change in one input while everything else is held constant. Mathematically they are the partial derivatives of the Black-Scholes pricing formula, which is why they can be computed exactly from the same inputs that price the option itself.
For anyone trading or hedging options, the Greeks are more useful than the price alone. The price tells you what an option is worth today; the Greeks tell you how that value is likely to move as the market shifts. This calculator returns the five first-order and second-order Greeks most traders rely on, Delta, Gamma, Theta, Vega and Rho, for a European call or put.
Delta, Gamma, Theta, Vega and Rho Explained
Delta measures directional exposure: it is the expected change in the option price for a change of one in the share price, and it doubles as the share-equivalent position used in delta hedging. Gamma is the second derivative, the rate at which Delta itself changes as the share moves. Because Delta is only a local approximation, a position with high Gamma needs frequent rehedging, and Gamma is greatest for at-the-money options close to expiry.
Theta captures the cost of time. An option is a wasting asset, and Theta measures how much value it sheds with each passing day, all else equal, a headwind for buyers and a tailwind for sellers. Vega quantifies sensitivity to implied volatility: when the market expects larger swings, premiums for both calls and puts rise, and Vega tells you by how much per one-point move in volatility. Rho, the sensitivity to the risk-free interest rate, is the quietest Greek for short-dated options but grows in importance for long-dated contracts such as LEAPS.
How Traders Use the Greeks
Professional desks rarely look at a single option in isolation. They aggregate the Greeks across an entire book so that the portfolio Delta, Gamma, Theta, Vega and Rho each describe one dimension of total risk. A common goal is to be delta-neutral, holding offsetting positions so the book barely moves with small changes in the share price, while remaining deliberately long or short Gamma, Theta or Vega depending on the view being expressed.
Income strategies lean heavily on Theta: a seller of covered calls or cash-secured puts is collecting time decay and watching Vega in case volatility spikes against them. Directional traders watch Delta and Gamma to size and adjust their exposure. Volatility traders structure straddles and spreads around Vega, going long when they expect volatility to expand and short when they expect it to contract. In every case, the Greeks turn a static price into a forward-looking risk map.
Black-Scholes Assumptions and Limitations
Because these Greeks are derived from the Black-Scholes-Merton model, they inherit its assumptions. The model presumes that the share price follows a log-normal random walk with constant volatility, that the risk-free rate and dividend yield are constant, that markets are frictionless with no transaction costs, and that the option is European and exercised only at expiration. None of these conditions holds perfectly in real markets.
In practice, implied volatility varies across strikes and maturities, the so-called volatility smile or skew, so a single volatility input is an approximation. Early exercise can be optimal for American options, and large jumps violate the smooth-path assumption. The Greeks therefore work best as a guide for small, near-term moves; for large shocks or long horizons, traders supplement them with higher-order Greeks, scenario analysis, and models that relax the constant-volatility assumption. For the full theoretical price alongside intrinsic and time value, use the companion option pricing calculator.
Frequently Asked Questions About the Option Greeks Calculator
The option Greeks are partial derivatives of the Black-Scholes option price that measure how the price responds to each input. Delta measures sensitivity to the share price, Gamma to the change in Delta, Theta to the passage of time, Vega to implied volatility, and Rho to the risk-free interest rate. Together they describe an option position's risk profile.
Theta measures time decay, the change in an option's value as one day passes, all else equal. For someone who bought a call or a put, the option steadily loses extrinsic value as expiry approaches, so Theta is usually negative, and for the seller that same decay works in their favour. It is not a universal rule. A deep in the money European put, and a call on a share with a large dividend yield, can both show a positive Theta, because the holder benefits from time passing rather than losing by it. This calculator prints whichever sign the model produces and captions it to match.
On this calculator, Vega is the change in option price for a 1 percentage point change in implied volatility (the raw Black-Scholes Vega divided by 100), and Rho is the change in option price for a 1 percentage point change in the risk-free interest rate (also divided by 100). Theta is the change per calendar day (the annual figure divided by 365).
Yes. A continuous dividend yield reduces the forward price of the share, which lowers a call's Delta and value and raises a put's. This calculator uses the Black-Scholes-Merton extension, discounting the share price by e^(-qT) so that Delta, Theta, and the option price all reflect the dividend yield you enter.
See the Bigger Picture of Your Wealth
The Greeks measure option risk, but they are only one slice of your finances. With a free Worthmap account, you can record what you own and owe in each currency, see your net worth in one base currency over time, and use the stock screener and AI analysis. The free plan is in beta.
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Educational use only. This tool provides estimates for informational purposes and does not constitute financial, investment, tax, or legal advice. Results are based on inputs you provide and mathematical models, they do not guarantee future performance. Always consult a qualified financial adviser before making investment decisions.