Options Greeks Calculator
Estimate European call and put delta, gamma, theta, vega, and rho, then compare how the sensitivities change across spot prices and time.
Earlier editorial review
- Reviewed
- 2026-09-25
- Methodology
- 1.1
Sources
How the calculator works
Enter the underlying spot price, strike price, days to expiry, annual volatility in percent, and annual risk free rate in percent. Choose call or put to select which option type is used in the spot, time, and sensitivity tables. The results show both call and put Greeks at the same inputs.
The spot table uses 21 prices from 20% below to 20% above the entered spot. The time table recomputes theta at shorter remaining terms, ending at one day. When less than one day remains, it shows the entered fractional expiry instead.
The sensitivity table applies the linear spot change S × (1 ± σ√T), where σ is annual volatility as a decimal and T is years to expiry. It holds strike, volatility, rate, and expiry fixed, then recalculates the selected option's delta, gamma, theta, and vega.
Change one input at a time to see which assumptions move the estimates. The calculator does not fetch live option prices or volatility data, so use current contract inputs from a source you trust.
Step by step
- Enter the option inputs and choose call or put.
- Compare call and put Greeks at the entered assumptions.
- Review the spot, time, and volatility scaled spot sensitivity tables.
Worked example
For spot 100, strike 100, 365 days, volatility 20%, and a 5% annual rate, call delta is 0.6368, put delta is −0.3632, gamma is 0.0188, and call vega is 0.3752 per volatility point.
The call theta is −0.0176 per calendar day, and call rho is 0.5323 per rate point. Values are per one underlying share unit and are rounded to four decimals.
When to use this calculator
Use the tables to compare model sensitivities for a European call or put while changing spot or remaining time and holding other assumptions fixed.
Check the option style, dividend policy, quote date, contract size, and volatility convention before comparing these estimates with a broker screen.
Common interpretation errors
Vega and rho are changes per one percentage point, not per 100 percentage points. The calculator does not multiply values by a standard 100 share option contract size.
Theta is per calendar day. Check the convention used by your broker before comparing its displayed theta with this estimate.
Model equations
T = days to expiry ÷ 365
d1 = [ln(S ÷ K) + (r + σ² ÷ 2) × T] ÷ (σ × √T)
d2 = d1 − σ × √T
Call delta = N(d1), put delta = N(d1) − 1
Gamma = φ(d1) ÷ [S × σ × √T]
Call theta = [−Sφ(d1)σ ÷ (2√T) − rKe^(−rT)N(d2)] ÷ 365
Put theta = [−Sφ(d1)σ ÷ (2√T) + rKe^(−rT)N(−d2)] ÷ 365
Vega = S × √T × φ(d1) ÷ 100
Call rho = KTe^(−rT)N(d2) ÷ 100
Put rho = −KTe^(−rT)N(−d2) ÷ 100
S is spot, K is strike, σ is annual volatility as a decimal, and r is the annual continuously compounded rate as a decimal. Theta is reported per calendar day. Vega and rho are reported per one percentage point change. All values are per one underlying share unit.
Assumptions and limits
Inputs must be finite. Spot and strike must be positive, days to expiry must be above zero and at most 730, annual volatility above zero and at most 200%, and annual risk free rate from −50% to 50%. This European option model assumes no dividends, constant volatility, and a continuously compounded annual rate. It does not model early exercise, discrete dividends, volatility skew, bid and ask spreads, liquidity, assignment, taxes, contract quantities, or portfolio interactions. The volatility scaled spot change is a simplified linear scenario, not a statistical spot standard deviation.
Key terms
- Delta
- Delta estimates option value sensitivity to a one unit change in the underlying price.
- Intrinsic value
- Intrinsic value is the amount by which an option is in the money at a stated spot price, before any time value or transaction costs.
- Annual volatility assumption
- Annual volatility is the assumed yearly standard deviation of the underlying return, entered as a percentage.
Compare related tools
Compare these sensitivities with the Black Scholes Option Pricer to see the matching theoretical call and put premiums under the same inputs.
Option Breakeven Calculator focuses on payoff at expiry. This page shows model sensitivities before expiry. Margin Call Calculator covers a separate borrowing scenario.
FAQ
How does the calculator produce the Greeks?
The calculator uses the Black Scholes model for European options with no dividends. It calculates call and put Greeks at the entered spot, strike, expiry, volatility, and rate. The normal distribution is approximated numerically.
What units do the Greek values use?
Delta estimates price sensitivity to a one unit change in the underlying. Gamma measures how delta changes with the underlying price. Theta is the model value change for one calendar day less. Vega and rho are sensitivity to a one percentage point change in volatility and the annual rate.
What do the tables show?
The spot table recalculates the selected option's Greeks at 21 spot levels from 80% to 120% of the entered price. The time table recalculates theta at remaining expiry values down to one day. If expiry is under one day, it shows the entered fractional day.
What do the volatility scaled spot scenarios mean?
The table applies a linear spot change S × (1 ± σ√T), where σ is entered annual volatility as a decimal and T is years to expiry. Applying a log return volatility scale directly as a spot percentage is a simplified scenario. These rows are not statistical spot standard deviations, probability ranges, or forecasts. A nonpositive shocked spot is unavailable.
Does the time table predict an option's future value?
The theta table recalculates the model at shorter remaining terms while holding the other inputs fixed. It is a set of snapshots, not a forecast of an option's market price or realized profit and loss. Volatility, rates, dividends, and market prices can change over time.
Related tools
Use the Black Scholes Option Pricer for theoretical premiums, Option Breakeven Calculator for expiry payoff, Margin Call Calculator for borrowing risk, and Stock Chart for underlying price history.