What is option gamma?

Gamma is the rate of change of an option's delta for a $1 increase in the underlying price. If a call has delta 0.50 and gamma 0.05, a $1 stock rise moves delta to approximately 0.55. Gamma is always positive for long options and negative for short options.

Is gamma the same for calls and puts?

Yes. By Black-Scholes put-call parity, gamma is identical for a call and a put with the same strike and expiry. This tool shows one value that applies to both.

When is gamma highest?

Gamma peaks for at-the-money options close to expiration. As an option moves deep in- or out-of-the-money, or as expiry is far away, gamma falls toward zero.

How do I enter time to expiration?

Enter years as a decimal. For example: 1 month ≈ 0.083, 3 months = 0.25, 6 months = 0.5, 1 year = 1.0. A quick way: divide calendar days by 365.

What units does gamma have?

Gamma is expressed as delta per dollar — dimensionally (delta / $). For a contract covering 100 shares, multiply the per-share gamma by 100 to get the dollar-delta change per $1 move.

Does this work for American options?

This calculator uses the European Black-Scholes formula. American options, which allow early exercise, have slightly different gamma, especially for deep-in-the-money puts. For most equity calls (no dividend), the approximation is close.

Option Gamma Calculator

Compute option gamma from stock price, strike, expiry, volatility, and risk-free rate — instantly shows how fast delta changes per $1 move.

Option Parameters

Stock Price (S) — current underlying price

Strike Price (K)

Time to Expiry (T) — in years

Implied Volatility (σ) — annualized %

Risk-Free Rate (r) — annualized %

Gamma

Option Gamma (call = put)

—

delta change per $1 move in underlying

Low gamma — High gamma

Supporting Values

—

standardized log-return

N′(d1)

—

normal PDF at d1

Delta

Call

—

Put

—

for reference

Vega

—

$/1% vol move

Model Inputs

S = —

K = —

T = — yr

σ = —%

r = —%

σ√T = —

Summary

Gamma measures how much an option's delta changes for every $1 move in the underlying asset. It is identical for calls and puts at the same strike and expiry (Black-Scholes symmetry). High gamma means delta is unstable — the option's directional exposure can shift quickly. This tool uses the Black-Scholes closed-form formula: Gamma = N'(d1) / (S * sigma * sqrt(T)), where d1 = (ln(S/K) + (r + sigma^2/2)*T) / (sigma*sqrt(T)) and N'() is the standard normal PDF. All calculations run client-side; no data is sent anywhere.

How it works

Enter the current stock (underlying) price in dollars.
Set the option strike price and time to expiration in years (e.g., 0.25 for 3 months).
Input the annualized implied volatility as a percentage (e.g., 25 for 25%).
Enter the annualized risk-free interest rate as a percentage.
Gamma and supporting values update instantly; the result applies equally to calls and puts.

Use cases

Estimate how quickly your delta hedge will drift after a stock move.
Compare gamma across different strikes to find the most sensitive option.
Understand gamma risk before entering a short-options position.
Check how near-expiry vs. far-expiry options differ in gamma exposure.
Verify option pricing homework or practice for the CFA or FRM exam.
Model gamma scalping potential for a long-gamma volatility strategy.

Frequently Asked Questions

Last updated: 2026-06-15 · Reviewed by Nham Vu