Gamma Calculator
The formula
What the gamma tells you
How fast delta moves — the convexity you buy in options. Long gamma means your position self-improves on rallies and de-risks on drops (rebalance profits), and it is purchased with theta: the daily rent printed on your statement.
Calculation: Γ = φ(d1)/(Sσ√T) — closed-form Black-Scholes gamma (convexity per $1 spot move). Enter your inputs and every substitution is shown below the result.
Reading the result
Compare gamma across strikes: it peaks at-the-money and near expiry. A 30-delta OTM weeklies position is gamma with a short fuse — enormous convexity and enormous bleed.
Rules of thumb: 0DTE ATM gamma is ~10–50× its monthly cousins; dealer gamma flips mark the squeeze zones
Limitations and best practice
Gamma and theta are the same money viewed from two axes; anyone quoting huge gamma numbers without the theta cost is selling you half a trade. Also realized gamma P&L needs realized movement — gamma only pays if the stock actually travels.
This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Frequently asked questions
Why do dealers talk about gamma so much?
Is gamma bigger ITM or OTM?
How does gamma create “gamma squeeze”?
Why does gamma explode near expiry?
Source & methodology
Hull; standard BS second derivative.
Gamma: what this tool answers
This page was written for one job: turning your own inputs into a defensible figure, with the working shown. Gamma is the kind of number people argue about from memory. This page ends that argument with arithmetic you can watch happen: enter your figures, get Option gamma in real time, and see every substitution printed below.
The useful way to hold Gamma is as a ratio with a story attached: Γ = φ(d1)/(Sσ√T) — closed-form Black-Scholes gamma (convexity per $1 spot move) says how the parts combine, and the 0.011 /$1 figure above is simply that sentence written in numbers. Everything that follows unpacks one clause of the sentence at a time.
Most confusion about Gamma comes from mixing up the input you control with the input you merely observe. The formula treats them identically, but your decisions should not: one deserves measurement, the other deserves a defensible estimate.
What makes a calculation page trustworthy is that its copy is derived from its own arithmetic: here option gamma = 0.011 /$1, recomputed every time a field changes, and the sensitivity section ranks the inputs that move the result — Underlying price first, at ≈59.5 % of the headline for a ten-percent error either way in that input — which is the thread the rest of this guide pulls on.
How Gamma is computed, line by line
Here is the complete model this tool runs — Γ = φ(d1)/(Sσ√T) — closed-form Black-Scholes gamma (convexity per $1 spot move) — with each input explained below. If a competitor’s page gives you a different answer from the same inputs, this is the text that settles which of you is right.
Underlying price ($) (example value 125) is a plain measured quantity — the unit shown in the label is the unit the formula expects. If your source quotes a figure before and after some deduction, decide which one the formula wants and be consistent for every field.
Strike ($) (example value 109) is a measured number in the unit named by the label; the formula does not convert for you. Replace the example with the figure from your own records — the tool recomputes instantly and the printed steps follow your numbers.
Time to expiry (years) (example value 1) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. Use the value as of today, not as of the last time you looked — time fields drift silently.
Risk-free rate (%) (example value 5) is a plain measured quantity — the unit shown in the label is the unit the formula expects. Rates are the most mis-transcribed input on any page like this; copy it from the document rather than retyping from memory.
Implied volatility (%) (example value 27) is a plain measured quantity — the unit shown in the label is the unit the formula expects. Rates are the most mis-transcribed input on any page like this; copy it from the document rather than retyping from memory.
Option type (example value Call) is a categorical input — the option you choose decides which numbers the formula uses. This input feeds the formula directly; a defensible figure here is worth more than false precision anywhere else.
A fully worked Gamma example
Abstract formulas are hard to trust, so here is the complete substitution using the default inputs, written the way an examiner would want it. Starting figures: Underlying price ($), Strike ($), Time to expiry (years), Risk-free rate (%). Run to the end, the option gamma resolves to 0.011 /$1 — Each $1 underlying move changes delta by 0.0108 — a $5 intraday swing reshapes the position by 0.05 delta; ATM near-term is where gamma lives on the bands this tool uses.
- Γ = φ(d1)/(S·σ·√T) → Γ = 0.01084
- Δ moves 0.0108 per $1 of spot
- Long options = long gamma; short options = short gamma — the sign that drives all vol trading
Delta change per 2% move — 0.027. Compare it against the main result of 0.011 /$1 before drawing conclusions.
Convex P&L per 2% move — $0.03 /share. Read next to the headline, this is the figure that shows the shape of the trade-off.
Γ per contract (per share basis) — 1.084. Compare it against the main result of 0.011 /$1 before drawing conclusions.
Gamma-days to ATM expiry — 183 days. This is the number experienced users quote when the headline alone would mislead.
Keep this worked example open while you enter your own figures: matching the shape of the substitution is the fastest way to spot a unit or convention mistake.
Scenario table: Gamma at ±10 % and ±20 % of the key input
The honest version of any estimate is a corridor, and this one is cheap to produce: Gamma was recomputed at 5 points along the dominant input, with every other field left untouched.
| Underlying price setting | Option gamma |
|---|---|
| 80 % of the example value | 0.020 /$1 |
| 90 % of the example value | 0.017 /$1 |
| example inputs | 0.011 /$1 |
| 110 % of the example value | 0.005 /$1 |
| 120 % of the example value | 0.002 /$1 |
That spread — 0.002 /$1 at the low end, 0.020 /$1 at the high — is what a careful read of Gamma looks like: a band you can state out loud, with the reason for each edge. Reproduce it in the form above by editing Underlying price alone; the substitution steps will follow your figures exactly.
Where Gamma is fragile — and where it is not
This list was computed for this specific engine just now: each numeric input was nudged ±10 % while every other field held its example value, and the option gamma was recalculated from scratch. Read it as a map of where Gamma is fragile — drawn for the example inputs, which is the map you want when deciding what to measure carefully.
- Underlying price: ten percent up gives 0.005 /$1, ten percent down gives 0.017 /$1 — ≈59.5 % of the option gamma either way
- Strike +10 % → Gamma = 0.015 /$1 · −10 % → 0.006 /$1 (the option gamma shifts ≈48.6 %)
- Nudge Implied volatility by ±10 % and Gamma lands between 0.010 /$1 and 0.011 /$1 (sensitivity ≈3.5 %)
- Time to expiry +10 % → Gamma = 0.011 /$1 · −10 % → 0.011 /$1 (the option gamma shifts ≈2.7 %)
- Nudge Risk-free rate by ±10 % and Gamma lands between 0.011 /$1 and 0.011 /$1 (sensitivity ≈1.1 %)
Underlying price is the dominant lever here: ten percent either way moves the result by about 59.5 %, from 0.005 /$1 to 0.017 /$1. Measure that input from a document rather than from memory, and treat Strike as the second priority (≈48.6 % per ten percent). Everything below that can stay approximate, which is a licence to stop chasing data that would not change the decision.
Interpreting the Gamma verdict
The value above only becomes useful the moment you know what it is being measured against. The default case lands in the “Each $1 underlying move changes delta by 0.0108 — a $5 intraday swing reshapes the position by 0.05 delta; ATM near-term is where gamma lives” band, and bands are deliberately wide because real situations overlap. The sensitivity list shows how far a modest input error moves you along that ladder: for Underlying price, ±10 % covers 0.005 /$1 to 0.017 /$1. The practical reading rules: ask what would have to change to move you one band. If the answer is “a small, plausible input difference”, the band itself is not the finding — the uncertainty is.
The comparison worth making is not with somebody else’s Gamma but with the version of your own situation measured last quarter — same formula, same conventions, different inputs.
How people get Gamma wrong
Gamma and theta are the same money viewed from two axes; anyone quoting huge gamma numbers without the theta cost is selling you half a trade. Also realized gamma P&L needs realized movement — gamma only pays if the stock actually travels. This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Comparing a Gamma computed here with a figure from another source that uses different conventions. Same name, different denominator — the disagreement is usually in the definitions, not the data.
One mistake is specific to this engine: assuming every input matters equally. The computation above shows Underlying price dominating — a careful figure there beats false precision everywhere else.
A final trap is presentation: reporting Gamma to more decimal places than the inputs support. The tool prints what the arithmetic gives; you should quote only what your least precise field justifies.
Six things to confirm before acting on Gamma
- Record the date and the inputs alongside the number so future-you knows what was assumed.
- Note the date and the inputs beside the number so the figure can be audited later.
- Put Underlying price under a magnifier; the sensitivity table above is the reason why.
- Check that every field the formula needs actually arrived from a document, not from recollection.
- Compare the output against one published benchmark or a colleague’s independent estimate.
- Run the ±10 % stress on the top two levers and check that your conclusion survives both.
Five steps from raw inputs to a figure you can defend
The tool does the arithmetic; the routine below is what makes the arithmetic trustworthy. Five steps, a minute total — and afterwards you will know not just what the number is, but which assumption produced it.
Step 1 — collect, then type. Everything this tool asks for is listed above (underlying price ($), strike ($), time to expiry (years), risk-free rate (%), implied volatility (%), option type). Pull each figure from something you can point at — paperwork, a dashboard, a label — before touching a field. Guesswork at the input stage cannot be repaired at the interpretation stage. Say the answer out loud before you save it; if it sounds wrong, the model did not change, your understanding did.
Step 2 — baseline before exploration. Get one defensible Option gamma on screen before you start nudging numbers. Without a baseline, every variation looks interesting and none of them means anything. Most surprises in numbers are surprises about inputs, not about formulas.
Step 3 — play with the inputs on purpose. Ten percent up, ten percent down, one field at a time. Within a few minutes you will know this calculation better than most people who quote its results. The inputs are the part of the work that nobody else can do for you.
Step 4 — stress before you commit. A decision that survives a ten-percent squeeze on its two biggest inputs needs no luck to be sound. One that does not survive is a decision about hope, not about arithmetic. When two sources disagree, it is almost never the arithmetic that differs.
Step 5 — schedule the next run. In Investing & Markets the inputs drift quietly. Put a reminder a quarter out, re-enter the same fields, and read the change rather than the level. Suspiciously tidy answers deserve the same scrutiny as untidy ones.
From calculation to decision: where Gamma earns its keep
Most Options & Derivatives disagreements are arithmetic disagreements in disguise. When Option gamma of 0.011 /$1 sits on the table with its working shown, the conversation stops being about who sounds more confident and starts being about which input is wrong. Comparisons are cheap: run the identical calculation for the alternative and look at the gap.
The companion outputs — Delta change per 2% move and Convex P&L per 2% move — exist for the second stage of that screen: the headline sizes the prize, while the companions describe the trade-off you are accepting to get it. If a result feels obviously right, that is the moment to check the inputs hardest.
Nothing here is stored or transmitted, so the habit of checking is free: open the page, re-enter current figures, compare with the number you saved last time. Write the figure down before moving on; memory flatters whichever number you saw last.
People also ask about Gamma
What affects Gamma the most?
Measured on this engine, Underlying price is the dominant lever: moving it ±10 % shifts the option gamma across 0.005 /$1 to 0.017 /$1 — about 59.5 % of the headline, with Strike next at ≈48.6 %. The ranked list in the sensitivity section is computed live, not asserted from a template.
Which matters more: strike or underlying price?
For Gamma, Underlying price wins the head-to-head (≈59.5 % against ≈48.6 % per ten-percent change). Knowing which input dominates is the difference between careful work and merely slow work.
What is a typical Gamma?
With the example inputs on this page the result is 0.011 /$1, labelled “Each $1 underlying move changes delta by 0.0108 — a $5 intraday swing reshapes the position by 0.05 delta; ATM near-term is where gamma lives”. “Typical” varies with situation, which is why every result here ships with its verdict band and its sensitivity list: they turn one figure into a range you can locate yourself inside.
How do I calculate Gamma by hand?
Use the stated model — Γ = φ(d1)/(Sσ√T) — closed-form Black-Scholes gamma (convexity per $1 spot move) — and substitute in the order the tool prints (it starts from Γ = φ(d1)/(S·σ·√T) → Γ = 0.01084). On the example inputs the hand route lands on 0.011 /$1, exactly what the calculator shows. A spreadsheet reproduces it in two or three cells; doing it once by hand is what makes the automated answer trustworthy.
What happens to Gamma if underlying price changes by 10 %?
Try it in the form above and the printed substitution will follow you; the pre-computed answer for the defaults is 0.005 /$1 to 0.017 /$1 across the ten-percent probe, i.e. ≈59.5 % sensitivity on the option gamma.
Is the Gamma result of 0.011 /$1 good or bad?
Neither, on its own — the label “Each $1 underlying move changes delta by 0.0108 — a $5 intraday swing reshapes the position by 0.05 delta; ATM near-term is where gamma lives” is the band this figure falls in for the example inputs, and your own inputs will place you elsewhere on the same ladder. Judge the number against your history and your alternatives, and remember that a ten-percent error in Underlying price alone moves it by ≈59.5 %.
What affects Gamma the most?
Sensitivity depends on where you start, but the inputs Underlying price ($) and Strike ($) typically move Gamma further than the rest because they enter the formula multiplicatively. If you can only measure two things well, measure those and hold the others at conservative defaults.
Does Gamma account for fees and taxes?
Only what you put in. Fees belong inside Underlying price ($) where they shrink returns before compounding touches them; taxes are outside the scope of a pre-tax Gamma and should be layered on top before decisions.
Why do dealers talk about gamma so much?
Because their aggregate hedge flows are a function of client gamma: long-gamma dealers sell rallies and buy dips, short-gamma dealers amplify both.
Is gamma bigger ITM or OTM?
Neither — gamma is an ATM phenomenon and collapses at both wings even though delta differs.
Is my data private on this page?
Yes — computation happens locally in your browser, with no account, no tracking of your inputs and nothing sent to a server. The printed formula is the whole story of what happens to your figures.
Glossary for Gamma
- Delta change per 2% move
- 0.027 on the example inputs — a companion figure printed beside the headline of Gamma so that no result is read in isolation.
- Convex P&L per 2% move
- $0.03 /share for the Gamma worked case; it sits next to the main result because it carries context the headline leaves out.
- Γ per contract (per share basis)
- 1.084 for the Gamma worked case; it sits next to the main result because it carries context the headline leaves out.
- Option gamma
- The primary output of this tool: 0.011 /$1 for the default inputs, computed exactly from Γ = φ(d1)/(Sσ√T) — closed-form Black-Scholes gamma (convexity per $1 spot move).
- Worked example
- The step-by-step substitution printed above, so the arithmetic can be re-derived by hand or in a spreadsheet.
- Verdict band
- The interpretation attached to a result (“Each $1 underlying move changes delta by 0.0108 — a $5 intraday swing reshapes the position by 0.05 delta; ATM near-term is where gamma lives” on these inputs), which turns a bare number into a position on a scale.
- Sensitivity (±10 %)
- How far the Gamma moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
Method, sources and what this tool cannot tell you
There is no black box on this page — the engine evaluates Γ = φ(d1)/(Sσ√T) — closed-form Black-Scholes gamma (convexity per $1 spot move). Source of record: Hull; standard BS second derivative. Specialist software layers extra coefficients on top of the same algebra; none are hidden here, and that transparency is what makes a disagreement traceable to a specific input instead of a black box.
Nothing here replaces a qualified professional, and nothing here is approximate either — the arithmetic is exact, and the honesty is in the inputs you supply. The design constraint was set by usefulness rather than by comfort: an estimate you can interrogate beats an answer you have to trust.
Next steps after the calculation
Re-run the calculation with your own figures, stress the two most sensitive inputs by ±10 %, and only then act on the result.
The audience here is people who need one trustworthy number before their next decision. Everything you need to defend the result — formula, substitution, sensitivity, source — is printed above, so the only remaining variable is the honesty of your inputs.