Theta Calculator
The formula
What the theta tells you
The daily rent on an option — how much value evaporates if the market does nothing. It is the counterparty of gamma: the price paid for holding convexity, and the income of every premium-selling strategy.
Calculation: Θ = ∂V/∂(calendar day): closed-form BS theta ÷ 365. Enter your inputs and every substitution is shown below the result.
Reading the result
Theta as a share of premium per day normalizes across strikes: 1%/day is slow bleed, 5%/day is a weeklies fire hose. Compare theta to vega — one vol-point can erase a whole day of decay.
Rules of thumb: 30-dte ATM put on 20% vol bleeds ~0.15–0.3%/day of spot value; sellers price ≥1%/day to bother
Limitations and best practice
Theta is not linear: ATM decay steepens into expiry, while deep ITM/OTM options have flat theta and big gap risk instead. And calendars have holidays — real desks count trading days, not calendar days.
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
Is theta “guaranteed” income for sellers?
Why is my ITM option’s theta tiny?
How do weekends affect theta?
What is theta vs vol risk?
Source & methodology
Hull — BS theta, one-day re-pricing.
How Theta works — and what your result really means
You are here because you need a specific number, and you want to see how it was produced before you rely on it. Theta 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 Theta per day in real time, and see every substitution printed below.
Every investing metric in Investing & Markets is a bet about the future priced in today’s language. Theta translates that bet: Θ = ∂V/∂(calendar day): closed-form BS theta ÷ 365. The translation is mechanical and reliable; the judgement is deciding whether the inputs you feed it are honest forecasts or wishful numbers.
Like most useful measures, Theta is a summary, and summaries hide as much as they reveal. The companion outputs and the input table are here to reopen what the headline compressed.
Nothing below is stock text pasted around a number: the worked example computes theta per day = $-0.02 /share/day from this tool’s own defaults, and the sensitivity section ranks the inputs that move the result — Strike first, at ≈37.1 % of the headline for a ten-percent error either way in that input. Work down the page and by the end you could re-derive the result in a spreadsheet from memory.
How Theta is computed, line by line
The engine implements a single stated model: Θ = ∂V/∂(calendar day): closed-form BS theta ÷ 365. There is no hidden coefficient and no login-gated precision — the formula printed is the formula executed, which is also what makes the result citable.
Underlying price ($) (example value 125) is a quantity rather than a category — precision here is cheap and worth having. Use the figure exactly as the source document states it, not a rounded memory of it — an omitted line is the classic silent error.
Strike ($) (example value 100) is a measured number in the unit named by the label; the formula does not convert for you. This input feeds the formula directly; a defensible figure here is worth more than false precision anywhere else.
Time to expiry (years) (example value 1) is a measured number in the unit named by the label; the formula does not convert for you. 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 measured number in the unit named by the label; the formula does not convert for you. Check the convention first: if the source says “6.5 % per year”, type 6.5 and let the formula do the rest.
Implied volatility (%) (example value 23) is a measured number in the unit named by the label; the formula does not convert for you. 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. If you are unsure what belongs in this field, look at the printed steps: the substitution shows exactly how the engine uses it.
What each “Option type” choice actually does: Call → $-0.02 /share/day · Put → $-0.01 /share/day That table is the honest answer to “does this option matter”, re-derived from the formula rather than hard-coded into page copy.
A fully worked Theta example
Rather than describe the calculation, here it is end to end — every substitution in order, starting from the inputs above. Starting figures: Underlying price ($), Strike ($), Time to expiry (years), Risk-free rate (%). Run to the end, the theta per day resolves to $-0.02 /share/day — Near-flat theta — deep ITM or long-dated; decay is not your problem here on the bands this tool uses.
- Θ = [−Sφ(d1)σ/(2√T) ∓ rKe^(−rT)N(±d2)] ÷ 365 = -$0.02
- Long options pay theta; short options collect it (that is the vol seller’s paycheck)
- Theta/vega ≈ -0.2: how many vol-points of move offset one day of decay
Theta per contract/day — $-1.78. Read next to the headline, this is the figure that shows the shape of the trade-off.
2-week decay — $-24.90 /contract. Read next to the headline, this is the figure that shows the shape of the trade-off.
Premium consumed in 14 days — 0.9 of premium. Read next to the headline, this is the figure that shows the shape of the trade-off.
Theta/vega ratio — -0.18. This is the number experienced users quote when the headline alone would mislead.
Overwrite any input above and every line of this example updates with it — the substitution is live, not a screenshot of somebody else’s numbers.
Scenario table: Theta at ±10 % and ±20 % of the key input
The honest version of any estimate is a corridor, and this one is cheap to produce: Theta was recomputed at 5 points along the dominant input, with every other field left untouched.
| Strike setting | Theta per day |
|---|---|
| 80 % of the example value | $-0.01 /share/day |
| 90 % of the example value | $-0.01 /share/day |
| example inputs | $-0.02 /share/day |
| 110 % of the example value | $-0.02 /share/day |
| 120 % of the example value | $-0.03 /share/day |
Across 5 settings of Strike, the result spans $-0.03 /share/day to $-0.01 /share/day. A decision that only works at one row of this table is a decision waiting for an input to move. Reproduce it in the form above by editing Strike alone; the substitution steps will follow your figures exactly.
Where Theta 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 theta per day was recalculated from scratch. It is the fastest honest answer to “what matters most in Theta?” — and it is specific to these defaults, because sensitivity moves with the starting point.
- Nudge Strike by ±10 % and Theta lands between $-0.02 /share/day and $-0.01 /share/day (sensitivity ≈37.1 %)
- Nudge Underlying price by ±10 % and Theta lands between $-0.02 /share/day and $-0.01 /share/day (sensitivity ≈26.9 %)
- Implied volatility +10 % → Theta = $-0.02 /share/day · −10 % → $-0.02 /share/day (the theta per day shifts ≈10.3 %)
- Nudge Risk-free rate by ±10 % and Theta lands between $-0.02 /share/day and $-0.02 /share/day (sensitivity ≈5.7 %)
- Time to expiry: ten percent up gives $-0.02 /share/day, ten percent down gives $-0.02 /share/day — ≈0.8 % of the theta per day either way
Strike is the dominant lever here: ten percent either way moves the result by about 37.1 %, from $-0.02 /share/day to $-0.01 /share/day. That is where a careless figure does the most damage, so check it against a source, and treat Underlying price as the second priority (≈26.9 % per ten percent). Everything below that can stay approximate, which is a licence to stop chasing data that would not change the decision.
What a Theta of $-0.02 /share/day means in practice
A number on its own is trivia; a number against a range is intelligence. The verdict attached to the default calculation — “Near-flat theta — deep ITM or long-dated; decay is not your problem here” — is one band on a ladder your own figure may sit somewhere else on. Before treating the band as fact, note its width: ten percent either way on Strike already spans $-0.02 /share/day to $-0.01 /share/day. The practical reading rules: compare against your own history before comparing against other people; treat band boundaries as zones, not walls — one point on the wrong side of a threshold rarely changes a real outcome; and when a companion output contradicts the headline, believe the pair.
Related measures answer related questions, and the distinctions matter: Theta is the quantity, Theta per day is this tool’s reading of it, and the decision that follows belongs to neither of them separately.
Why Theta results go wrong — and how to prevent it
Theta is not linear: ATM decay steepens into expiry, while deep ITM/OTM options have flat theta and big gap risk instead. And calendars have holidays — real desks count trading days, not calendar days. 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.
Reporting the headline and quietly discarding Theta per contract/day. The companions are where the shape of the trade-off survives the rounding.
One mistake is specific to this engine: assuming every input matters equally. The computation above shows Strike dominating — a careful figure there beats false precision everywhere else.
The subtlest error is answering the wrong question precisely. Confirm that theta per day is actually the quantity your decision needs — the arithmetic is flawless either way, which is what makes the mistake invisible.
Theta verification checklist
- Compare the output against one published benchmark or a colleague’s independent estimate.
- Record the date and the inputs alongside the number so future-you knows what was assumed.
- Check Strike before anything else: it is the measured dominant input, ≈37.1 % of Theta per ten percent.
- Check that every field the formula needs actually arrived from a document, not from recollection.
- Re-run the calculation with a ±10 % stress on the two most sensitive inputs.
- Confirm the answer against one independent method or published benchmark for Theta.
Step by step: getting a trustworthy Theta out of this tool
Using a calculator well sounds trivial, but the difference between a decision-grade figure and a throwaway one lives entirely in the routine. The routine for Theta takes a minute to learn and applies to every input above.
Step 1 — one document, one pass. Open the statement, label or record that holds underlying price ($), strike ($), time to expiry (years), risk-free rate (%), implied volatility (%), option type and transcribe straight into the form. Transcription from a single source removes the mismatch errors that appear when figures are assembled from three different places. Write the assumptions in the same file as the result, and future arguments take minutes instead of meetings.
Step 2 — compute the version you would not be embarrassed by. If a stranger audited your inputs, which set would you hand over? Enter that set, read the result, and treat everything else as upside. The test of a good estimate is not that it feels right but that it changes what you do.
Step 3 — change one input at a time. Nudge a single field by ten percent, watch the headline and its companions move, then undo it. Two or three fields will dominate — the sensitivity table above already ranks them for this engine. Write the figure down before moving on; memory flatters whichever number you saw last.
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. Write the assumptions in the same file as the result, and future arguments take minutes instead of meetings.
Step 5 — write the one-line memo. “Theta per day = $-0.02 /share/day on this date, from these inputs.” That line is the entire deliverable; everything else on this page is how you earned the right to write it. A calculation you cannot explain to somebody else is a calculation you cannot defend.
The real-world conversations Theta settles
Most Options & Derivatives disagreements are arithmetic disagreements in disguise. When Theta per day of $-0.02 /share/day 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. Rounding early is the quietest way to introduce a permanent error.
Professionals in Options & Derivatives use this style of calculation as a screening filter before spending real money or effort: a quick Theta check eliminates weak options in minutes, and the survivors earn the deeper, slower analysis. Write the assumptions in the same file as the result, and future arguments take minutes instead of meetings.
There is a personal-administration use people overlook: periodic self-checking. Theta quietly drifts as life changes — rates move, bodies change, costs compound — and re-running it a few times a year catches drift while correction is still cheap. If the answer changes your behaviour, it deserves a second run with different assumptions.
People also ask about Theta
What affects Theta the most?
Measured on this engine, Strike is the dominant lever: moving it ±10 % shifts the theta per day across $-0.02 /share/day to $-0.01 /share/day — about 37.1 % of the headline, with Underlying price next at ≈26.9 %. The ranked list in the sensitivity section is computed live, not asserted from a template.
Which matters more: underlying price or strike?
Strike, by a factor of about 1.4. Concretely: ten percent on Strike is worth ≈37.1 % of Theta, the same nudge on Underlying price only ≈26.9 %. That ranking is re-computed for each page from that page’s own defaults.
How much does the “Option type” choice change the answer?
The spread is not cosmetic: this choice alone takes Theta from $-0.02 /share/day to $-0.01 /share/day with every other input frozen, which is more influence than most of the numeric fields on this page can claim.
What is a typical Theta?
With the example inputs on this page the result is $-0.02 /share/day, labelled “Near-flat theta — deep ITM or long-dated; decay is not your problem here”. “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 Theta by hand?
Three steps: write the formula (Θ = ∂V/∂(calendar day): closed-form BS theta ÷ 365), insert your values, and simplify. The worked example section shows exactly that chain for the default inputs; replicating it once on paper teaches you more about Theta than any number of calculator runs.
What happens to Theta if strike changes by 10 %?
On these inputs a ±10 % change in strike takes Theta to $-0.02 /share/day against the $-0.02 /share/day example — around 37.1 % of the headline. The same test on every other field is in the sensitivity section.
Is the Theta result of $-0.02 /share/day good or bad?
Neither, on its own — the label “Near-flat theta — deep ITM or long-dated; decay is not your problem here” 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 Strike alone moves it by ≈37.1 %.
How do I calculate Theta manually?
Write down the inputs, then follow the printed steps in order — Θ = ∂V/∂(calendar day): closed-form BS theta ÷ 365. A spreadsheet replicates it with two or three cells. The manual route is worth doing once to build intuition; after that the calculator saves time and eliminates transcription slips.
Can I predict future returns with Theta?
No tool predicts; Theta computes implications. Use it to ask "if these inputs hold, what follows" — then stress the assumptions.
Is theta “guaranteed” income for sellers?
No — it is the small, steady side of a gamma/vega trade; one 2-sigma day can cost 20 days of theta.
Why is my ITM option’s theta tiny?
Its value is intrinsic, and intrinsic does not decay; only the small time-value layer burns.
Do I need an account to use this Theta calculator?
No, and no data leaves the tab. The engine runs in the page itself, which is why the worked example, the bands and the sensitivity ranking all respond instantly to your keystrokes.
Glossary for Theta
- Theta per contract/day
- $-1.78 on the example inputs — a companion figure printed beside the headline of Theta so that no result is read in isolation.
- 2-week decay
- $-24.90 /contract on the example inputs — a companion figure printed beside the headline of Theta so that no result is read in isolation.
- Premium consumed in 14 days
- 0.9 of premium for the Theta worked case; it sits next to the main result because it carries context the headline leaves out.
- Theta per day
- The primary output of this tool: $-0.02 /share/day for the default inputs, computed exactly from Θ = ∂V/∂(calendar day): closed-form BS theta ÷ 365.
- 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 plain-language label — here “Near-flat theta — deep ITM or long-dated; decay is not your problem here” — mapping the computed figure onto experience-based ranges for Investing & Markets.
- Sensitivity (±10 %)
- How far the Theta moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
Methodology, sources and limits
Everything above runs on one stated formula, applied without hidden coefficients: Θ = ∂V/∂(calendar day): closed-form BS theta ÷ 365. Source of record: Hull — BS theta, one-day re-pricing. Where a professional version of this calculation differs, it differs in inputs and jurisdiction-specific coefficients, not in the algebra — which is why re-checking your inputs beats hunting for a second calculator.
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.
Turning this Theta into a decision
Save the number together with its inputs and today’s date; a Theta figure without context is unusable the moment an input changes.
Whoever you are (people who need one trustworthy number before their next decision), the next step is the same: replace the example inputs with your own, note the date, and re-run whenever a figure moves. In Investing & Markets, a dated figure is a trend, and an undated one is a rumour.