Max Pain Calculator
Find the strike where the total value of expiring calls and puts is lowest, using open interest you enter per strike.
Max pain is a single price computed from an expiring options chain: the settle at which every call and put still open would be worth the least in total. It is arithmetic performed on open interest, not a model of anything and not a forecast, and the distance between those two descriptions is where nearly all the confusion about the figure lives. This max pain calculator runs that sum across the strikes you enter and reports the total at every one of them, not only the lowest.
Formula: max pain = strike minimising sum of call and put intrinsic value x open interest
Your figures
Units of the underlying one contract controls. It differs by product and by venue — take it from your own contract specification.
Optional — where the underlying is now. Adds the distance from the strike found and the total value at that price.
Results
Max pain strike
US$100.00
the lowest total across the 5 strikes entered
- Total in-the-money value at that strikeWhat every contract on the chain would be worth if the underlying settled there.
- US$4,250,000.00
- Distance from the current priceThe strike found sits below the current price.
- -US$2.00 · -1.96%
- Total value if it settled at the current priceThe same sum evaluated at today's price rather than at a strike.
- US$5,330,000.00
- Strikes counted
- 5
- Total call open interest
- 18,800
- Total put open interest
- 16,400
- Put / call open interest ratioPut open interest divided by call open interest, across the strikes entered.
- 0.87
- Settling at US$90.001,200 calls · 3,400 puts · 90% of the highest total on the chain
- US$12,600,000.00
- Settling at US$95.002,100 calls · 4,800 puts · 48% of the highest total on the chain
- US$6,700,000.00
- Settling at US$100.00 — the lowest5,200 calls · 5,100 puts · 30% of the highest total on the chain
- US$4,250,000.00
- Settling at US$105.006,400 calls · 2,200 puts · 50% of the highest total on the chain
- US$6,950,000.00
- Settling at US$110.003,900 calls · 900 puts · 100% of the highest total on the chain
- US$13,950,000.00
What this means
Of the 5 strikes entered, settling at US$100.00 leaves the smallest total in-the-money value: US$4,250,000.00, against US$13,950,000.00 at the most expensive settle on the list. That total is every call's settle less its strike, plus every put's strike less the settle, each counted only where it finishes in the money, multiplied by its open interest and by the contract multiplier. It is a description of the open interest as entered and nothing more: it is not a forecast, it says nothing about where the underlying will settle, and it is recomputed to a different answer as soon as the chain changes.
- Every contract counted has a buyer and a seller. The figure describes where the entered open interest is worth least, not where anyone is able or inclined to move the price.
- Only the strikes you enter are tested. Leaving strikes off the chain changes the totals and can change which strike comes out lowest.
- The multiplier scales every total by the same factor, so it changes the money on screen but never which strike is the minimum.
- Open interest changes daily, and both sides of it are held by someone. The result is only as current as the chain typed in.
- Values every in-the-money contract at intrinsic value on the settle date. It ignores the premium already paid or received, and any contract closed before expiry.
Max pain strike: US$100.00
The link reopens this calculator with the same numbers. Nothing you enter is sent to a server.
Continue with these figures
About the Max Pain calculation
The calculation is small. Pick a candidate settle price, work out what each contract that finishes in the money would have to pay out, multiply by the open interest at that strike and by the contract multiplier, and add it all up. Repeat for every strike on the chain and keep the smallest total. That strike is max pain.
An options max pain figure is a description of where the open interest sits, and it is worth stating plainly what it does not claim. It does not say the underlying will settle there, that anyone is able to push it there, or that a position ought to be arranged around it. Every contract counted has a buyer and a seller, open interest changes daily, and the answer is recomputed to a different strike as soon as the chain does.
What it is genuinely good for is showing the shape of a chain. The table of totals across every strike says far more than the minimum alone: a chain with a deep, narrow minimum is concentrated somewhere, and a chain whose totals barely differ across five strikes is telling you the figure has nothing much to point at.
Max Pain formula
for a candidate settle price P:
value(P) = multiplier × Σ [ max(0, P − K) × callOI(K)
+ max(0, K − P) × putOI(K) ]
summed over every strike K on the chain
max pain = the P that minimises value(P)
only the strikes themselves are tested as candidates,
because value(P) is piecewise linear in P with kinks
at exactly those strikes
put / call ratio = total put OI ÷ total call OI- P
- A candidate settle price for the underlying at expiry.
- K
- One strike on the chain, with its own open interest on each side.
- callOI(K)
- Contracts of call open interest at strike K. A blank side counts as none.
- putOI(K)
- Contracts of put open interest at strike K.
- max(0, P − K)
- What a call is worth at settle P: the amount it is in the money, or nothing.
- multiplier
- Units of the underlying one contract controls, applied identically to every term.
- value(P)
- Total cash owed to holders of expiring contracts if the underlying settles at P.
Testing only the strikes is not a shortcut, it is exact. Between two adjacent strikes no option changes from being in the money to out of it, so the set of contracts paying out is fixed and every payout term is a straight line in P. A sum of straight lines is a straight line, so on each gap the total is linear and its lowest point on that gap must sit at one end. Every candidate minimum is therefore a strike, and searching between them cannot find anything better.
The two halves of the sum never overlap, which is what gives the function its V shape. Calls pay out only on strikes below the settle and puts only on strikes above it, so as P rises the call term grows monotonically and the put term shrinks monotonically. The minimum is wherever those two opposing slopes cross, which is why it lands in the middle of the open interest rather than at an end of the chain.
The multiplier scales every candidate settle by the same factor, so it changes every total on the page and never changes which strike is smallest. That is worth knowing because it means an incorrect multiplier does not corrupt the answer, only the money attached to it. The same is not true of the strikes: leaving strikes off the chain removes terms from every sum unevenly, and can genuinely move the minimum.
Ties are real and are reported rather than hidden. A symmetric or thinly populated chain often produces two or more strikes with the same total, and picking one of them to display would present an ambiguous chain as a precise answer. The comparison uses a small tolerance rather than exact equality, because two candidate settles reach the same total by adding up different terms and can differ in the last bit or two purely from floating-point rounding.
The put / call ratio alongside it is the crudest possible summary of the same data — total put open interest over total call open interest, across the strikes entered. It is included because it is often quoted next to max pain, and because seeing both makes it obvious that neither figure knows which side of any contract was opened by whom.
One structural caveat sits underneath all of it: the sum values every in-the-money contract at intrinsic value on the settle date and ignores the premium already paid or received. It measures what is owed at expiry, not anyone's profit, and it counts contracts that will in practice be closed or rolled before expiry ever arrives.
Max Pain: a worked example
A five-strike chain running from 90 to 110, with the underlying currently at 102 and 100 units per contract, testing each strike as a settle price.
- Settle at 90puts only: (5×4,800 + 10×5,100 + 15×2,200 + 20×900) × 100 = 12,600,000
- Settle at 95calls 600,000 + puts 6,100,000 = 6,700,000
- Settle at 100calls (10×1,200 + 5×2,100) × 100 = 2,250,000
- Settle at 100, puts(5×2,200 + 10×900) × 100 = 2,000,000, so the total is 4,250,000
- Settle at 105calls 6,500,000 + puts 450,000 = 6,950,000
- Settle at 110calls only: 13,950,000
- Max pain100 — the smallest of the six totals
- At the current 1023,950,000 + 1,380,000 = 5,330,000
- Put / call ratio16,400 ÷ 18,800 = 0.87
The 100 strike carries the lowest total at 4,250,000, against 13,950,000 at the most expensive settle on the list — so the minimum is deep rather than marginal, and the chain does point somewhere. It sits 2.00 below the current price of 102, where the same sum comes to 5,330,000. All of that describes the open interest as typed in and nothing else.
How to use the Max Pain calculator
- Add one row for each strike on the expiry you are measuring, and enter the call and put open interest against it. A side with no open interest can be left blank and counts as zero.
- Use open interest rather than volume. Open interest is the number of contracts still outstanding, which is what would have to be settled; volume is how many changed hands today and double-counts positions that were opened and closed.
- Enter the units per contract from the contract specification. It scales every total but never changes which strike comes out lowest.
- Enter the current price if you have it, to see the distance from the strike found and what the same sum comes to at today's price.
- Read the whole table, not only the headline. The spread between the lowest and highest totals is what tells you whether the minimum is meaningful or the chain is nearly flat.
- If several strikes are flagged as sharing the minimum, treat the answer as a range rather than a price — the chain has not singled one out.
- Re-enter the chain on the day you care about. Open interest changes daily, and so does the answer.
Limitations of the Max Pain calculator
Every calculation makes assumptions. These are the ones that matter here.
- It is a description of open interest, not a forecast. It says where the entered contracts would be worth least, not where the underlying will settle or where anyone is capable of moving it.
- Only the strikes typed in are tested. Omitting strikes, particularly ones carrying large open interest, changes every total and can change which strike is lowest.
- Open interest is a stale figure by the time it is published, usually reflecting the previous session, and it moves substantially in the final days before an expiry.
- Every contract counted has a buyer and a writer. The sum treats the chain as one pool of liabilities, which no single participant either owns or controls.
- Contracts are valued at intrinsic value on the settle date. The premium already paid or received is ignored, as is any position closed or rolled before expiry.
- It handles a single expiry. A chain with weekly and monthly series outstanding has several answers, and mixing them into one table produces a figure that describes none of them.
- Deep in-the-money open interest carries the most weight in the sum, because its payout distance is largest, even though those contracts are the least likely to be left open into settlement.
Frequently asked questions about Max Pain
Does max pain theory mean the underlying tends to settle at that strike?
This calculator makes no such claim and computes no such statistic. The figure is the strike minimising total in-the-money value across the open interest entered, which is a description of a chain at one moment. Both sides of every contract are held by someone, and the calculation contains nothing about anyone's ability or incentive to move a price.
Should max pain be computed from open interest or from volume?
Open interest. It counts contracts still outstanding, which is what would have to be settled at expiry, and it is the quantity the formula assumes. Volume counts contracts traded during a session and double-counts anything opened and closed the same day, so using it inflates strikes that were busy rather than strikes where positions remain.
Why does the calculator only test the strikes and not prices in between?
Because the total is piecewise linear in the settle price, with kinks only where a strike sits. Between two strikes the same contracts are in the money throughout, so the total traces a straight line and its lowest point on that segment is at one end. Checking intermediate prices cannot beat a strike, so the answer is exact rather than approximated.
What does it mean when several strikes share the lowest total?
That the chain does not single out a price. Symmetric or thinly populated open interest often produces a genuine tie, and the calculator lists every strike sharing the minimum rather than picking one. Treat a tie as a range: the arithmetic has found several settle prices with equal claim to being the smallest.
Does the contract multiplier change the answer?
It changes every cash figure and never changes the strike. Because the same multiplier is applied to each candidate settle, it scales the whole set of totals uniformly, so the smallest one stays smallest. Getting it wrong therefore misstates the money on the page while leaving the strike identified correctly.
Can I include several expiries at once?
Not meaningfully. Options expiring on different dates settle against different prices, so summing them measures a scenario in which they all settle together, which never happens. Run one expiry at a time and compare the results, rather than merging weekly and monthly open interest into a single chain.
Is this a pin risk calculator?
No, and the two measure different things. Pin risk is what a writer carries when the underlying settles on or beside a single strike and assignment on that contract becomes unpredictable. This page sums the whole chain's expiring open interest to find where it would be worth least in total, which says nothing about whether any individual contract is exercised.
Last reviewed . See our methodology and editorial policy.
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