Liquidation Price Calculation: Why a 100x Long Dies in 0.5%

It is 03:14 UTC. A trader you will never meet has just opened a long: one unit of BTC at $2,000, 100x leverage, isolated margin. The app will show them a liquidation price of $1,989.95 — a 0.503% move and they are gone. They will treat that number as a fact about their trade, a line the market has to cross before it is allowed to hurt them.

You know better, because you are the one who chose it. You are the risk engine. You sit behind the exchange, and every liquidation price on the venue is a decision you made. Five decisions, actually, and I want to walk you through the shift in the order you make them.

Decision one: how much room do you allow?

The trader thinks you allow them everything. You do not. Start with the naive model they carry in their head — leverage L, entry P₀, nothing else — and the number is clean, round, and wrong.

Their margin per unit is P₀ / L. Their loss per unit at price P is P₀ − P. Dead when loss equals margin:

• P₀ − P = P₀ / L
• P = P₀ × (L − 1) / L

At L = 10 and P₀ = $2,000 that gives $1,800 — a −10.000% move. Tidy. Also not how you work.

You never let a position run to zero. You close it while something is left, and the something you keep is the maintenance margin: a slice of the notional, set by position size, that must stay in the account at all times. The kill condition is not “loss equals margin.” It is “equity equals maintenance requirement.”

• P₀ / L + (P_liq − P₀) = mmr × P_liq
• P_liq = P₀ × (L − 1) / (L × (1 − mmr))

At 10x, entry $2,000, mmr = 0.50%: $1,809.05. Your rule just took $9.05 of runway off the same trade — 45 basis points of breathing room removed by changing nothing the trader can see.

One rigour note you should carry. Your actual maintenance requirement is not notional × mmr; it is notional × mmr − maintenance amount, where the maintenance amount is a per-tier deduction that stops the requirement from jumping at a tier boundary. For BTCUSDT that deduction is zero in tier 1 and non-zero only from tier 2 up. Every position in this article sits in tier 1, so the arithmetic is exact, not approximate. Above tier 1, the liquidation would come out slightly further away than the formula predicts.

Here is the ladder you generate, entry $2,000, mmr 0.50%:

Leverage	Liquidation price	Drop to liquidation
2x	1005.03	−49.749%
5x	1608.04	−19.598%
10x	1809.05	−9.548%
20x	1909.55	−4.523%
25x	1929.65	−3.518%
50x	1969.85	−1.508%
75x	1983.25	−0.838%
100x	1989.95	−0.503%
125x	1993.97	−0.302%

Now change only mmr, holding 100x and $2,000:

Maintenance margin rate	Liquidation price	Drop to liquidation
0.40%	1987.95	−0.602%
0.50%	1989.95	−0.503%
0.65%	1992.95	−0.352%
1.00%	2000.00	0.000%

Read the last row. At a 1.00% maintenance rate and 100x, the liquidation price is the entry price. The position is dead on arrival. Not risky. Dead. Hold that; it is the ending.

And mmr is not a constant you picked for fun. On Binance’s USDⓈ-M BTCUSDT perpetual it is tiered by position size:

Tier	Notional (USDT)	Max leverage	Maintenance rate
1	0 – 300,000	150x	0.40%
2	300,000 – 800,000	100x	0.50%
3	800,000 – 3,000,000	75x	0.65%
4	3,000,000 – 12,000,000	50x	1.00%

The rate is a function of size, not leverage. Two traders, same BTC, same 50x: the one holding $500k sits in tier 2 at 0.50%; the one holding $5m sits in tier 4 at 1.00% and gets taken out sooner. Bigger positions die earlier, and you call that a feature, because a big position is the one that can hurt the book.

Decision two: which price do you watch?

The trader watches the last traded price, the one on the chart. You do not. You trigger liquidation on the mark price — a smoothed, composite estimate: an index aggregated from major spot venues, plus a 30-second moving-average basis, blended with the funding term. The last price is whatever the most recent trade on one venue happened to print.

• The last price draws the chart and calculates realised PnL. 2) The mark price triggers liquidation and calculates unrealised PnL. 3) They are not the same number, and the trader cannot trade the mark price.

This is where “quote versus fact” stops being philosophy. Open a short with the mark price at 17,000 and the system prints your liquidation at 17,006. Then, inside a single second, the mark price jumps from 17,000 to 17,100. The trader does not get liquidated at 17,006. They get liquidated at 17,100, and 17,100 is what lands in the liquidation history. The formula did not change. The input did. The number you quoted was 17,006; the number they died at was 17,100 — a 0.55% gap, and on the way through, the mark price was never a price at which they could have clicked sell.

Decision three: who pays the rent?

Not you. Them — and their margin pays it before the market does anything. A regular Binance USDⓈ-M taker pays 0.05% of notional per fill; open and exit, 0.10% of notional, charged on notional, which is margin × leverage. At 100x that is 10% of their margin gone before the chart moves. Their room was about 0.503% of price = $10.05 on a $20 margin. Round-trip taker fees on $2,000 of notional cost $2.00 — roughly one fifth of the entire room. Their effective runway drops from 0.503% to about 0.40%. The fee did not move the chart. It moved their entry.

Funding is worse, because funding is a clock, and the clock runs while they sit still. You settle it every 8 hours by default — 00:00, 08:00, 16:00 UTC. The fixed interest component alone is 0.01% per interval, about 0.03% a day. Your own documentation states the consequence plainly: if the wallet balance is insufficient, funding is deducted from position margin, “which may affect your liquidation price.”

Do the arithmetic. Funding is charged on notional, so at 100x one neutral interval is 0.01% × 100 = 1% of their margin every eight hours, 3% a day. That is the quiet case. The BTCUSDT funding cap is ±0.30% per interval — and the cap is not a round number somebody liked, it is 0.75 × the 0.40% maintenance rate, your own published rule. At the cap, funding is 0.30% × 100 = 30% of their margin every eight hours, 90% in a single day. A 100x isolated position whose whole runway is 0.503% can be liquidated by the funding schedule alone, with the price standing perfectly still. The market does not have to come for them. The clock does.

And the clock accelerates exactly when they can least afford it. Since May 2025, when a funding settlement lands on the cap or the floor, you shorten that contract’s interval from eight hours to one hour until it normalises. The worst funding they will ever pay is therefore the funding they pay most often.

Decision four: what backs the position?

Up to here you assumed the margin at risk is the margin they assigned. That is the isolated definition, and the $1,989.95 at 100x is a real isolated number.

Cross margin redefines the word. Now the entire USDⓈ-M wallet backs every position, and the liquidation price depends on the wallet balance, the unrealised PnL of other positions, and their maintenance margin. Same entry, same leverage, different number.

Take the same 100x long with $1,000 in the cross wallet instead of $20 of isolated margin. The collateral available to the contract is no longer $20; it is about $1,000. Liquidation lands near $1,005, where a $1,000 loss exhausts a $1,000 buffer. The number moved by $985. Isolated said $1,989.95; cross said $1,005 — same trade, same exchange, same second.

And cross is not a gift. That $1,000 is one number until a second position opens, at which point its maintenance margin is subtracted from the collateral backing the first, and the first position’s liquidation price climbs back toward entry. The trader did not change the first trade. They changed your view of their margin, and the quote moved. That is why “where is my liquidation” has no stable answer. Isolated, it is a number. Cross, it is a running calculation.

Decision five: how much leverage may you sell?

Back to the dead-on-arrival row. The maintenance rate does not just nudge the number; it bounds whether the position can exist.

For a long, liquidation must happen below entry, or there is nothing to liquidate. Set the ratio below 1:

• (L − 1) / (L × (1 − mmr)) < 1
• L − 1 < L − L × mmr
• mmr < 1 / L, equivalently L < 1 / mmr

That is your ceiling. Push leverage to exactly 1 / mmr and the liquidation price collapses onto the entry price — the 1.00% / 100x row from decision one.

• At a 0.50% maintenance rate, the wall is 1 / 0.005 = 200x. 2) At Binance’s lowest tier, 0.40%, the wall is 1 / 0.004 = 250x.

So the maximum leverage any venue can offer is bounded by 1 / mmr. That is why you do not sell a 1,000x bitcoin contract. Not kindness, and not paternalism dressed up as risk management. Algebra. A 1,000x contract would require a maintenance rate below 0.10%, and a rate that thin cannot absorb the gap between the price that triggers a liquidation and the price the liquidation order actually fills at. When the gap exceeds the buffer, the position goes bankrupt, the insurance fund pays the difference, and if the fund empties, auto-deleveraging fires and you force-close some profitable stranger on the other side to balance the book. The maintenance rate is the knob that keeps all of that from happening. It cannot be turned to zero. Therefore leverage cannot be turned to infinity. The wall is real, and it is built from the one parameter the trader never got to choose.

Binance’s own numbers sit comfortably inside the wall rather than at it. The published top tier for BTCUSDT is 101–150x against a 0.40% maintenance rate — a 250x algebraic ceiling, and a venue that chose to stop at 150. It gates the top of that range too: since December 2025 a newly opened futures account cannot use more than 20x in its first 30 days, and since August 2025 regular-user sub-accounts are capped at 5x. A venue choosing numbers well short of the algebraic limit, because it would rather keep the insurance fund solvent than win an advertising contest it already won.

End of shift

So the next time the app quotes a liquidation price, remember whose chair it came from. It is not a fact about the trade. It is not the market’s opinion. It is a computed output of the risk engine, fed by a maintenance rate that moves with size, triggered by a mark price nobody can trade, eroded by fees charged on money the trader does not have and a funding clock that never stops.

(The End)