The contract profit and loss calculation formula that most people don't know (valuable insights)

Where should we close the position for the highest profit when the price rises/falls? How much should we set the stop loss to be the most "cost-effective"? How much does the price need to rise/fall to break even? Many friends might not have a good understanding of these, so today I will take everyone through a math problem, and we will calculate and discuss together!
No nonsense, let's get straight to the point and explain from three situations: profit, loss, and breakeven.
profit formula
Maximize benefits after considering the risks of returns!
1. USDT Standard (Linear Contract)
Long Position Profit:
Profit (USDT) = N × C × ( P - P₀ ) × L
N: Number of shares
C: Each denomination (e.g., 0.001 BTC)
P: Closing price, P₀: Opening price
L: Leverage
Example: Go long 1 contract of BTC at 60,000, with a face value of 0.001 BTC, 10x, and it rises to 66,000.
Profit = 1 × 0.001 × (66,000−60,000) × 10 = 60 USDT
2. Currency-based (Inverse Contract)
The earnings are settled in BTC, and the formula is completely different!
Long Position Profit (Unit: BTC):
Profit (BTC) = N × ( / P0 - 1 / P)
Short Selling Earnings (Unit: BTC):
Profit (BTC) = N × ( / P - 1 / P0)
Example: Go long 1000 contracts at BTC 60,000 (each contract is worth 1 USD in coin margin), rising to 66,000
Revenue = 1000 × (1/60,000 − 1/66,000) ≈ 0.001515 BTC
Equivalent to USDT ≈ 0.001515 × 66,000 ≈ 100 USDT
Where should I close my position to maximize profits?
Core features of currency-based: strong profitability in low-price areas (because of the 1/P curve)
Loss formula
Calculate the best stop-loss point without considering other factors on the rise/fall!
1. USDT-based loss
Loss (USDT) = N × C × (P₀ - P) × L
2. Currency-based loss (long position)
Loss (BTC) = N × ( / P0 - 1 / P)
Example: Long 1000 contracts at 60,000, drop to 54,000
Loss = 1000 × (1/54,000 − 1/60,000) ≈ 0.001543 BTC
Equivalent to ≈ 83.3 USDT
How much should you stop loss to be the most "cost-effective"?
Calculation of stop-loss price in coin position (opening long, accepting loss of X BTC)
P stop loss = 1/(1/P0 + X/N)
Example: Open 1000 positions with 60,000, accepting a loss of 0.001 BTC
Stop loss price = 1 / (1/60000 + 0.001/1000) ≈ 54,545
Return on Investment Formula
How much do you need to short/long, and how much does it need to rise/fall to break even?
1. USDT-based return
Loss rate r, the required reverse increase to break even: Required increase = r / ( * (1 - r) )
2. Currency-based return (calculated in BTC)
Assuming you have lost Y BTC, you need to earn back Y BTC to break even.
Recover losses after going long
Current position value = Original value − Y BTC
The break-even price P' satisfies: N(1/P0-1/P')=Y
But simpler: reverse calculate using the current account BTC balance.
Practical formula (lost Y BTC, current price P₁):
For example: opened 1000 contracts at 60,000, now dropped to 50,000, lost 0.003 BTC
Break-even price = 1 / (1/50,000 − 0.003/1000) ≈ 100,000!
It has to rise to 100,000 to break even!
USDT-Based vs Coin-Based Overview Table
Remember the summary in three sentences (Universal for both versions)
USDT based: Profit is based on price difference × leverage, linear calculation is straightforward.
Currency-based: Profit depends on the reciprocal difference of 1/P, lower price earns more BTC.
It's hard to break even!
USDT-based: lose 50% to double
Coin-based: A loss of 50% may require the price to rise to 2 to 3 times to break even!
Suggestion: Always calculate how much you can lose in BTC/USDT before opening a position!