> For the complete documentation index, see [llms.txt](https://yummy-docs.gitbook.io/yummy-docs/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://yummy-docs.gitbook.io/yummy-docs/perpetual-futures-basics/formulas-and-definitions.md).

# Formulas and Definitions

## Margin and Balance Formulas

**Futures Margin Ratio**\
Current margin ratio = `total_collateral_value / sum(abs(position_notional_i))`
\
\
**Total Collateral**\\

Total collateral of the user (doesn’t account for any pending orders, includes unsettled PnL) = total\_balance + upnl + pending\_short\_USDC

**Free Collateral**
\
Available collateral/balance to trade (accounts for any pending orders, includes unsettled PnL) = collateral + upnl - total\_initial\_margin\_with\_orders - pending\_short\_USDC\
​
\
**Portfolio Value**
\
Total potfolio value including position notionals = USDC Balance + (non USDC assets) \* mid\_price + unsettled pnl

**Withdrawable Balance**
\
Collateral available to withdraw (excludes unsettled PnL) = total\_balance - total\_initial\_margin\_with\_orders - positive\_upnl

Ex. 1 user’s total\_balance = 100 USDC, unsettled PnL = -40 USDC, => total\_collateral is then 60 USDC. User has a position which takes up 20 USDC maintenance margin, then free\_collateral or withdrawable\_balance = 60 - 20 = 40 USDC

Ex. 2 user’s total\_balance = 100 USDC, unsettled PnL = 40 USDC, => total\_collateral is then 100 USDC. User has a position which takes up 20 USDC maintenance margin, then free\_collateral = 100 - 20 = 80 USDC and withdrawable\_balance = 80 - 40 = 40 USDC<br>

**Initial Margin Ratio**

```
IMR i = Max(1 / Max Account Leverage, Base IMR i, IMR Factor i * Abs(Position Notional i)^(4/5))
initial_margin_i = abs (position_notional_i * IMR_i)
weighted_initial_margin_ratio_i =  abs (position_notional_i / total_notional ) * IMR_i
initial_margin_ratio = sum (weighted_initial_margin_ratio_i)
```

**Maintenance Margin Ratio**

```
MMR i = Max(Base MMR i, (Base MMR i / Base IMR i) * IMR Factor i * Abs(Position Notional i)^(4/5))
maintenance_margin_i= abs (position_notional_i * MMR_i)
weighted_maintenance_margin_ratio_i = abs (position_notional_i / total_notional ) * MMR_i
maintenance_margin_ratio = sum (weighted_maintenance_margin_ratio_i)
```

## Positions PnL

**Unrealized PnL** = `position_qty * (mark_price - avg_open)`

**Liquidation Price**

```
Qi = position_qty

liquidation_price  = max[( Mark Price + ( total_collateral_value - total_notional * MMR ) / ( |Qi| * MMRi - Qi )), 0]
```

**Notional** = `position_notional_i = abs(mark_price_i * position_qty_i)`

**Fut Notional or Total Notional** = `sum (abs (position_notional_i))`

{% hint style="info" %}
Unsettled PnL is retrieved from the API and cannot be calculated
{% endhint %}

### Order placement formulas <a href="#order-placement-formulas" id="order-placement-formulas"></a>

#### [​](https://orderly.network/docs/introduction/trade-on-orderly/perpetual-futures/formulas-definitions#max-order-quantity)Max Order Quantity <a href="#max-order-quantity" id="max-order-quantity"></a>

```
newOrderSize  = (total_collateral_value - others_IM) * min(1/Base_IMR_i,maxLeverage_account) / markPrice

IMR i = Max(1 / Max Account Leverage, Base_IMR_i, IMR Factor i * Abs(Position Notional i)^(4/5))

MMR i = Max(Base MMR i, (Base MMR i / Base IMR i) * IMR Factor i * Abs(Position Notional i)^(4/5))

aftertrade_IMR.i → Max(1 / Max Account Leverage, Base_IMR_i, IMR Factor i * Abs(After Trade Position Notional i)^(4/5))

```

```
If total_collateral_value < total_initial_margin_with_orders
    if (side == buy && position_qty >=0 ) or (side == sell && position_qty < 0)
        return 0
    else
        if side == buy
            return max( abs(position_qty) - pending_long_qty, 0 )
        else
            return max( position_qty + pending_short_qty, 0 )
else
    newOrderSize = (total_collateral_value - others_IM) * min(1/Base_IMR_i,maxLeverage_account) / markPrice
    calculate afterTradeIM
    newTotalIM = othersIM + afterTradeIM
    if side = buy
        others = -holding - pendingLongQty
    else
        others = holding + pendingShortQty
    
    if totalCollatValue >= newTotalIM
        return max(0, newOrderSize * 99.5% + others)
    else
        newOrderSize_iter = ITERATE()
        return max(0, newOrderSize_iter * 99.5% + others)
        
with : 
total_collateral_value = total_balance + upnl + pending_short_USDC
total_initial_margin_with_orders =  sum (position_notional_with_orders_i * IMR_i (with_orders))
position_qty_with_orders_i = max[abs(position_qty + sum_position_qty_buy_orders),abs(pos_qty + sum_position_qty_sell_orders)]
position_notional_with_orders_i = abs(mark_price_i * position_qty_with_orders_i)
others_IM = sum[i#j)(initial_margin_with_orders_i) (where j represents the pair i on which the order is being placed)
```