# Math

Calculations used in the YieldBlox protocol.

## Utilization Ratio Calculations

### Utilization Ratio

Used to calculate the current utilization ratio for an asset.

### Originating Utilization Ratio

Used to calculate the originating utilization for an asset.

### Utilization Tracker Delta *depreciated*

Used to calculate the utilization tracker delta of a transaction. This allows the protocol to measure an asset's average utilization ratio over a period of time.

### Utilization Adjustment *depreciated*

Used to calculate the necessary utilization ratio delta adjustment.

### Average Utilization Ratio *depreciated*

Used to calculate the average utilization ratio for a loan.

## Accrued Interest Tracker Updates

Used to calculate accrued interest tracker updates

## Liability Token Calculations

Equations used to calculate the value of liability tokens and user liabilities.

### Liability Tokens Issued

The number of liability tokens issued to a user when they borrow from the pool.

### Liability Token Value

The value of a single liability token. Used when calculating the value of a user's liability.

### Liabilities Outstanding

Liabilities Outstanding for a given asset

## Interest Rate Calculations

Interest rates change based on the interest threshold and rates below.

### Base Interest Rate

### Interest Rate - Threshold One

### Interest Rate - Threshold Two

### Interest Rate - Threshold Three

### Average Interest Rate

### Originating Interest Rate

### Stable Rate

Used to calculate the stable interest rate for a loan.

## Minimum Collateral Requirement

Used to calculate the minimum collateral required for a loan.

## Pool Token Calculations

### Pool Token Issuance

Used to calculate the number of pool tokens issued to a user account.

### Pool Token Value

Used to calculate the value of a pool token

## Maximum Liquidation Amount

Used to calculate the maximum amount of a loan's value the liquidator is allowed to liquidate in order to reach a health factor of 1.02.

## Health Factor

Used to calculate an account's health factor.

## Maximum Liability

Used to calculate the maximum liability an account can hold at one time.

## YBX Issuance

Used to calculate how much YBX to issue.

## Issuance Ratio

Used to calculate how much YBX to issue per liability or pool token

Where:

## Pessimistic Block-Weighted Average Position Size

Used to calculate the pessimistic block-average position size for a given collateral or liability position. Used to calculate YBX issuance for a position

Where:

## YieldBlox Default Protection Amount

Used to calculate how much of the user's liability should be taken on as pool debt as part of the Default Protection Program.

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