Gas

Ethereum: 

• gas fee = units of gas used * (base fee + priority fee)
• Fees are denominated in gwei, where 1 gwei = one-billionth (0.000000001) ETH.  some text
  • The smallest denomination of ETH is wei.
  • 1 gwei = 1 billion wei.
  • Wei allows gas prices to be calculated with more precision.
  • Here is a simple gwei converter to calculate the differences.
• Total gas paid is divided into two categories, base fee and priority fee. 
• The base fee is set by the protocol and dynamically adjusts up or down based on network congestion. 
• The priority fee is set by users as a tip to validators.
• Priority fees are not mandatory, but help entice validators to include a transaction in the next block.
  ‍

Example: A user wants to execute a transaction on Ethereum that consumes 21,000 gas units, with the following fee structure:

• Base Fee: 10 gwei 
• Priority Fee: 2 gwei 
  ‍

Calculation:

1. Find gas fee per unit:
   Base Fee + Priority Fee = 10 gwei + 2 gwei = 12 gwei/unit

2. Calculate total gas fee:
   Total Gas Fee = Units of Gas Used * Gas Fee Per Unit
   Total Gas Fee = 21,000 gas units * 12 gwei/unit = 252,000 gwei

3. Convert to ETH:
   Since 1 gwei = 0.000000001 ETH, the total gas fee in ETH is:
   252,000 gwei * 0.000000001 ETH = 0.000252 ETH

The total gas fee for this transaction is 0.000252 ETH.

‍

Base (OP Stack):

• An Ethereum L2 built on Optimism (OP Stack)
• ‍Uses a FastLZ compression estimator to more accurately charge L1 data usage per transaction
• Gas fees are the sum of:some text
  • Execution gas fee: Identical to Ethereum - gas fee = units of gas used * (base fee + priority fee).
  • L1 data fee: Covers the cost for an OP transaction on Ethereum and is influenced by Ethereum’s current base fee.
    ‍

L1 data fee calculation:

The L1 data fee consists of:

1. Estimated transaction size, determined using the compressed size of the signed transaction and the Fjord linear model.

• estimatedSizeScaled = max⁡(minTransactionSize × 10^6, intercept + fastlzCoef × fastlzSize)some text
  • takes highest number (minTransactionSize × 10^6) or (intercept+fastlzCoef×fastlzSize)
  • minTransactoinSize: Minimum transaction size in bytes
  • interceprt: Fixed parameter that can be positive or negative
  • fastlzCoef: FastLZ coefficient
  • fastlzSize: The size of the FastLZ compressed signed transaction
    ‍

2. Weighted gas price multiplier, which depends on Ethereum's base fee and blob base fee.

• l1FeeScaled = baseFeeScalar × l1BaseFee × 16 + blobFeeScalar × l1BlobBaseFeesome text
  • blob: Large chunk of data stored temporarily and used to improve scalability
  • baseFeeScalar: Scales Ethereum base fee by 10^6
  • l1BaseFee:  Current Ethereum base fee
  • blobFeeScalar: Scales Ethereum blob fee by 10^6
  • l1BlobBaseFee: Current Ethereum blog gas price
    ‍

3. The final L1 data fee is computed using the scaled values of transaction size (estimatedSizeScaled ) and weighted gas price multiplier (l1FeeScaled ).

• l1Cost = (estimatedSizeScaled × l1FeeScaled)/10^12
  ‍

Example:

Suppose the following arbitrary parameters:

• minTransactionSize: 128 bytes
• intercept: 10,000
• fastlzCoef: 500
• fastlzSize: 150 bytes
• baseFeeScalar: 2,000,000
• blobFeeScalar: 1,000,000
• l1BaseFee: 20 gwei
• l1BlobBaseFee: 15 gwei
  ‍

1.  Estimate Transaction Size:

     estimatedSizeScaled = max⁡(128 × 10^6, 10,000 + 500 × 150)

     estimatedSizeScaled = max⁡(128,000,000,   85,000)

     estimatedSizeScaled = 128,000,000
‍

2.  Calculate Weighted Gas Price Multiplier:

     l1FeeScaled = 2,000,000 × 20 gwei × 16 + 1,000,000 × 15 gwei

     l1FeeScaled = 640,000,000 + 15,000,000 = 655,000,000 gwei
‍

3.  Calculate Final L1 Data Fee:

     l1Cost = (128,000,000 × 655,000,000 gwei)/10^12

     l1Cost = 83,840 gwei
‍

Convert to ETH by dividing the gwei amount by 1,000,000,000

1 ETH = 1,000,000,000 gwei 83,840 gwei/1,000,000,000 = 0.00008384 ETH

L1 data fee = 0.00008384 ETH

Total cost would be the L1 data fee (0.00008384 ETH) + the execution fee.

‍