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Transaction fee

warning

Ideally this would not exist in a vacuum and instead benefit from a general explanation on Cardano transactions.

note

This file is hand-written and currently not checked for correctness. The domain is very small and hence this would make for a great testing ground for techniques to ensure consistent, but also approachable documentation.

This is a write-up of how transaction fees are calculated. In fact, the minimum transaction fee for transaction to be deemed valid by the Cardano ledger.

This document describes the situation as of

  • Protocol version: 10
  • Era: Conway

See also:

Inputs

  • Transaction bytes, CBOR-encoded
  • Resolved inputs (= unspent outputs), CBOR-encoded
  • Protocol Parameters
    • minFeeConstant
    • minFeeCoefficient
    • minFeeReferenceScripts
    • prices.memory
    • prices.steps

warning

TODO: Include transaction CDDL to reference individual parts (e.g. transaction_output) TODO: Explain protocol parameters somewhere

Algorithm

At a high level, the fee is composed of

  • a minimum constant,
  • plus a cost per transaction byte,
  • plus a cost per reference script byte,
  • plus an execution cost per budgeted script redeemer.

Calculate the base fee by adding the minFeeConstant to (minFeeCoefficient * serialized transaction length in bytes). These numbers are all integers, so you shouldn’t end up with a fractional amount of lovelace.

warning

TODO: Explain resolving input and reference inputs

Next, calculate the untagged size of each scriptRef on each of the transaction inputs and reference inputs. Specifically, each scriptRef field is serialized as a cbor tag, an integer plutus version, and then the raw script bytes. We’re interested in the size of the raw script bytes only.

Next, calculate the reference script fee. First, sum up the length in bytes of each of script reference into scriptRefLengths. The minFeeReferenceScripts parameter consists of a base, a multiplier, and a range. (Note that in conway, the multiplier and the range are hard coded, rather than protocol parameters, but the intention is to change this at the next hardfork.)

To calculate the fee, starting from a baseFee of minFeeReferenceScripts.base and remaining bytes of sum(scriptRefLengths), until remaining bytes is zero, add baseFee * min(remainingBytes, minFeeReferenceScripts.range), scale baseFee by minFeeReferenceScripts.multiplier, and decrease remainingBytes by min(remainingBytes, minFeeReferenceScripts.range). This calculation can result in rational values (as the multiplier can be rational), and so you should take the ceiling as a last step.

Finally, to calculate the evaluation fee, for each redeemer, multiply the redeemer execution units budget (memory and steps) by the corresponding protocol parameters (prices.memory and prices.steps), and add them up. These are fractional parameters, so you may end with a fractional amount of lovelace, and you should take the ceiling.

The final minimum fee is the base fee, plus the reference script fee, plus the evaluation fee.

Example

Lets do a decently complex worked example, from mainnet transaction with id (body hash)

f06e17af7b0085b44bcc13f76008202c69865795841c692875810bc92948d609

The transaction bytes are:

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

This is 1358 bytes and you can inspect it using https://cbor.nemo157.com/

Among the inputs and reference inputs, there are 2 inputs which, when resolved, contain reference scripts:

  • reference input f5f1bdfad3eb4d67d2fc36f36f47fc2938cf6f001689184ab320735a28642cf2#0 with 2469 bytes
  • reference input fa46a1d162c59cece3308c5a9d4db9ff2ea17f9c0146ff821c9b445588b017c9#0 with 15728 bytes

And there are three redeemers:

  • Spend#0 with a budget of 1057954 memory units, and 335346191 steps
  • Spend#2 with a budget of 28359 memory units, and 8270119 steps
  • Withdraw#0 with a budget of 40799 memory units, and 12323280 steps

The protocol parameters at the time were:

  • minFeeConstant: 155381 lovelace
  • minFeeCoefficient: 44 lovelace per byte
  • minFeeReferenceScripts:
    • base: 15 lovelace
    • multiplier: 1.2
    • size increment: 25600 bytes
  • prices.memory: 0.0577 lovelace per memory unit
  • prices.steps: 0.0000721 lovelace per step

Thus:

  • The base fee is 155381 + 44 * 1358 = 215133 lovelace.
  • The total reference scripts length is 2469 + 15728 = 18197 and fall under the 25,600 byte increment, so it costs 15 lovelace per byte: 15 * min(18197, 25600) = 15 * 18197 = 272955 lovelace
  • And the execution costs are ceil(1057954 * 0.0577 + 335346191 * 0.0000721 + 28359 * 0.0577 + 8270119 * 0.0000721 + 40799 * 0.0577 + 12323280 * 0.0000721) = ceil(90697.606839) = 90698 lovelace.

Thus, the total minimum fee is 578786 lovelace.

Note that historically calculating this has been pretty opaque, and so many people have resorted to slightly padding the minimum fee, and I believe this is why the on-chain minimum fee (which is declared in the transaction body) is 601677 lovelace.