Minimum ada value requirement

UTXOs on the ledger may contain a heterogeneous collection of tokens, including ada, which is a limited resource in the Cardano system. Requiring some amount of ada to be included in every UTXO (where that amount is based on the size of the UTXO, in bytes), limits the maximum total size taken up by UTXO entries on the ledger at any given time.

The maximum possible UTXO size (the sum of the sizes of all UTXO entries) is implicitly adjusted by raising and lowering the min-ada-value variable. In this way, the constraint protects the Cardano ledger from growing beyond a certain size. A ledger without a size bound is vulnerable to being populated by so much data that users will unable to process it (or run a node) with machines meeting the recommended specifications for running a node.

The ada-only case

Because of the min-ada-value constraint, a guaranteed bound on the number of entries in an ada-only UTXO is

max No. UTxOs <= (total ada in circulation) / (minimum ada value)

This formula bounds the number of UTXO entries, but says nothing about adjusting for the size of each entry, because all UTXO entries that contain only ada are (close enough to) the same size. The size of the UTXO set is bounded by

max UTxO size <= (max No. UTxOs) * (max UTxO entry size) + overhead

In the multi-asset Cardano ledger, UTXO entries have different sizes. In particular, any entries containing a non-ada asset contain records of the Policy IDs, asset names, and quantities of each of the non-ada assets. To maintain the max UTxO size bound on the UTXO stored on the ledger with variable entry sizes, we must adjust the minimum ada value for each UTXO entry (based on its size).

Below, we present a calculation and a more detailed justification for this adjustment.

Minimum ada value calculation

The minimum ada amount required to be contained in every ada-only UTXO with no additional data (ie, a UTXO containing only the address and ada amount) is a protocol parameter of the Cardano system, called : minUTxOValue

The size of such a UTXO has an upper bound : adaOnlyUTxOSize

We can calculate the upper bound of the UTXO size u containing non-ada tokens : sizeBound (u)

We want to calculate the min-ada required to be contained in u : minAda (u)

A minUTxOValue amount of ada pays for adaOnlyUTxOSize bytes of UTXO storage on the ledger. To make the min-ada-value proportional for all UTXOs, the following proportion must be satisfied :

minUTxOValue / adaOnlyUTxOSize = minAda (u) / sizeBound (u)

The min-ada calculation for any UTXO approximates the above formula. This uses the constants,

coinSize = 0 (note: this is an implementation error, and will be changed to the correct value, 2, in the next fork. This will decrease the minimum ada value by a small percentage)

utxoEntrySizeWithoutVal = 27

adaOnlyUTxOSize = utxoEntrySizeWithoutVal + coinSize = 27

The functions used in the formula below are :

• quot a b is the quotient of (a, b), ie. quot 11 5 = 2 because 11 = 5 * 2 + 1

• numAssets : the number of distinct AssetIDs in B, eg. if B = [(policyID1, myAssetNameSBS, 10), (policyID1, yourAssetNameSBS, 5), (policyID2, someAssetNameSBS, 250), (policyID3, someAssetNameSBS, 43)]

  numAssets B = 4

• numPIDs : the number of distinct PolicyIDs in B eg. if B is as above, numPIDs B = 3 (which are policyID1, policyID2, policyID3)

• sumAssetNameLengths : the sum of the length of the ByteStrings representing distinct asset names eg. if B is as above,

  sumAssetNameLengths B = length myAssetNameSBS + length yourAssetNameSBS + length someAssetNameSBS

• pidSize : the length of the hash of a policy (ie, the length of the PolicyID). These lengths are the same for all policies, and are dictated by the current hashing algorithm used to compute payment and staking address hashes.

  pidSize B = 28 currently (also, in the next era)

• roundupBytesToWords converts bytes to 8-byte long words, rounding up roundupBytesToWords b = quot (b + 7) 8

• size B is size of the token bundle B in 8-byte long words : size B = 6 + roundupBytesToWords (((numAssets B) * 12) + (sumAssetNameLengths B) + ((numPids B) * pidSize))

For a UTXO containing a token bundle B the min-ada-value calculation is as follows :

• Case 1 : Token bundle B in the UTxO u contains only ada (no other tokens) minAda (u) = minUTxOValue

• Case 2 : Token bundle B in the UTxO u contains ada as well as other tokens minAda (u) = max (minUTxOValue, (quot (minUTxOValue, adaOnlyUTxOSize)) * (utxoEntrySizeWithoutVal + (size B)))

As a consequence of this design,

• It is impossible to make outputs containing only custom tokens

• The number of each token kind in an output can slightly affect the min-ada-value of this output. This is because the minimum UTXO value takes memory overhead into account when storing it on a running computer. The increase in ada value affects the memory overhead insignificantly, however, adding more multi-assets affects this value much more. The reason for this is that the names and policy IDs of each of the types of tokens take up additional space in the output.

• Sending custom tokens to an address always involves sending the min-ada-value of ada to that address alongside the custom tokens (by including the ada in the same output). If - the address is not spendable by the user sending the tokens, the ada sent alongside the tokens no longer belongs to the sender.

• Before transferring custom tokens, users may choose to use off-chain communication to negotiate who supplies the ada to cover the min-ada-value in the output made by the transferring transaction

• To recover the ada stored alongside custom tokens in an output O, the user must either: a) Spend the output O, and burn the custom tokens stored therein b) Spend an output O and an output O’, and consolidate the tokens therein with the same collection of types of custom tokens stored in another output (spent within the same transaction)

Eg. (CryptoDoggiesPolicy, poodle, 1) contained in O can be consolidated with (CryptoDoggiesPolicy, poodle, 3) in O’, for a total of (CryptoDoggiesPolicy, poodle, 4) in a new output made by the consolidating transaction.

• Splitting custom tokens into more outputs than they were contained in before the transaction getting processed requires using, in total, more ada to cover the min-ada-value, as ada is needed in the additional outputs.

Example min-ada-values and calculations

Ada-only minUTxOValue (in lovelace)	1,000,000 (1 ada)
utxoEntrySizeWithoutVal	27
coinSize	0
txoutLenNoVal	14
txinLen	7
coinsPerUTxOWord (in lovelace)	37,037

	One policyID, no asset names	One policyID, one 1-character asset name (ii)	One PolicyID, one 32-character asset name (iii)	One PolicyID, 110 32-character names (iv)	60 PolicyIDs, each with one 32-character name
size of value	11	12	15	615	546
minUTxO	1,407,406	1,444,443	1,555,554	23,777,754	21,222,201
minUTxO (in ada)	1.407406	1.444443	1.555554	23.777754	21.222201

• 1. : 6 + FLOOR (((1 * 12) + 0 + (1 * 28) + 7) / 8) = 11

• 2. : 6 + FLOOR (((1 * 12) + 1 + (1 * 28) + 7) / 8) = 13

• 3. : 6 + FLOOR (((1 * 12) + 32 + (1 * 28) + 7) / 8) = 15

• 4. : 6 + FLOOR (((110 * 12) + 32*110 + (1 * 28) + 7) / 8) = 615

• 22. : 6 + FLOOR (((60 * 12) + 60*32 + (60 * 28) + 7) / 8) = 546