## Formula explanation

All information for calculations are taken from these documents:

- Cardano monetary policy
- Cardano staking explained
- AdaTracker charts (to approximate transaction number)
- “Antipalos” project stats calculated from official explorer

### Parameters require for calculations:

- INFL – the level of inflation in yearly percentile reserve decrease
- YEAR – number of full years since the launch of the staking
- STAKE – your stake in coins
- TOTAL_STAKE – total stake in the system in coins
- TX_EPOCH – average number of transactions each epoch (5 days)
- TX_SIZE – average size of a transaction
- TAX – the percentage of profits taxed towards the treasury
- POOL_FEE – the percentage of profits that pool takes as a fee

### Full formula:

MINT = 13,887,515,354 * (1 – INFL)YEAR * inflation

FEES = ((73 * TX_EPOCH) * 0.155381) + ((73 * TX_EPOCH) * TX_SIZE * 0.000043946)

RESULT = (((MINT + FEES) – TAX) * (STAKE / TOTAL_STAKE)) – POOL_FEE

### Detailed explanation:

#### Minted coins

First we calculate how much coins will be issued this year as an inflation:

MINT = 13,887,515,354 * (1 – INFL)YEAR * INFL

The 13 billions number is taken from the monetary policy and represents the total reserve of coins not issued from the beginning. These coins will be gradually issued thru minting using formula above to calculate the amount. Formula is taken from the staking explanation post.

For example: if we take an **arbitrary example** of 5% reserve decrease, and calculated it for the second year (1 whole year after launch), then it would give us:

13,887,515,354 * (1 – 5%)1 * 5% = 659,656,979.315

Just under 660 millions of newly minted ADA in the second year of staking.

The MINT value now gives us notion of how much **new** coins will be issued to reward people. But there are also fees that users pay to send coins or execute any transactions. Total fees for the whole year are calculated like this:

#### Fees

TX_YEAR = 73 * TX_EPOCH

FIXED_FEES = TX_YEAR * 0.155381

SIZE_FEES = TX_YEAR * TX_SIZE * 0.000043946

FEES = FIXED_FEES + SIZE_FEES

TX_YEAR gives us the average number of transactions for the whole year. One year consists of 73 epochs. For now it’s fixed, but in theory also may change. Best practice would be to make it a separate parameter EPOCH_YEAR

FIXED_FEES is the number of all transactions per year multiplied by the **fixed transaction cost** as described in the staking explanation post. It also might change in the future so would be best to define parameter TX_FEE_FIXED

SIZE_FEES is the sum of all bytes of all transactions per year multiplied by the **byte cost** as described in the staking explanation post. It also might change in the future so would be best to define parameter TX_FEE_PER_BYTE

For example: if we take current average number of transaction from the actual tracker it would be around 15,000. And if we take an average transaction size to be 458 byte, as can be seen in the statistics. Then we could calculate:

TX_YEAR = 73 * 15,000 = 1,095,000

FIXED_FEES = 1,095,000 * 0.155381 = 170,142.195

SIZE_FEES = 1,095,000 * 458 * 0.000043946 = 22,039.35846

FEES = 170,142.195 + 22,039.35846 = 192,181.55346

#### Tax

UNTAXED_REWARD = MINT + FEES

TAXED_REWARD = UNTAXED_REWARD – TAX

UNTAXED_REWARD is the total pool of reward for all stakers in the system, but before tax is subtracted. Once we subtract some percentage of the total pool into treasury – we get the final TAXED_REWARD – total reward distributed among all stakers.

For example: if we take TAX to be 20% just as an arbitrary rational example (IOHK proposed 20% tax for ETC, but it might end up being be 25% for Cardano, or some other number), then calculations would go like:

UNTAXED_REWARD = 659,656,979.315 + 192,181.55346 = 659,849,160.868

TAXED_REWARD = 659,849,160.868 – 20% = 527,879,328.694

SHARE = STAKE / TOTAL_STAKE

REWARD_SHARE = TAXED_REWARD * SHARE

Any arbitrary staker (in the pool or not) may calculate his **AVERAGE** share of the rewards, by calculating his SHARE in the total stake of the system. This parameter of the total stake is actually the most important one, because it directly and in the most significant way affects how much coins a user will receive by staking **the same** amount of coins. The lower total stake – the greater you share can be with the same coins staked.

For example: if we take TOTAL_STAKE to be 15 billion (just as an arbitrary completely random example, no one knows how many actual coins will be staked) and we take out stake to be 42 thousand coins, then calculations would go like:

SHARE = 42,000 / 15,000,000,000 = 0.0000028

REWARD_SHARE = 527,879,328.694 * 0.0000028 = 1,478.06212

This shows us that a person with a 42K coins stacked would receive **ROUGHLY** about 1,478.06212 in a year, but **ONLY IF** there would be 15 billions of total stake.

#### Pools fees

RESULT_REWARD = 1,478.06212 – 5% = 1,404.159014

Pools might take fees of different size and they will define those at the moment of the pool registration. For example: if we take a **completely arbitrary** number of 5%, then calculations would go like:

This gives us the final **APPROXIMATE** yearly profit of 1,404.159014 for a 42K stake, or 3.34%.