<p>As explained in the <a href="https://docs.cardano.org/en/latest/explore-cardano/understanding-pledging-and-rewards.html#distributing-rewards" rel="noreferrer">docs</a>, rewards come from:</p>
<ul>
<li>Transaction fees (increases in time if adoption and network traffic increases)</li>
<li>Monetary expansion (decreases in time)</li>
</ul>
<p>The sum of these is denoted by <code>R</code> and the share of rewards that a given pool gets is given by:</p>
<blockquote>
<p><a href="https://i.sstatic.net/QwqEx.png" rel="noreferrer"><img src="https://i.sstatic.net/QwqEx.png" alt="enter image description here" /></a></p>
<p>where: R - total available rewards for this epoch</p>
<p>a0 - pledge influence factor (can be between 0 and infinity)</p>
<p>z0 - relative pool saturation size, i.e. 0.5% based on a number of
desired pools (k=200)</p>
<p>σ - stake delegated to the pool (including stake pledged by the owners
and stake delegated by others)</p>
<p>σ’ = min(σ, z0) - as σ, but capped at z0</p>
<p>s - stake pledged by the owners</p>
<p>s’ = min(s, z0) - as s, but capped at z0</p>
</blockquote>
<p>About monetary expansion and issuance, you may check <a href="https://docs.cardano.org/en/latest/explore-cardano/cardano-monetary-policy.html" rel="noreferrer">this section of the docs</a>.
Essentially, every epoch, a fixed fraction <code>ρ</code> is taken from the ADA reserves and is added into <code>R</code>. From the docs:</p>
<blockquote>
<p>Calculating the ‘reserve half life’ (that is, the time that it takes for half of the reserve to be used up) visualizes the impact of choosing a specific value of ρ over another. This was the subject of much discussion, and eventually, the value assigned was 0.3%. The reason why is that mathematical projections showed that a ρ (the fixed percentage of ada going into the virtual pot every epoch) value of 0.3% would mean a reserve half-life of four to five years. In simple terms, just half of the remaining reserve would be used every four to five years.</p>
</blockquote>

CC BY-SA 4.0
2021-05-31T13:15:53.937Z
Based on that information can we say that this percentage of 4.6% annual return will be approximately the same or over the years this can decrease substantially?
I am asking because based on that information I will be able to better plan the future of a foundation which will funded from the rewards.
Petar Enchev
CC BY-SA 4.0
2021-06-01T08:40:59.923Z
At best, you can define different scenarios under different assumptions. Perhaps a simple lower bound could be established assuming that `R` is mainly given by monetary expansion and ignore transaction fees. In that case, rewards should decrease by 50% every 4-5 years. But a more general analysis should also consider projections on network growth. I'll leave that work to you ;)
vaz
CC BY-SA 4.0
2021-06-01T14:55:01.180Z
Charles mentioned that over the time the idea is the rewards to be ensured by the transactions fees when we have billion of transactions.
I just wanted to see if there is something else to this question (like the formula above).
Petar Enchev
CC BY-SA 4.0
2021-06-01T19:25:34.083Z
That's correct. By network growth I mean more transactions and hence more fees. You would need to evaluate different scenarios to get a better idea.
vaz
CC BY-SA 4.0
2021-09-23T11:11:00.850Z
The link to the formula is not available anymore. It can now be found here:
https://testnets.cardano.org/en/testnets/cardano/get-started/pledging-and-rewards/
Sandro
CC BY-SA 4.0
2021-05-31T09:27:23.963Z
2021-05-31T09:27:23.963Z
vaz
<p>I remember that initially the percentage of rewards for delegators was around 5.12% visiting <a href="https://cardano.org/calculator/?calculator=delegator" rel="noreferrer">Cardano Calculator</a>. Now they are approximately 4.6083%.</p>
<p>How this is calculated?
Will the percentage decrease over the years?</p>

<staking><rewards>
How are Staking rewards calculated?
# How are Staking rewards calculated?

(Asked by: username_0 on 2021-05-31)

I remember that initially the percentage of rewards for delegators was around 5.12% visiting [Cardano Calculator](https://cardano.org/calculator/?calculator=delegator). Now they are approximately 4.6083%.

How this is calculated?
Will the percentage decrease over the years?

**Tags:** staking, rewards

---

## 1 answers

### Answer by username_1 on 2021-05-31. Score: 8 | Accepted answer

As explained in the [docs](https://docs.cardano.org/en/latest/explore-cardano/understanding-pledging-and-rewards.html#distributing-rewards), rewards come from:

* Transaction fees (increases in time if adoption and network traffic increases)
* Monetary expansion (decreases in time)

The sum of these is denoted by `R` and the share of rewards that a given pool gets is given by:

> [![enter image description here](https://i.sstatic.net/QwqEx.png)](https://i.sstatic.net/QwqEx.png)
>
> where: R - total available rewards for this epoch
>
> a0 - pledge influence factor (can be between 0 and infinity)
>
> z0 - relative pool saturation size, i.e. 0.5% based on a number of
> desired pools (k=200)
>
> σ - stake delegated to the pool (including stake pledged by the owners
> and stake delegated by others)
>
> σ’ = min(σ, z0) - as σ, but capped at z0
>
> s - stake pledged by the owners
>
> s’ = min(s, z0) - as s, but capped at z0

About monetary expansion and issuance, you may check [this section of the docs](https://docs.cardano.org/en/latest/explore-cardano/cardano-monetary-policy.html).
Essentially, every epoch, a fixed fraction `ρ` is taken from the ADA reserves and is added into `R`. From the docs:

> Calculating the ‘reserve half life’ (that is, the time that it takes for half of the reserve to be used up) visualizes the impact of choosing a specific value of ρ over another. This was the subject of much discussion, and eventually, the value assigned was 0.3%. The reason why is that mathematical projections showed that a ρ (the fixed percentage of ada going into the virtual pot every epoch) value of 0.3% would mean a reserve half-life of four to five years. In simple terms, just half of the remaining reserve would be used every four to five years.

> **Comments:**
> **username_0**: Based on that information can we say that this percentage of 4.6% annual return will be approximately the same or over the years this can decrease substantially? I am asking because based on that information I will be able to better plan the future of a foundation which will funded from the rewards.  
> **username_1**: At best, you can define different scenarios under different assumptions. Perhaps a simple lower bound could be established assuming that `R` is mainly given by monetary expansion and ignore transaction fees. In that case, rewards should decrease by 50% every 4-5 years. But a more general analysis should also consider projections on network growth. I'll leave that work to you ;)  
> **username_0**: Charles mentioned that over the time the idea is the rewards to be ensured by the transactions fees when we have billion of transactions. I just wanted to see if there is something else to this question (like the formula above).  
> **username_1**: That's correct. By network growth I mean more transactions and hence more fees. You would need to evaluate different scenarios to get a better idea.  
> **username_2**: The link to the formula is not available anymore. It can now be found here: https://testnets.cardano.org/en/testnets/cardano/get-started/pledging-and-rewards/  

---

