<p>Average coins/day for a miner can be estimated by comparing the miner's hashrate with the hashrate of the network.  </p>

<p><img src="https://latex.codecogs.com/gif.latex?Cm/day%20%3D%20subsidy%20*%20%281440%20/%20blocktime%29%20*%20%28Hm%20/%20Hn%29" alt="Cm/day = subsidy * (1440 / blocktime) * (Hm / Hn)"></p>

<p>where,</p>

<p><code>Cm</code> is total coins for the miner<br>
<code>subsidy</code> is the number of coins/block a miner gets as a reward<br>
<code>blocktime</code> is the average time per block<br>
<code>Hm</code> is the miner's hashrate (Hash/sec)<br>
<code>Hn</code> is the total network hashpower (Hash/sec)<br>
<code>1440</code> is minutes per day</p>

<h3>Bitcoin</h3>

<p>Since the total network hashpower is unknown, it must be estimated based on the current difficulty. This can be done by noting that Difficulty <code>D</code></p>

<p><img src="https://latex.codecogs.com/gif.latex?D=hashrate/7158388.055" alt="D=hashrate/7158388.055"></p>

<p>Because</p>

<pre><code>difficulty = hashrate / (2^256 / max_target / intended_time_per_block) 
           = hashrate / (2^256 / (2^208*65535) / 600)
           = hashrate / (2^48 / 65535 / 600) 
           = hashrate / 7158388.055
</code></pre>

<p>see <a href="https://bitcoin.stackexchange.com/a/5557/60443">Relationship Between Hashrate and Difficulty</a></p>

<p>So, for bitcoin given a current difficulty of <code>5,949,437,371,610</code> an Antminer S9 with a hashrate of about 14TH/s:</p>

<p><img src="https://latex.codecogs.com/gif.latex?Hn%20%3D%205%2C949%2C437%2C371%2C610%20*%207158388.055%20%3D%2042%2C588%2C381%20TH/s" alt="Hn = 5,949,437,371,610 * 7158388.055 = 42,588,381 TH/s"></p>

<p><img src="https://latex.codecogs.com/gif.latex?Cm/day%20%3D%2012.5%20*%20%281440%20/%2010%29%20*%20%2814e12%20/%2042588381e12%29%20%3D%200.00059171068" alt="Cm/day = 12.5 * (1440 / 10) * (14e12 / 42588381e12) = 0.00059171068"></p>

<p><strong>Note</strong>: This is an average value, so with a large enough pool and enough days, your earnings will average to this formula (this does not account for the difficulty and network hashpower changing, of course).</p>

CC BY-SA 4.0
2018-08-05T05:45:06.887Z
Thank you for your answer! Everything's clear now. But one question: D=hashrate/7158388.055 what is 7158388.055 in this formula?
fipsi
CC BY-SA 4.0
2018-08-05T13:58:17.927Z
https://bitcoin.stackexchange.com/a/5557/60443
JBaczuk
CC BY-SA 4.0
2019-06-23T12:49:59.643Z
`Cm/day = subsidy * (1440 / blocktime) * (Hm/Hn)` seems wrong to me, because hash ratio is represented in `Hash/Sec`, but `1440` factor is number of minutes in day. To get true result of mined coin in 24h, we need to change `minutes/day factor` into `seconds/day factor` which is `86400`
Maciej Chmielewski
CC BY-SA 4.0
2019-06-23T16:58:17.190Z
Hash ratio Hm/Hn is unitless. Block time is in minutes thus 1440 min/day
JBaczuk
CC BY-SA 4.0
2018-08-04T20:26:41.770Z
2018-08-05T14:06:30.003Z
2018-08-05T14:06:30.003Z
JBaczuk
<p>Sorry for the noob question I'm pretty new to crypto coins and all this stuff. :)</p>

<p>I wonder why the formula <code>&lt;your hashrate&gt; / &lt;coin difficulty&gt;</code> gives the mined coins as a result...<br><hr>Formula mentioned on <a href="https://xmg.minerclaim.net/index.php?page=statistics&amp;action=pool" rel="nofollow noreferrer">xmg.minerclaim.com</a><br><strong>Quote:</strong></p>

<blockquote>
  <p>"XMG/Day" is calculated by the current Hashrate/Difficulty. Due to the
  fact that difficulty is constantly changing, this is only a rough
  estimate.</p>
</blockquote>

<p><hr><br></p>

<p>Example (<a href="https://xmg.minerclaim.net/index.php?page=statistics&amp;action=pool" rel="nofollow noreferrer">from altcoin Coin Magi</a>):</p>

<p>If I have a hashrate of 3.211 MH/s and the coins difficulty is 2.599 (approximately) then my earnings per <strong>second</strong> (because it's H/s) should be  </p>

<blockquote>
  <p>3,211,000 / 2.599 = ~1235.47 coins per second</p>
</blockquote>

<p>and</p>

<blockquote>
  <p>1235.47 * ( 60 * 60 *24 ) = 106744608 coins per day</p>
</blockquote>

<p>How can this be? The 'fastest' miner (highest hashrate) has 3.211 MH/s and is 'only' earning 32.892 XMG per day?</p>

<p>Did I do something wrong? Is minerclaim wrong? And what's a good formula to calculate mined coins per day?</p>

<p>Thanks in advance!</p>

<difficulty><earnings><math>
How to calculate coins mined per day?
fipsi
# How to calculate coins mined per day?

(Asked by: username_0 on 2018-08-04)

Sorry for the noob question I'm pretty new to crypto coins and all this stuff. :)

I wonder why the formula `<your hashrate> / <coin difficulty>` gives the mined coins as a result...

---

Formula mentioned on [xmg.minerclaim.com](https://xmg.minerclaim.net/index.php?page=statistics&action=pool)  
**Quote:**
> "XMG/Day" is calculated by the current Hashrate/Difficulty. Due to the
> fact that difficulty is constantly changing, this is only a rough
> estimate.

---

  

Example ([from altcoin Coin Magi](https://xmg.minerclaim.net/index.php?page=statistics&action=pool)):

If I have a hashrate of 3.211 MH/s and the coins difficulty is 2.599 (approximately) then my earnings per **second** (because it's H/s) should be

> 3,211,000 / 2.599 = ~1235.47 coins per second

and

> 1235.47 \* ( 60 \* 60 \*24 ) = 106744608 coins per day

How can this be? The 'fastest' miner (highest hashrate) has 3.211 MH/s and is 'only' earning 32.892 XMG per day?

Did I do something wrong? Is minerclaim wrong? And what's a good formula to calculate mined coins per day?

Thanks in advance!

**Tags:** difficulty, earnings, math


---

## 1 answers

### Answer by username_1 on 2018-08-04. Score: 5 | Accepted answer

Average coins/day for a miner can be estimated by comparing the miner's hashrate with the hashrate of the network.

![Cm/day = subsidy * (1440 / blocktime) * (Hm / Hn)](https://latex.codecogs.com/gif.latex?Cm/day%20%3D%20subsidy%20*%20%281440%20/%20blocktime%29%20*%20%28Hm%20/%20Hn%29)

where,

`Cm` is total coins for the miner  
`subsidy` is the number of coins/block a miner gets as a reward  
`blocktime` is the average time per block  
`Hm` is the miner's hashrate (Hash/sec)  
`Hn` is the total network hashpower (Hash/sec)  
`1440` is minutes per day

### Bitcoin

Since the total network hashpower is unknown, it must be estimated based on the current difficulty. This can be done by noting that Difficulty `D`

![D=hashrate/7158388.055](https://latex.codecogs.com/gif.latex?D=hashrate/7158388.055)

Because

```
difficulty = hashrate / (2^256 / max_target / intended_time_per_block) 
           = hashrate / (2^256 / (2^208*65535) / 600)
           = hashrate / (2^48 / 65535 / 600) 
           = hashrate / 7158388.055

```

see [Relationship Between Hashrate and Difficulty](https://bitcoin.stackexchange.com/a/5557/60443)

So, for bitcoin given a current difficulty of `5,949,437,371,610` an Antminer S9 with a hashrate of about 14TH/s:

![Hn = 5,949,437,371,610 * 7158388.055 = 42,588,381 TH/s](https://latex.codecogs.com/gif.latex?Hn%20%3D%205%2C949%2C437%2C371%2C610%20*%207158388.055%20%3D%2042%2C588%2C381%20TH/s)

![Cm/day = 12.5 * (1440 / 10) * (14e12 / 42588381e12) = 0.00059171068](https://latex.codecogs.com/gif.latex?Cm/day%20%3D%2012.5%20*%20%281440%20/%2010%29%20*%20%2814e12%20/%2042588381e12%29%20%3D%200.00059171068)

**Note**: This is an average value, so with a large enough pool and enough days, your earnings will average to this formula (this does not account for the difficulty and network hashpower changing, of course).

> **Comments:**
> **username_0**: Thank you for your answer! Everything's clear now. But one question: D=hashrate/7158388.055 what is 7158388.055 in this formula?  
> **username_1**: https://bitcoin.stackexchange.com/a/5557/60443  
> **username_2**: `Cm/day = subsidy * (1440 / blocktime) * (Hm/Hn)` seems wrong to me, because hash ratio is represented in `Hash/Sec`, but `1440` factor is number of minutes in day. To get true result of mined coin in 24h, we need to change `minutes/day factor` into `seconds/day factor` which is `86400`  
> **username_1**: Hash ratio Hm/Hn is unitless. Block time is in minutes thus 1440 min/day  

---

