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Hopefully an easy Question. I was updating some data tables and wanted to estimate monthly yield based on difficulty and known hashrate of the miner in this cash 110 TH/S.

I had it in my head the formula would be =(110,000,000 * 6.25 * 600 * 30)/67.31 or =(H/S * reward * seconds * days / difficulty)

I'm wildly off, and could use some assistance. I was using the below reference cells when attempting to calculate. Any help would be appreciate. Thanks all!

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  • I think I fixed it. I didn't use the full network difficulty face palm. I'm now getting the expected yields. Commented Dec 15, 2023 at 15:20
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    110,000,000 H/s are only 110 MH/s. You are missing a factor of 1,000,000 (see e.g. bitcoin.stackexchange.com/a/21498/5406). Does bitcoin.stackexchange.com/a/135/5406 answer your question?
    – Murch
    Commented Dec 15, 2023 at 15:30
  • Something is still off then. Cause If 1 Th/S = 1,000,000,000,000, 110 would = 110,000,000,000,000. Using my same formula and accounting for network difficulty of 67,305,906,902,031.00, I am getting 6,129 BTC yield...Which is massively off the mark. Commented Dec 15, 2023 at 15:41

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Here are two methods to calculate an estimate for your profitability.

1. Your share of the reward is proportional to your share of the hashrate

There are an expected 144 blocks per day each producing a subsidy of 6.25 ₿. That’s an expected total of 900 new bitcoins per day. Your miner has 110 TH/s (1.1×1014 H/s). Mining pools are currently self-reporting a total hashrate of 525.35 EH/s (5.2535×1020 H/S).
Your expected revenue R is a proportion of the total reward equal to your proportion of the hashrate:

R / 900 ₿ = 110 TH/s / 525.35 EH/s  
R = 900 ₿ × 1.1E14 / 5.2535E20  
R = 90,000,000,000 sats × 1.1 / 5,253,500  
R = 18,844.6 sats

Obviously this would be increased by the fees collected by these blocks and the increased block production we see most of the time.

2. Your revenue is proportional to the number of hashes you produce compared to the expected hashes it takes to find a block

H    your hashrate in Hash/s
D    the current difficulty
S    the block subsidy
R    your revenue per day

Finding a block takes an expected D×248/65,535 hashes. The current difficulty is 67,305,906,902,031. There are 60×60×24 = 86,400 seconds per day.

R = H × seconds_per_day × S / (D×2^48/65,535)
R = H × 86,400 × S × 65,535 / (D×2^48)
R = 1.1e14 H/s × 3600×24 s × 6.25 ₿ × 65,535 / (67,305,906,902,031×2^48) = 0.000205479 ₿
R = 20,457.9 sats

I used the current subsidy for the reward of a block here, but you would have to adjust that with the expected fees collected which currently are significant. Checking my calculation against the results of Nicehash’s profitability calculator puts the above estimates in the right ballpark when considering the recent substantial fees:

Result of plugging the same values into Nicehash’s profitability calculator estimates a an approximate income of 28,252 sats.

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  • Can you explain how you got D×2^48? I was tracking from other sources around 2^32 (can't vouch for accuracy) Commented Dec 15, 2023 at 17:48
  • 2^32 = 4,294,967,296 is a very close estimate, but the actual value is 2^48/65,535 = 4,295,032,833. See e.g. bitcoin.stackexchange.com/a/5557/5406
    – Murch
    Commented Dec 15, 2023 at 18:19

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