SummaryA hash with n leading hex zeros takes 16n attempts on average, so each extra zero costs 16 times more work. At 137 GH/s, the measured sustained rate of the single USB ASIC behind this site, that is about 0.03 seconds for 8 zeros, 8 seconds for 10, 2 minutes for 11, 34 minutes for 12, 9 hours for 13, 6 days for 14 and 97 days for 15. Those are averages. Half of all searches finish in under 70% of the average, and about 1 in 20 takes more than three times as long.
The arithmetic
A SHA-256 hash, written in hex, is 64 digits. Each digit is one of 16 values and, for mining purposes, each is as good as random. The chance that the first digit is 0 is 1 in 16. The chance that the first two are both 0 is 1 in 256. The chance that the first n are all 0 is 1 in 16n.
So the expected number of attempts to get n leading zeros is 16n, and the expected time is that divided by your hash rate:
expected seconds = 16^n / hashes per secondEight zeros is 168 = 232, about 4.3 billion attempts. That was Bitcoin's original difficulty in 2009.
Strictly, a Bitcoin target is a number the hash must be below, not a count of zeros, so real difficulty moves in finer steps than 16×. The tiers on this site use targets that line up with whole zeros, which keeps the arithmetic this simple.
The table
Average time to find a hash with n leading hex zeros, at three hash rates:
| Zeros | Expected hashes | 1 MH/s | 137 GH/s | 200 TH/s |
|---|---|---|---|---|
| 8 | 4.29 × 109 | 72 min | 0.03 s | 21 µs |
| 9 | 6.87 × 1010 | 19 h | 0.5 s | 0.34 ms |
| 10 | 1.10 × 1012 | 13 days | 8 s | 5.5 ms |
| 11 | 1.76 × 1013 | 204 days | 2.1 min | 0.09 s |
| 12 | 2.81 × 1014 | 8.9 years | 34 min | 1.4 s |
| 13 | 4.50 × 1015 | 143 years | 9.1 h | 23 s |
| 14 | 7.21 × 1016 | 2,283 years | 6.1 days | 6 min |
| 15 | 1.15 × 1018 | 36,534 years | 97 days | 1.6 h |
| 16 | 1.84 × 1019 | 584,542 years | 4.3 years | 26 h |
The three columns:
- 1 MH/s is a CPU-scale rate. Your own machine will differ. The browser vs ASIC tool measures what your browser does.
- 137 GH/s is what this site's miner sustains: one GekkoScience Compac F USB stick with a single BM1397 chip, measured over a 30-minute run. I wrote up how that number was measured.
- 200 TH/s is the rated speed of one current industrial machine. Bitmain lists the Antminer S21 at that figure.
For other rates or other zero counts, use the leading zeros calculator.
Mean, median and luck
The table gives the mean. Mining does not deliver the mean. Each hash is an independent try with the same tiny chance, so the waiting time follows an exponential distribution, and that distribution is lopsided.
- The median is the mean times ln 2, about 0.69. Half of all searches are done by then.
- About 63% are done by the mean.
- About 5% take more than 3 times the mean, and about 1% take more than 4.6 times.
Take 12 zeros at 137 GH/s. The mean is 34 minutes. The median is 24 minutes. One search in twenty runs past 1.7 hours, and one in a hundred past 2.6 hours. On the other side, about one in ten finishes inside the first 3.6 minutes.
The searches also have no memory. Twenty minutes into an unlucky 12-zero search, the expected time remaining is still 34 minutes. Nothing has been used up. This is why I quote 12-zero strikes as "about 35 minutes on average, occasionally a few hours" and not as a fixed time.
Where Bitcoin itself sits
The genesis block needed 8 zeros and happened to get 10. Bitcoin's difficulty is readjusted every 2,016 blocks to keep blocks about ten minutes apart, and it has risen enormously as miners added hardware.
When I checked on 10 November 2026, the network difficulty was about 148 trillion. A block then needs about 6.4 × 1023 hashes on average, which is about 1619.77. The current target forces at least 19 leading hex zeros, and the 15 most recent block hashes had 19 zeros (seven of them), 20 (seven) or 21 (one). The whole network, estimated at roughly 960 EH/s, produces one of those about every ten minutes.
This site's USB stick would need about 147,000 years for one Bitcoin block at that difficulty. That gap is the point of the table: 12 zeros is a real half hour of a real ASIC's work, and it is still seven or eight hex digits short of what the network does every ten minutes.
The blocks this site mines stop at 8, 10, 11 or 12 zeros and are standalone, not part of Bitcoin's chain. If you want one with your own line in it, the tiers are here.