Proof Of Work Time Calculator

Work out proof of work time instantly with clear inputs, formula shown and shareable results.

About Proof Of Work Time Calculator

A proof of work requiring b leading zero bits succeeds with probability 2^-b per attempt, so the expected number of hashes is 2^b. Because attempts are independent, the time is exponentially distributed: reaching 95 percent confidence takes about three times the mean, which is why individual solve times vary so widely around the expectation.

Formula

Proof-of-work timing

P(success per hash) = 2^-b; expected hashes = 2^b; hashes for confidence c = 2^b x ln(1/(1-c))

Worked example

With the default values below, Proof Of Work Time Calculator returns Expected time to solve of 3.36 s. Change any input above and every figure here is recalculated in your browser.

Inputs used

Leading zero bits requiredaccepts 1–80: 24
Hash rateminimum 1 H/s: 5,000,000 H/s
Confidence of finding a solutionaccepts 1–99.99 %: 95 %

Results

Expected time to solve: 3.36 s
Expected hashes required: 16,777,216
Time for the chosen confidence level: 10.05 s
Success probability per hash: 5.960e-8

Step by step

1Values used
2Proof-of-work timing
3Expected time to solve= 3.36 s
4Expected hashes required= 16,777,216
5Time for the chosen confidence level= 10.05 s
6Success probability per hash= 5.960e-8

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why does each extra bit double the work?

The success probability halves with every additional required zero bit, so expected attempts double. Difficulty is exponential in the bit count.

Where is small-scale proof of work used outside cryptocurrency?

Anti-abuse tokens such as Hashcash for email and client puzzles for rate limiting, where a few hundred milliseconds of client work is negligible for one request and prohibitive for millions.