Random Number Quality Calculator

Run the NIST SP 800-22 monobit frequency test on a bitstream sample and estimate its min-entropy per bit.

About Random Number Quality Calculator

The monobit test is the first of the NIST SP 800-22 battery: it checks whether the count of ones sits inside the normal distribution expected of a fair coin, with standard deviation √n ÷ 2. Min-entropy is a stricter measure than Shannon entropy because it assumes the attacker always guesses the most likely value. A biased or stuck entropy source silently weakens every key, nonce and token derived from it, and monobit failure is the cheapest early warning that a hardware RNG or a virtualised entropy pool has degraded.

Formulas

Random Number Quality

s_obs = |ones − zeros| ÷ √n and p-value = erfc(s_obs ÷ √2); the stream passes when p ≥ α.

n: Sample size in bits
s_obs: Normalised absolute imbalance between 1s and 0s
α: Significance level, conventionally 0.01

Min-entropy estimate

min-entropy per bit = −log₂(max(p₁, 1 − p₁)), the most-likely-outcome bound.

Worked example

With the default values below, Random Number Quality Calculator returns Monobit p-value of 0.6171. Change any input above and every figure here is recalculated in your browser.

Inputs used

Bits in the sampleminimum 100 bits: 1,000,000 bits
Number of 1 bits observedminimum 0 bits: 500,250 bits
Significance level αaccepts 0–0.1: 0.01

Results

Monobit p-value: 0.6171
Test Statistic s_obs: 0.5000
Proportion of 1 Bits: 50.0250%
Min-entropy per Bit: 0.9993 bits
Expected 1-bit Count Range: 498712 – 501288 ones at 99% confidence
Assessment: PASS — the bitstream is consistent with a fair random source

Step by step

1Values used
2Random Number Quality
3Min-entropy estimate
4Monobit p-value= 0.6171
5Test Statistic s_obs= 0.5000
6Proportion of 1 Bits= 50.0250
7Min-entropy per Bit= 0.9993 bits
8Expected 1-bit Count Range= 498712 – 501288 ones at 99% confidence
9Assessment= PASS — the bitstream is consistent with a fair random source

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.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

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

Frequently Asked Questions

How is Random Number Quality calculated?

s_obs = |ones − zeros| ÷ √n and p-value = erfc(s_obs ÷ √2); the stream passes when p ≥ α. The monobit test is the first of the NIST SP 800-22 battery: it checks whether the count of ones sits inside the normal distribution expected of a fair coin, with standard deviation √n ÷ 2. Min-entropy is a stricter measure than Shannon entropy because it assumes the attacker always guesses the most likely value.

Why does Random Number Quality matter?

A biased or stuck entropy source silently weakens every key, nonce and token derived from it, and monobit failure is the cheapest early warning that a hardware RNG or a virtualised entropy pool has degraded.

What values do I need to enter?

This calculator takes 3 inputs: Bits in the sample, Number of 1 bits observed, Significance level α. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

Is passing monobit enough?

No. It only detects an imbalance in the overall count — an alternating 0101… stream passes perfectly. Run the full SP 800-22 battery (runs, longest-run, spectral, serial) and treat monobit as a smoke test.

What sample size do I need?

SP 800-22 recommends at least 100 bits for monobit, but a meaningful assessment needs 10⁶ bits or more so the test can detect small biases.