About

Producing statistically sound random number sets requires more than calling Math.random. This generator uses the crypto.getRandomValues API when available, providing cryptographically secure pseudorandom output suitable for simulations, sampling, and lottery-style draws. You configure the range [min, max], quantity n, step constraint s, uniqueness, sorting order, and distribution model. Misconfigured parameters - requesting 500 unique integers from a pool of 100 - produce silent data gaps in naive tools. This tool validates constraints before generation and reports conflicts explicitly.

Three distribution modes are supported: uniform, Gaussian (normal via the Box-Muller transform with configurable μ and σ), and weighted custom ranges. The step parameter restricts output to the arithmetic sequence min + k ⋅ s, useful for generating multiples or fixed-resolution grids. Exclusion lists remove unwanted values from the output pool before sampling. Note: Gaussian mode produces floating-point results clamped to [min, max]; extreme σ values relative to range width will cluster output near the mean and increase rejection rate.

Formulas

Uniform integer generation maps a secure random byte to the target range using rejection sampling to eliminate modulo bias:

X = min + step ⋅ floor(U ⋅ poolSize)

where U ∈ [0, 1) is a uniform random float and poolSize = floor((max − min) ÷ step) + 1.

For Gaussian distribution, the Box-Muller transform converts two uniform samples into a standard normal variate:

Z = √−2 ⋅ ln(U₁) ⋅ cos(2πU₂)

The output is then scaled and shifted: X = μ + σ ⋅ Z, then clamped to [min, max].

For unique generation, the Fisher-Yates shuffle is applied to the full pool array and the first n elements are selected, guaranteeing O(n) time without retry loops when n ≤ poolSize. When the pool exceeds 1,000,000, a Set-based rejection method is used instead to avoid memory exhaustion.

Where min = lower bound, max = upper bound, step = spacing, n = count, μ = mean, σ = standard deviation, U₁ and U₂ = independent uniform random samples.

Reference Data

Parameter	Default	Range	Description
Minimum	1	−1,000,000 to 1,000,000	Lower bound (inclusive)
Maximum	100	−1,000,000 to 1,000,000	Upper bound (inclusive)
Count	10	1 to 100,000	Numbers to generate
Step	1	0.001 to 1,000,000	Spacing between valid values
Decimals	0	0 to 10	Decimal places in output
Unique	No	Yes / No	Prevent duplicate values
Sort	None	None / Asc / Desc	Output ordering
Distribution	Uniform	Uniform / Gaussian / Weighted	Statistical distribution model
Mean (μ)	50	Any within range	Center of Gaussian bell curve
Std Dev (σ)	15	> 0	Spread of Gaussian distribution
Exclusions	Empty	Comma-separated	Values to exclude from output
Delimiter	Newline	Newline / Comma / Space / Tab / Custom	Separator between output numbers
Prefix	Empty	Any string	Prepended to each number
Suffix	Empty	Any string	Appended to each number
Max Pool (Unique)	-	Computed	(max − min) ÷ step + 1 − exclusions

Frequently Asked Questions

When uniqueness is enabled, the tool first computes the valid pool: all values from min to max at the given step, minus excluded values. If the requested count exceeds this pool size, generation is refused with an explicit error showing the maximum available. For example, range [1, 10] with step 2 yields pool {1, 3, 5, 7, 9}. Excluding 5 leaves 4 values. Requesting 5 unique numbers from this set is impossible and flagged.

Uniform distribution gives every valid value equal probability. Gaussian (normal) distribution clusters results around the mean μ with spread controlled by σ. Approximately 68% of values fall within ±1σ of the mean, 95% within ±2σ, and 99.7% within ±3σ. Values outside [min, max] are rejected and resampled. If σ is very small relative to the range, most output concentrates near μ. If σ is very large, the clamping at boundaries creates edge-piling artifacts.

When your browser supports the Web Crypto API (all modern browsers do), the tool uses crypto.getRandomValues() as the entropy source, which is cryptographically secure. The output is suitable for token generation, nonce creation, and unbiased sampling. On legacy browsers without crypto support, the fallback is Math.random(), which is NOT cryptographically secure and should not be used for security-sensitive applications.

Step defines the minimum spacing between valid values. A step of 0.5 with range [0, 10] produces candidates {0, 0.5, 1.0, 1.5, ..., 10.0}. The decimal places setting controls display formatting only - it does not override step constraints. If step is 1 but decimals is set to 2, output shows "7.00" not "7.34". For true decimal randomness, set step to match your desired precision (e.g., step = 0.01 for cent-level values).

The generator caps output at 100,000 numbers. For uniform non-unique generation, this completes in under 100ms on modern hardware. Unique generation with a large pool may take longer due to Fisher-Yates shuffle over the full pool array. If the pool array would exceed 10 million entries (e.g., range [0, 10000000] with step 1 and unique enabled), the tool switches to a Set-based rejection sampling method that uses less memory. A progress indicator appears for operations exceeding 200ms.

Yes. In Weighted mode, you define up to 5 sub-ranges with relative weights. For example: [1-10] weight 3, [11-50] weight 1. The tool normalizes weights into probabilities (75% and 25% respectively), selects a sub-range via CDF lookup, then generates uniformly within that sub-range. This is useful for simulating real-world distributions like income brackets or scoring curves where certain ranges should appear more frequently.