Random integers within a range.
Integer: Result = floor(U × (max − min + 1)) + min Decimal: Result = U × (max − min) + min
For a uniform discrete (integer) distribution, each integer in the closed range [min, max] is equally likely. The formula maps a uniform random variable U drawn from [0, 1) to an integer in [min, max]:
Result = floor(U × (max − min + 1)) + min
For a uniform continuous (decimal) distribution, no rounding step is applied:
Result = U × (max − min) + min
In both cases U is a pseudo-random value produced by a cryptographically suitable algorithm (such as the Mersenne Twister or a CSPRNG) seeded with an unpredictable entropy source.
Result = floor(0.7342 × (50 − 1 + 1)) + 1 = floor(0.7342 × 50) + 1 = floor(36.71) + 1 = 36 + 1 = 37
Result: 37
With a minimum of 1, a maximum of 50, and the pseudo-random seed value U = 0.7342, the generator returns 37. Every integer from 1 to 50 had exactly a 1-in-50 (2%) chance of being selected, confirming the result is unbiased and uniformly distributed across the range.
Random number generators fall into two broad categories:
1. Pseudo-Random Number Generators (PRNGs) Most software RNGs, including this tool, use deterministic algorithms — such as the Mersenne Twister (MT19937) — seeded with a high-entropy value (e.g., system clock, mouse movement, OS noise). They are statistically random (pass all standard randomness tests) but technically reproducible if the seed is known. PRNGs are perfectly suitable for games, simulations, sampling, and everyday decisions.
2. True Random Number Generators (TRNGs) TRNGs harvest physical entropy — radioactive decay, atmospheric noise, thermal fluctuations — to produce numbers that are genuinely non-deterministic. Services like RANDOM.ORG use atmospheric noise for this purpose. TRNGs are used in cryptography and security-critical applications.
This calculator uses a uniform distribution, meaning every number in the range has the same probability of being selected. The probability of any single integer outcome in [min, max] is:
P = 1 / (max − min + 1)
For a range of 1–10, each number has a 10% chance. For 1–100, each has a 1% chance.
If you need reproducible results (e.g., for testing), a seeded RNG lets you replay the same sequence. For everyday use, a fresh entropy seed ensures each run is independent.
Set min = 1 and max = 10 in integer mode and click Generate. Each of the 10 integers has a 10% probability of being selected.
For a uniform integer distribution, the probability is 1 ÷ (max − min + 1). For the range 1–6 (a die), that's 1/6 ≈ 16.67% for each face.
By default, yes — each draw is independent, so the same number can appear more than once, just like rolling a die repeatedly. Enable a 'unique numbers only' option if your use case requires no duplicates (e.g., a lottery draw).
The generator is automatically seeded with high-entropy system data (such as the current timestamp combined with OS-level randomness) each time you click Generate, ensuring different results every session.
A random number table is a pre-printed list of random digits used before computers existed. An RNG generates fresh values on demand and is far more convenient and just as statistically valid for sampling and simulation.
It uses a high-quality pseudo-random number generator (PRNG) seeded with unpredictable system entropy. For games, simulations, giveaways, and most everyday uses, it is statistically indistinguishable from true randomness. For cryptographic security applications, a hardware-based TRNG or CSPRNG is recommended.
Yes. Use the quantity field to request a batch of numbers. Each number is drawn independently, so duplicates are possible unless you specifically enable a 'no repeat' option.
The generator supports any integer range that fits within standard 64-bit integer limits (approximately −9.2 × 10¹⁸ to +9.2 × 10¹⁸), making it suitable for virtually any practical application.
Absolutely. Set your minimum to a negative value (e.g., min = −50, max = 50) and the generator will produce numbers across that signed range with equal probability.
Physically rolling a fair die or flipping a fair coin also produces uniform outcomes, but this tool is faster, works for arbitrary ranges, and can generate hundreds of numbers instantly. A coin flip is equivalent to setting min=0, max=1 in integer mode.
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