9
90
58
66
58
0
0
0
0
0
99
9
90
58
66
58
0
0
0
0
0
99
A Random Number Generator (RNG) produces numerical values that appear to lack any predictable pattern. Random numbers are essential in statistics for sampling, simulation, bootstrapping, permutation tests, and Monte Carlo methods. They are also widely used in cryptography, gaming, lottery systems, and scientific experimentation.
This generator uses a deterministic pseudo-random algorithm based on a seed value. Given the same seed, it always produces the same sequence — making results reproducible. Change the seed to generate a completely different set of numbers. You can specify the range (minimum to maximum), how many numbers to generate (up to 10), and the number of decimal places for precision control.
This generator uses a hash-based pseudo-random number generation approach. For each output number i, the algorithm computes:
$$r_i = \left| \sin(\text{seed} \times a_i + i) \times m_i \right| \mod 1$$
Where aᵢ and mᵢ are unique constants for each output position, ensuring different numbers even with the same seed. The result rᵢ is a value in [0, 1), which is then scaled to the desired range:
$$\text{output}_i = \text{min} + (\text{max} - \text{min}) \times r_i$$
Finally, the result is rounded to the specified number of decimal places:
$$\text{output}_i = \frac{\lfloor \text{output}_i \times 10^d + 0.5 \rfloor}{10^d}$$
This approach, while not cryptographically secure, produces well-distributed pseudo-random numbers suitable for educational purposes, quick sampling, and non-security applications. The sine-based hash function creates sufficient entropy from the seed to produce numbers that pass basic randomness tests.
True random number generators (TRNGs) harvest entropy from physical processes like atmospheric noise, radioactive decay, or thermal fluctuations. For applications requiring true randomness (cryptography, high-stakes gambling), dedicated hardware or services like random.org should be used instead.
The distinction between pseudo-random (deterministic, reproducible) and true random (non-deterministic, unreproducible) is fundamental in both statistics and computer science.
The generated numbers are uniformly distributed across the specified range. Key points for interpretation:
For statistical applications, verify the randomness properties of your generated numbers using tests like the chi-square goodness-of-fit test for uniformity.
Inputs
Results
Generating 5 random integers between 1 and 50 with seed 42. Change the seed to get different numbers for each draw.
Inputs
Results
Three uniform random values in [0, 1] with 4 decimal places, useful as probability inputs for Monte Carlo simulation.
This is a pseudo-random number generator — it is deterministic. The same seed always produces the same sequence. To get different numbers, simply change the seed value. This reproducibility is actually a feature, not a bug: it allows you to recreate the exact same 'random' sequence for debugging, peer review, or replication of experiments.
No. These are pseudo-random numbers generated by a mathematical formula. They appear random and pass basic statistical tests for uniformity, but they are completely determined by the seed. For true randomness, you need physical sources of entropy (atmospheric noise, radioactive decay, etc.). For most statistical applications, pseudo-random numbers are perfectly adequate.
No. This generator is not cryptographically secure. The algorithm is predictable — knowing the seed allows anyone to reproduce the entire sequence. For cryptographic applications, use dedicated cryptographic pseudo-random number generators (CSPRNGs) like those built into operating systems (/dev/urandom on Linux) or cryptographic libraries.
This generator produces uniformly distributed numbers. To generate numbers from other distributions (normal, exponential, etc.), you can use transformation methods. For example, the Box-Muller transform converts pairs of uniform random numbers into standard normal values: Z = √(−2 ln U₁) × cos(2π U₂).
Any integer works as a seed. Different seeds produce different sequences. In practice, using the current time (in milliseconds) as a seed provides a convenient way to get different numbers on each run. For reproducible research, document the seed value used so others can replicate your results exactly.
For integer generation (0 decimal places) in a range of size R, there are R+1 possible values. The generator can produce any of these values, but with only 10 outputs per run, duplicates are possible. The probability of duplicates follows the birthday problem: for k numbers in a range of N, the duplicate probability is approximately 1 − e^(−k(k−1)/(2N)).
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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