AtlasCalcsUtility Calculation Suite
2026-08-07 10 min

Random Number Generator

Generate random integers and decimals between any two values with duplicate control, sorting, precision, bulk draws up to 1000, and a live distribution histogram.

Calculator

Range

Lower Limit
Upper Limit
Number of Results

Options

Allow Duplicates
Yes No
Sort Results
None Ascending Descending
Type
Integer Decimal
Results update on demand
Stats update automatically
Results update live as you type
Status:Range 1 – 100100 outcomesCoverage 5.0%

Random Draw Summary

Range1 – 100
Distinct values100
Expected mean50.5000
Draws requested5 (with replacement)
Sample mean—

Batch Diagnostics

Coverage of range5.0%
Observed spanno batch yet
Expected std dev28.8661

Results

Normal

Distinct Values in Range

100

Inclusive count of possible outcomes

Expected Mean

50.5000

(min + max) / 2 for a uniform draw

Expected Std Dev

28.8661

Uniform-distribution spread

Requested Draws

5

How many values each generation returns

Range Coverage

5.0%

Draws divided by distinct values

Sample Mean

—

Mean of the last generated batch

Sample Min – Max

—

Observed span of the last batch

Duplicate Policy

With replacement

Whether repeats are allowed

Browser PRNG draws mapped uniformly onto your inclusive range. Uniformity is statistical, not cryptographic — use a CSPRNG or hardware source for security-critical draws.

Visualizations

Draw Distribution (10 equal-width bins)

1B1
1B2
1B3
1B4
1B5
0B6
0B7
0B8
0B9
0B10

Range Coverage

Covered5%

Draws vs Distinct Values

Draws5

Formula

A unit uniform draw rand in [0,1) is stretched over the closed range. Integers land on the whole-number lattice with probability 1/rangeSize each; decimals land on a 10^-p grid between min and max.

integer = min + floor(rand × ((max − min) + 1))

Alternative Form

decimal = round((min + rand × (max − min)) × 10^p) / 10^p

Variables

SymbolNameUnitDescription
randUnit uniform draw[0,1)Output of Math.random()
NRange sizecountDistinct inclusive outcomes
min, maxRange limitsvalueInclusive endpoints, ordered first
pPrecisionplacesDecimal places in decimal mode
E[X]Expected meanvalue(min + max) / 2
SDUniform std devvalue(max − min) / √12

Explanation

Uniformity comes from giving every sub-interval of [0,1) equal width. Scaling and flooring preserves equal widths, so each integer inherits an equal slice of probability.

Derivation

Let U ~ Uniform[0,1). For integers with N outcomes, P(X = min+k) = P(k/N ≤ U < (k+1)/N) = 1/N. For decimals, the same U is scaled by (max−min), shifted by min, then rounded to p places.

Step-by-Step Calculation

Follow each step to understand how the result is calculated from your inputs.

Step 1

Order the limits and measure the closed range.

rangeSize = floor(max) − floor(min) + 1 (integers)
Min:1
Max:100
Intermediate: from 1 through 100 inclusive
Result: 100 distinct outcomes
Step 2

Map a unit uniform draw onto the range.

integer = min + floor(rand × rangeSize)
rand in [0,1):Math.random()
rangeSize:100
Intermediate: each outcome gets probability 1 / rangeSize
Result: each value has p = 1.00e-2
Step 3

Handle decimals on a fixed grid when requested.

decimal = round((min + rand × (max − min)) × 10^p) / 10^p
Type:integer
Precision:2
Intermediate: whole numbers only
Result: integer lattice preserved
Step 4

Enforce the duplicate policy.

without replacement: skip repeats until count is unique
Policy:with replacement
Draws:5
Intermediate: repeats allowed, one pass
Result: batch completes in one pass
Step 5

Apply the requested sort order after generation.

sort does not change the multiset, only its order
Sort:none
Intermediate: ascending / descending / generation order
Result: presentation order fixed without touching randomness
Step 6

Check the batch against uniform expectations.

E[X] = (min + max)/2; SD = (max − min)/√12
Expected mean:50.5000
Observed mean:no batch yet
Intermediate: coverage 5.0% of the range
Result: press Generate to sample
Final Answer
100

Worked Examples

See how the calculator works with different scenarios.

Scenario

Simulate one die roll with integers from 1 to 6.

Inputs

Min:1
Max:6
Type:integer
Draws:1

Calculation

rangeSize = 6 − 1 + 1 = 6 roll = 1 + floor(rand × 6) Example draw rand=0.52 → 1 + floor(3.12) = 4

Result

A single value 1–6, each with probability 1/6 ≈ 16.67%

Interpretation

Six equal slices of [0,1) map onto six faces. Repeating the draw converges to a flat histogram with mean 3.5.

Understanding Your Result

Your Result: Distinct Values in Range: 100

Typical range: Dice use 1-6, percentages 0-100, probabilities 0-1 decimals, lotteries match the ball pool such as 1-49. Coverage under 100% with duplicates off always succeeds; over 100% triggers the unique-shortfall warning.

What This Means

The headline numbers describe the sampling frame: how many distinct values exist, what their average should be, how many draws you take, and what share of the frame each batch covers.

Why It Matters

Naming the frame before drawing prevents the two classic errors — asking for more uniques than exist, and mistaking a browser PRNG for cryptographic randomness.

Professional Interpretation

For classroom demos and games the PRNG is ample. For regulated draws, cryptography, or gambling certification, replace it with a hardware or CSPRNG source such as random.org or NIST beacons.

Recommendations

  • •Keep unique draws at or below the range size
  • •Use decimals for continuous quantities, integers for counts
  • •Leave sort off when draw order is the experiment
  • •Batch large Monte Carlo runs in groups of 1000
  • •Switch to crypto randomness for anything security-critical
  • •Check the histogram: persistent tilt means a range bug

Educational Content

Introduction

This generator turns a unit uniform draw into fair outcomes in any interval you name. It supports whole numbers and fixed-precision decimals, unique-only sampling, sorting, and bulk batches with a live histogram.

Concept Explanation

Uniformity means equal probability per outcome. Stretching [0,1) over N outcomes gives each width 1/N; flooring assigns each slice to one integer. Decimals use the same stretch, then round to a 10^-p lattice.

Applications

▸Simulating dice, cards, roulette, and lottery draws
▸Drawing audit, survey, and A/B samples without bias
▸Feeding Monte Carlo estimates in class and finance
▸Assigning tournaments, winners, and lab groups fairly
▸Generating test data, PINs, and game content
▸Demonstrating uniform vs normal sampling in statistics

Benefits

  • •Any inclusive range, including negatives and BigInt-scale integers
  • •Unique-only mode for sampling without replacement
  • •Decimal precision from 1 to 10 places
  • •Bulk draws to 1000 with sort control
  • •Live histogram and coverage diagnostics

Limitations

  • •PRNG output, not suitable for cryptography
  • •Uniformity degrades past MAX_SAFE_INTEGER and on fine decimal grids
  • •No seed control, so sequences are not replayable
  • •At most 1000 draws per click

Best Practices

  • •Size the range before choosing the count
  • •Disable duplicates for lotteries, IDs, and brackets
  • •Match precision to the measurement, not the maximum
  • •Re-generate rather than hand-editing outliers
  • •Document min, max, count, and duplicate policy with results

Common Misconceptions

Myth: Bigger ranges are more random.
Truth: Randomness quality is the same; only the outcome count changes. A 1-6 die and a 1-6,000,000 draw are equally uniform per outcome.
Myth: Sorting makes results less random.
Truth: Sorting happens after generation and cannot bias the multiset — it only changes display order.
Myth: Seeing repeats means the generator is broken.
Truth: Repeats are expected with replacement. In 1-10 with duplicates on, repeats appear quickly by the birthday effect.
Myth: Decimals between 0 and 1 are continuous.
Truth: With precision p there are exactly floor(span×10^p)+1 grid points — 101 values at p=2 on [0,1].

Practical Tips

  • •Use 1-6 integers for a die, 0-1 decimals at 4 places for probabilities
  • •Turn duplicates off for lotteries, brackets, and unique IDs
  • •Keep sort on None when dealing order matters
  • •Cap batches at 1000 and loop for larger simulations
  • •Check coverage before promising unique delivery
  • •Use 2-4 decimal places unless science demands more
  • •Never use browser draws for passwords or key material

Common Mistakes

Asking for more uniques than the range holds
Widen the range or allow duplicates. A 1-6 range can yield at most 6 unique integers.
Using Math.random output for cryptography
Switch to crypto.getRandomValues or a audited CSPRNG for keys, tokens, and salts.
Forgetting the range is inclusive
Both endpoints can appear. A 1-100 integer draw can return exactly 1 or 100.
Mixing integer floors with decimal inputs
Integer mode floors limits first: 1.9 behaves as 1. Use decimal mode for fractional bounds.
Reading order into sorted output
Sorted output erases draw order by design. Keep sort None to study sequences.

Assumptions

This calculator makes the following assumptions to provide estimates:

Uniform PRNG core: Math.random is treated as uniform on [0,1) for mapping purposes.
Closed inclusive range: Both min and max can be drawn; integer mode floors fractional bounds.
Ordered limits: Limits are sorted internally so reversed inputs still work.
Fixed decimal lattice: Decimal draws round to exactly p places on a uniform grid.
Browser entropy: No seed control; each page load continues the engine-seeded stream.

Limitations

Be aware of these limitations when using this calculator:

Not cryptographic: Output is predictable given engine state and must not protect secrets.
Finite precision: Float and BigInt boundaries introduce small biases at extreme scales.
Batch cap: At most 1000 values per generation for responsiveness.
No replay: Without seed control, exact sequences cannot be reproduced on demand.

Frequently Asked Questions

Answers to common questions about this calculator.

What is a random number?
A random number is a value selected from a defined set where each possible value has an equal probability of being chosen, independently of previous selections. True random numbers show no pattern or predictability.
How does this random number generator work?
Enter a lower and upper limit plus a count, then press Generate. The tool maps JavaScript Math.random values in [0,1) onto your range: floor(rand * rangeSize) + min for integers, or min + rand * (max - min) rounded to your precision for decimals.
Is Math.random() truly random?
No. Math.random is a pseudo-random number generator (PRNG), typically xorshift128+ in modern engines. It is deterministic under the hood but statistically uniform enough for games, sampling, and teaching.
What is the difference between true random and pseudo-random?
True random numbers come from physical processes such as atmospheric noise or quantum effects and are unpredictable even in principle. Pseudo-random numbers come from algorithms and repeat if the seed repeats.
What are PRNGs?
Pseudo-random number generators are algorithms that iterate a state function to emit sequences that look random. Examples include Mersenne Twister, xorshift, and linear congruential generators.
What are TRNGs?
True random number generators (also called HRNGs) sample physical entropy — thermal noise, jitter, radioactive decay — and condition it into unbiased bits. They need hardware and are slower than PRNGs.
Can I use this generator for cryptography?
No. This tool uses Math.random, which is not cryptographically secure. For keys, tokens, or salts use crypto.getRandomValues or a vetted CSPRNG library.
Can random numbers be predicted?
PRNG output can be predicted once the algorithm and state are known. True random output cannot be predicted even with full knowledge of the past.
What is a seed?
A seed is the initial state of a PRNG. The same seed always replays the same sequence, which is useful for reproducible simulations and debugging. This tool does not expose a seed control.
What is entropy?
Entropy is the amount of unpredictability available to a generator. Operating systems collect it from mouse movement, keystroke timing, disk and network jitter, and hardware noise.
How do I generate unique numbers without duplicates?
Use the comprehensive mode, set Allow Duplicates to No, and keep the count at or below the range size. The generator skips repeats until it has collected enough unique values.
Why do I get a "only N unique values" warning?
You asked for more unique values than the range holds. A 1-6 integer range holds at most 6 unique values; asking for 10 unique values can only return 6.
How do I generate random decimals?
Choose Decimal type and a precision from 1 to 10 places. With min 0, max 1, precision 2 you get values like 0.37 or 0.91, each of the 101 grid points roughly equally likely.
How do I generate random integers?
Choose Integer type and integer limits. Every whole number from min through max inclusive has probability 1 / rangeSize. A 1-6 setup simulates a fair die.
What range can I use?
Integers use BigInt parsing so very large limits are accepted, though uniformity degrades past Number.MAX_SAFE_INTEGER. Decimals are limited by 64-bit float precision.
Can I generate negative random numbers?
Yes. Set the lower limit negative, for example -10 to 10, and every integer in that closed interval is equally likely.
Is there a limit on the number of results?
Yes, 1000 per generation to keep the page responsive. Generate in batches if you need more draws for a Monte Carlo experiment.
Does sorting affect randomness?
No. Sorting only reorders values after generation. Keep None when draw order matters, such as simulating dealing order, and sort for reports.
What precision should I pick for decimals?
Use 2-4 places for everyday values like prices or game coordinates and 6-10 for scientific work. Higher precision adds grid points but can expose float rounding.
What is a uniform distribution?
A uniform distribution gives every outcome equal probability. The histogram diagram on this page should look roughly flat across its 10 bins for large samples.
What is Monte Carlo simulation?
Monte Carlo methods repeat random sampling thousands of times to estimate integrals, option prices, or system reliability. This generator can supply the raw draws for small classroom versions.
What is random sampling?
Random sampling picks a subset where each member of the population has an equal chance of selection, removing selection bias from surveys and quality control.
Can I use this for lottery numbers?
Yes for casual play. Set the range to the ball pool such as 1-49, disable duplicates, and generate 6. Official draws use certified hardware, not a browser PRNG.
What is a CSPRNG?
A cryptographically secure PRNG is designed to resist prediction even after observing past output. Examples include /dev/urandom and the Windows CNG generator.
How are RNGs tested for fairness?
Suites such as NIST SP 800-22, Diehard, and TestU01 run frequency, runs, spectral, and serial tests looking for bias, correlation, or repeating structure.
What does the coverage percentage mean?
Coverage is count divided by range size times 100. Requesting 6 unique numbers from 1-49 covers about 12.2% of the pool.
Why does a single-value range always return the same number?
When min equals max the range size is 1, so every draw must equal that value. The expected mean, min, and max all coincide.
How do I pick a random winner from a list?
Number your entries 1 to N and generate one integer in that range. Each entry then has probability 1/N of winning.

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Glossary

Technical terms used in mortgage calculations explained in plain language.

RNG
A random number generator producing uniform draws over a range.
PRNG
Pseudo-random generator: fast deterministic algorithm mimicking randomness.
TRNG / HRNG
True (hardware) generator sampling physical entropy.
CSPRNG
Cryptographically secure PRNG resisting prediction attacks.
Seed
Initial PRNG state; identical seeds replay identical streams.
Entropy
Available unpredictability feeding secure generators.
Sampling with replacement
Draws where repeats are allowed; population is restored each pick.
Sampling without replacement
Draws where each value can appear at most once.
Uniform distribution
Every outcome has equal probability 1/N.
Coverage
Draws divided by distinct values, as a percentage.

Authoritative References

Trusted sources and standards referenced by this calculator.

Applicable Standards

NIST SP 800-22 randomness testing guidanceRANDOM.ORG true-randomness reference practice

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Page Information

Last Updated:

2026-08-07

Version:

2.0.0

License:

Free to use for educational and professional purposes.