Number Generators
184 tools
The number pickers are here — set a range, choose how many, control duplicates and sorting — but they are about twenty of the tools on this page. The rest is everything else numbers are for: probability you can simulate rather than only compute, graphs and optimisation problems, statistical datasets built to a specification, coordinates and geometry, number theory, bases and fractions, and calculators for a real-world figure. Sudoku, Kakuro and the other grid puzzles have a category of their own, Puzzles, and the best known are linked further down this page.
Showing 184 of 184 tools.
Random number pickers
- Random Number GeneratorGenerate one or many random numbers within any range, with optional duplicate control and sorting.
- Unique Random Number GeneratorGenerate a batch of random numbers with no repeats — every number in the set is different.
- Random Decimal GeneratorGenerate a random decimal number within any range, rounded to four decimal places.
- Random Percentage GeneratorGenerate a random percentage between 0% and 100%, or any custom range.
- Random Even Number GeneratorGenerate random even numbers within any range.
- Random Fraction GeneratorA proper fraction, automatically simplified to its lowest terms, with its decimal equivalent shown.
- Random Odd Number GeneratorGenerate random odd numbers within any range.
- Random Negative Number GeneratorGenerate random negative numbers within any range.
- Random Prime Number GeneratorA prime number within a range you choose, verified prime rather than just plausible-looking.
- Random Temperature GeneratorA temperature value in degrees Celsius, across an everyday weather range.
- Random Currency Amount GeneratorA monetary amount with a common currency symbol, to two decimal places.
- Random Decimal Range GeneratorA random decimal number within a range you choose.
- Random Sequence GeneratorA random arithmetic number sequence with a random start value and step.
- Weighted Random Number GeneratorA random number from your range, deliberately skewed toward the lower end.
- Random Multiple Of GeneratorA random multiple of any base number you choose.
- Random Signed Decimal GeneratorA random decimal between −100 and 100, positive or negative.
- Random Fraction Range GeneratorA random fraction with numerator and denominator each up to 20.
- Ratio GeneratorA random ratio in the form a:b, unsimplified.
- Percentage Split GeneratorSplits 100% into three random parts that always add up correctly.
- Random Percentile GeneratorA random percentile rank between the 1st and 99th.
Probability & simulation
- Permutation and Combination CalculatornPr and nCr side by side, exactly, with the difference between them worked through rather than assumed.
- Expected Value CalculatorThe long-run average of a set of weighted outcomes, with the variance beside it — and a note when the average is a result you can never get.
- Card Draw Probability CalculatorExact odds of drawing what you need from a deck, bag or pool — without replacement, which is the part people get wrong.
- Law of Large Numbers SimulatorRuns thousands of trials and shows the proportion settling while the raw gap between heads and tails grows.
- Coin Run Probability CalculatorHow likely a streak of heads really is — counted exactly across every possible sequence, then simulated so you can watch the two agree.
- Weighted Draw SimulatorDraws from options with different weights, and shows what you got beside what the weights predicted.
- Birthday Problem CalculatorHow many people before a shared birthday becomes likely — and the same arithmetic for IDs, codes and hashes.
- Random Walk SimulatorTakes a walk one coin flip at a time, draws the path, and says exactly how unusual the finish was.
- Bayes Update CalculatorWork out what a positive test actually means, using natural frequencies as well as probability — the calculation almost everyone gets wrong.
- Markov Chain SimulatorDefine states and transition probabilities, then simulate — with a long-run distribution quoted only when the chain genuinely has one.
- Binomial Experiment SimulatorRepeat a fixed run of trials thousands of times and watch the count of successes form its distribution, with theory shown beside it.
- Poisson Process SimulatorSimulate counts of independent events per interval and see why a Poisson process cannot have a tidy, narrow spread.
- Monty Hall SimulatorPlay the switch-or-stay problem a door at a time, or run it thousands of times with the exact theory and the observed rate reported separately.
- Secretary Problem CalculatorHow many candidates to see before choosing, and how often that lands you on the very best one.
- Coupon Collector SimulatorHow many random draws it takes to collect a full set, against the exact harmonic-number expectation.
- Gambler's Ruin SimulatorA bounded random walk between zero and a target, with the exact ruin probability alongside the observed one.
- Fair Results From a Crooked CoinTurns a coin that lands heads far more often than tails into perfectly even results, and shows the flips it discarded.
- Counterfeit Coin Weighing PlannerA plan for finding one odd coin among twelve in three weighings, with every case checked to give a different result.
- Balls in Bins SimulatorRandom allocation is far lumpier than it looks: the fullest bin against the even share, and empty bins against the exact formula.
- Parrondo's Paradox CalculatorTwo games that each lose money, and the random mix of them that wins — worked out exactly rather than simulated.
- Negative Binomial SimulatorHow many attempts it takes to reach a target number of successes, against the exact expectation of successes over probability.
- Traffic Flow SimulatorCars on a ring road move only into empty space, showing that a jam above half density is a property of the road rather than of any driver.
- Probability GeneratorA random '1 in N' probability statement with its equivalent percentage.
Statistics & significance tests
- Random Sample GeneratorDraw a sample without replacement from your own list, and see exactly how many different samples were possible.
- Bootstrap Sample GeneratorResamples your own numbers with replacement to show how much the average would move if you had collected a different sample.
- Survey Sample Size CalculatorHow many people you need to ask for a given margin of error, including the finite population correction most calculators leave out.
- Confidence Interval CalculatorTurn a count out of a sample into an interval, with a warning when the sample is too small for the usual approximation to be trusted.
- Sampling Distribution SimulatorTake a sample, take its mean, repeat — and watch means from even a badly skewed population pile up symmetrically.
- ANOVA Dataset GeneratorGrouped data with a known separation, and the full ANOVA table whose sums of squares are checked to split exactly.
- Permutation Test GeneratorTwo-group data with an exact permutation p-value, computed by trying every possible rearrangement of the labels rather than assuming a distribution.
- Rounding Bias DemonstratorThousands of values rounded two ways, measuring how far each method drifts the total from the truth.
- A/B Test Significance CalculatorRuns a two-proportion test on your conversion counts and is plain about what the p-value does and does not mean.
- Autocorrelated Series GeneratorTime series with a chosen serial correlation, showing the measured lag-1 correlation against the process value and what differencing does to it.
- Multivariate Normal GeneratorCorrelated multi-column samples built by Cholesky factorisation, with the factor proved to reproduce the requested covariance exactly.
- Branching Process SimulatorPopulation lines that either die out or grow without bound, with the exact extinction probability solved from the process's own equation.
- Statistical Power CalculatorWorks out the chance a test would detect a real effect of a given size, and how many people it would take to reach the usual eighty per cent.
- Simpson's Paradox GeneratorBuilds a table where one side wins every subgroup and loses overall, with the reversal verified group by group.
- Benford's Law CheckerCompares the leading digits of your numbers against Benford's law with a chi-square test, and is clear about what a poor fit does not prove.
- Changepoint Dataset GeneratorSeries containing a level shift at a known point, with the split independently recovered by minimising within-segment error.
- Heteroskedastic Data GeneratorRegression data whose noise grows with x, with the fitted slope and the residual spread at each end measured and compared.
- Time-to-Event Dataset GeneratorReliability-style lifetimes with right-censoring at a horizon you set, showing how badly a plain average of completed rows underestimates the truth.
- Normal Distribution Sample GeneratorA random sample from a normal (bell-curve) distribution, mean 50.
Number theory & matrices
- Magic Square GeneratorBuilds a genuine magic square of any size — every row, column and diagonal summing to the constant the size forces.
- Random Partition GeneratorSplits a whole number into random parts that add back up to it exactly, with no part rounded away.
- Tower of Hanoi SolverThe complete optimal move list for any number of discs, replayed against the rules and checked against the two-to-the-n bound.
- N-Queens Puzzle GeneratorQueens placed so none attacks another, with the placement re-verified and the total number of solutions counted exactly.
- Prime Gap GeneratorRuns of consecutive primes with the gap after each, twin pairs highlighted and every gap proved to contain no prime.
- Golomb Ruler GeneratorThe shortest ruler with a given number of marks on which no distance can be measured twice.
- Graeco-Latin Square GeneratorTwo Latin squares laid over each other so that every combination of symbols appears exactly once — impossible at six, as Euler found.
- Coprime Number GeneratorPairs sharing no factor beyond one, with a non-coprime counterexample and Euler's totient counted directly.
- Chinese Remainder Challenge GeneratorSystems of congruences with pairwise coprime moduli and the unique solution below their product, substituted back into every one.
- Recurrence Relation GeneratorLinear recurrences with their terms computed forward and the ratio of consecutive terms, which settles towards the characteristic root.
- Positive Definite Matrix GeneratorMatrices built to be positive definite and proved so twice — by Cholesky decomposition and by Sylvester's criterion.
- Stochastic Matrix GeneratorTransition matrices whose rows sum to exactly one, kept as integers over a common denominator so no rounding creeps in.
- Derangement GeneratorPermutations that leave nothing in its original place, counted by enumeration and by recurrence and required to agree.
- Interval Arithmetic GeneratorArithmetic on ranges rather than numbers, with thousands of sampled points confirming the true answer always lands inside.
- Langford Sequence GeneratorTwo of each number arranged so the two 3s have three things between them, and so on — which only works for some counts.
- Diophantine Equation GeneratorLinear equations in two unknowns over the integers, with the solvability test, a table of the solution family and the smallest non-negative answer.
- Set Partition GeneratorEvery way of splitting a small set into unlabelled groups, counted against the Bell number and broken down by group count.
- Symmetric Matrix GeneratorMatrices that equal their own transpose, with the trace, determinant and the count of entries that are actually free.
- Integer Composition GeneratorEvery ordered way to write a number as a sum, counted by enumeration and by the two-to-the-power formula.
- Condition Number GeneratorLinear systems with their condition number computed exactly, showing how far a tiny change to the inputs can move the answer.
- Random Fibonacci Number GeneratorA random number from the Fibonacci sequence, with its position shown.
- Random Matrix GeneratorA random 3x3 grid of numbers, for maths practice or placeholder data.
- Random Perfect Square GeneratorA random perfect square (n²) between 1 and 900, with its root shown.
- Composite Number GeneratorA random composite (non-prime) number within your chosen range.
- Factor GeneratorA random number shown with its complete list of factors.
- Geometric Sequence GeneratorA random geometric sequence with a whole-number ratio.
- Integer Partition GeneratorA random way to split a small number into positive whole-number parts.
- Costas Array GeneratorOne dot in every row and every column of a square board, arranged so that no two pairs of dots are the same distance apart in the same direction.
Dates & times
- Random Date GeneratorGenerate one or more random calendar dates within a chosen range, with weekday or weekend filters.
- Random Date Range GeneratorA start and end date pair, 3 to 30 days apart.
- Random Century GeneratorA century, from the 15th to the 22nd, with its year range.
- Random Decade GeneratorA decade label, from the 1920s to the 2020s.
- Random Duration GeneratorA random length of time, formatted as hours, minutes and seconds.
- Random Timestamp GeneratorA random ISO-8601 timestamp between 2020 and 2030, for test data or placeholders.
- Random Time of Day GeneratorA random 24-hour time, HH:MM.
- Random Date & Time GeneratorA friendly random date and time, e.g. '14 March 2027, 3:45pm'.
Practical calculators
- Appliance Running Cost CalculatorTurns watts into units and units into pounds for any appliance, keeps the standing charge separate, and works out how long a more efficient replacement takes to pay for itself.
- Tyre Size Comparison CalculatorCompares two tyre sizes: overall diameter, rolling circumference, ride height and what the speedometer will really be reading.
- Screen Size Comparison CalculatorTurns a screen's diagonal and shape into a real width, height and picture area, and compares two screens properly — by area, not by diagonal.
- Towing Weight CheckerChecks a car and trailer against all four limits at once — towing capacity, towball, gross train weight and noseweight — and shows the arithmetic for each.
- Aquarium Volume CalculatorWorks out how much water a tank really holds once the glass, the gravel and the freeboard are taken off, and what a water change comes to.
- Battery Life and Cable Drop CalculatorWorks out how long a battery really lasts in watt-hours rather than milliamp-hours, and how much voltage a cable run loses on the way.
- Unit ConverterConverts length, weight, volume, area, speed, time, data and temperature, with the exact defined factors and every unit shown at once.
- Bolt Circle CalculatorMarks out equally spaced holes round a circle: the divider setting between them, the angle of each, and its position across and up from the centre.
- Age CalculatorWorks out an age in years, months and days, and proves it by adding the answer back onto the birth date.
- Roman Numeral ConverterConverts numbers to Roman numerals and back, refusing forms like IIII that read correctly but are not how the number is written.
- Economic Order Quantity CalculatorThe order quantity that minimises total inventory cost, shown with the cost either side so the minimum can be seen rather than taken on trust.
- Reorder Point CalculatorThe stock level at which to reorder, splitting lead-time demand from safety stock and showing why safety stock grows with the square root of lead time.
- Cash Denomination Breakdown GeneratorBreaks an amount into notes and coins using the fewest pieces, proved against every alternative by dynamic programming.
Graphs & networks
- Travelling Salesman Problem GeneratorTour instances on random coordinates, solved exactly by Held-Karp, with the nearest-neighbour tour shown for comparison.
- Shortest Path GeneratorWeighted graphs with Dijkstra's shortest route, verified by the relaxation condition rather than by trusting the code.
- Minimum Spanning Tree GeneratorWeighted graphs with the cheapest spanning tree found by Kruskal and, at small sizes, confirmed against every other spanning tree.
- Flow Network GeneratorCapacitated networks with the maximum flow found by Edmonds-Karp and the minimum cut that proves it cannot be beaten.
- Bipartite Matching GeneratorPeople-to-slots problems solved to the largest possible matching, with the answer proved by building a minimum cover of the same size.
- Graph Colouring Challenge GeneratorColour the nodes so no edge has one colour at both ends, with the greedy answer and — at small sizes — a proof that fewer colours are impossible.
- Euler Path GeneratorTrails that use every edge exactly once, with the odd-degree count that decides whether one can exist at all.
- Topological Order GeneratorDependency graphs with a valid task order, every edge checked to point forwards and the number of alternative orders counted exactly.
- Knight's Tour GeneratorA knight's route visiting every square of the board exactly once, with every step re-checked as a legal knight move.
- Bipartite Graph GeneratorGraphs split into two sides with every edge crossing, or a graph that cannot be — with the odd cycle that proves it.
- Graph Traversal GeneratorThe same graph visited breadth-first and depth-first side by side, with the hop count each node sits at.
- Graph Centrality CalculatorDegree, closeness and betweenness for every node of a random network, with degrees and distances recomputed from scratch and betweenness sanity-checked before it is shown.
- Planar Graph GeneratorDraws a random graph that can be laid out with straight lines and no edge crossing another, with the drawing to prove it.
- Articulation Point GeneratorConnected graphs with their cut vertices found by depth-first search and confirmed by actually removing each node and counting the pieces.
- Non-Planar Graph GeneratorA graph that cannot be drawn without an edge crossing, together with the K5 or K3,3 hiding inside it that proves it — a proof you can walk by hand.
- Hamiltonian Path Challenge GeneratorGraphs where the puzzle is to visit every node exactly once, with every such path counted by exhaustive search.
- Graph Bridge FinderGraphs with their bridges identified — the edges that lie on no cycle — each one confirmed by deleting it and counting the pieces.
- Strongly Connected Components GeneratorDirected graphs partitioned into strongly connected components by Kosaraju, checked against mutual reachability computed from every node.
- Degree Sequence GeneratorDegree sequences tested for whether any simple graph can have them, with Havel–Hakimi shown step by step and the built graph's degrees recounted.
Coordinates & geometry
- Random Point in Radius GeneratorCoordinates spread evenly over the area inside a radius, not bunched at the centre, and placed on a sphere rather than a flat grid.
- Random Coordinate GeneratorA latitude/longitude coordinate, uniformly distributed across the globe — could land anywhere, ocean included.
- Voronoi Diagram GeneratorRegions of nearest-site ownership drawn by sampling, with every checked cell verified against every site and the region shares reported.
- Point Cloud GeneratorClustered two-dimensional points with the cluster labels kept, and the within-cluster and between-cluster distances measured.
- Random Triangle GeneratorTriangles with sides, angles and area computed from the coordinates, and no slivers — every angle is at least 15 degrees.
- Poisson Disc Point GeneratorPoints with a guaranteed minimum separation, placed by Bridson's algorithm and measured against a uniform scatter of the same size.
- Random Polygon GeneratorSimple polygons that never cross themselves, with the shoelace area, the perimeter and a convexity check.
- Convex Hull GeneratorRandom points with the smallest convex boundary around them, every point checked to lie on or inside it.
- Delaunay Triangulation GeneratorTriangulations where no triangle's circumcircle contains another point, tested triple by triple, with the smallest angle reported.
- Orthogonal Vector GeneratorWhole-number vectors that are exactly perpendicular, with every pairwise dot product shown as the integer zero it is.
- Random Compass Direction GeneratorA point on a 16-point compass, from North to North-northwest.
- Random Angle GeneratorAn angle in decimal degrees, from 0 up to (but not including) 360°.
- Random 3D Coordinate GeneratorA random three-dimensional (x, y, z) coordinate point.
- Random Angle Set GeneratorA set of three random angles in whole degrees.
- Vector GeneratorA random 2D vector with its magnitude shown.
Logic, games & automata
- Truth Table GeneratorThe full truth table for an expression you type — or one drawn for you — with the grouping shown fully bracketed and a tautology or contradiction verdict counted from the rows.
- Game of Life Pattern GeneratorRandom Life soups run until they settle, reporting whether they died, froze, or fell into a cycle — and the exact period.
- Nash Equilibrium GeneratorPayoff grids with every pure equilibrium found by testing each cell against every alternative for both players.
- Logic Simplification Challenge GeneratorDeliberately over-complicated expressions built by applying an identity backwards, with the law named and equivalence proved on every assignment.
- Elementary Cellular Automaton GeneratorAll 256 one-dimensional rules, run from a single cell or from noise, with the rule number decoded into its eight outputs.
- Dominant Strategy GeneratorGames solved by repeatedly removing strategies that are worse whatever the opponent does, with each removal recorded against the options still in play.
- Karnaugh Map Challenge GeneratorGrey-coded Karnaugh maps filled from a real expression, with the largest valid groups found and each one proved to cover only true cells.
Optimisation & scheduling
- Knapsack Problem Generator0/1 knapsack instances solved exactly by dynamic programming, with the value-per-weight answer shown alongside for comparison.
- Bin Packing Problem GeneratorPacking instances with bins of one size or several at different prices, each with an answer, a lower bound, and a plain statement of when the two meet.
- Makespan Scheduling Problem GeneratorJobs across identical machines, scheduled longest-first, with two lower bounds that often prove the schedule optimal.
- Flow Shop Schedule GeneratorTwo-machine job sequencing solved by Johnson's rule, confirmed against every possible order — a rare case where a simple rule is provably optimal.
- Newsvendor Problem GeneratorSingle-period stocking problems where every candidate quantity is evaluated against every demand outcome, so the best one is found rather than approximated.
- Transportation Problem GeneratorBalanced supply-and-demand shipping problems solved by the least-cost rule, with exhaustive search saying honestly whether that answer was optimal.
- Strip Packing GeneratorRectangles packed into a fixed-width strip with no overlaps, measured against the height no packing could beat.
- Set Cover Problem GeneratorCoverage problems where greedy selection is compared against the true minimum found by exhaustive search, so the cost of approximation is visible.
- Facility Location GeneratorWhere to place a few facilities among many demand points, solved greedily and compared against every possible combination.
- Guillotine Cutting GeneratorSheet layouts reachable only by edge-to-edge cuts, which is the constraint a panel saw actually imposes.
Identifiers & test values
- Base64 String GeneratorA Base64-encoded token built from cryptographically secure random bytes, for testing or placeholder data.
- Random MAC Address GeneratorA locally-administered MAC address for testing or placeholder data.
- Random IP Address GeneratorAn IPv4 address for test data or placeholder configs.
- Random Binary String GeneratorA string of 0s and 1s of a fixed length — not a converted number.
- Random Hex String GeneratorA string of hexadecimal characters of a fixed length — not a converted number.
- ISBN Example GeneratorAn ISBN-13-shaped example number with a correct check digit, for test data that has to pass validation.
- Barcode Number Example GeneratorA 12-digit UPC-A-shaped example number with a correct check digit — not a real, assigned barcode.
- Checksum Test Number GeneratorA fictional, mod-10-checksum-valid test number, for testing validation code.
Bases, fractions & notation
- Continued Fraction GeneratorExpands any fraction into its continued fraction and lists the convergents, each one after the whole part proved to be the best approximation for its denominator.
- Best Rational Approximation GeneratorFinds the closest fraction to a decimal within a denominator limit, proved by testing every denominator up to that limit.
- Repeating Decimal GeneratorTurns a fraction into its decimal expansion with the repeating block marked, and checks the period against the multiplicative order of ten.
- Egyptian Fraction GeneratorExpands a fraction into distinct unit fractions by the greedy method, added back up in exact big integers to prove the sum.
- Farey Sequence GeneratorLists every fraction between 0 and 1 with a bounded denominator, in order, with the neighbour identity checked on every consecutive pair.
- Expression Notation GeneratorShows one arithmetic expression in infix, prefix and postfix, with all three evaluated separately and required to agree.
- Random Binary Number GeneratorA number shown in binary, alongside its decimal value for reference.
- Random Hex Number GeneratorA number shown in hexadecimal, alongside its decimal value for reference.
- Roman Numeral GeneratorA number converted to Roman numerals, alongside the original figure.
- Random Scientific Notation GeneratorA random number formatted in scientific notation, e.g. 4.82 × 10^7.
- Octal Number GeneratorA random number shown in octal (base 8), alongside its decimal value.
Also useful for numbers
- Sudoku GeneratorPrint a sudoku with exactly one solution — 4x4, 6x6 or full 9x9, four difficulties, with the answer key and a seed to reprint it.
- Kakuro GeneratorCross-sum puzzles where every run adds to its clue using distinct digits — every clue satisfiable by construction.
- KenKen GeneratorArithmetic-cage puzzles on a Latin square, every one solved exhaustively to prove it has exactly one answer.
- Killer Sudoku GeneratorSudoku with cage totals in place of given digits: the grid is divided into cages, and only one grid fits them.
- Cryptarithm GeneratorSEND + MORE = MONEY puzzles where each letter stands for a different digit, every one solved and proved to have a single answer.
- Printable Puzzle Book GeneratorBuilds a printable book of up to 250 sudoku, mazes, word searches, nonograms, fill-in crosswords and codewords — sectioned, ramped from gentle to hard, numbered front to back, with an answer key that matches.
Choosing the right numbers tool
This is one of the three largest categories on the site and it is not all one thing. About twenty tools draw random numbers; the other hundred and sixty or so are the rest of what people come to numbers for. Where a number is drawn, ranges are inclusive at both ends throughout and every value is equally likely — the conversion from raw randomness into a range uses rejection sampling rather than the modulo shortcut, which quietly favours lower values. Where something is computed or constructed instead — a solvable puzzle, a graph with a stated property, a dataset with a known effect size — the page says what it guarantees.
- Random Number Generator
- The general case: set a range, pick how many numbers, and decide whether repeats are allowed.
- Unique Random Number Generator
- You need every number in the set to be different, without having to remember to turn duplicates off.
- Specialised number tools
- You want a particular shape of number — even, odd, negative, decimal, percentage or fraction — without configuring the general tool.
- Sudoku, Kakuro and the grid puzzles
- You want something to solve rather than something to draw. Those have their own category, Puzzles, and the ones with arithmetic in them are linked under “Also useful” above. Their solved relatives stay here — the magic square, N-Queens, the knight's tour and the Tower of Hanoi — because each of those pages hands you the finished answer rather than a problem.
- Probability and simulation tools
- You want to watch a result emerge over many trials — Monty Hall, the birthday problem, gambler's ruin — rather than read the formula for it.
- Statistical dataset generators
- You need numbers with a property you specified: a known effect size, a planted changepoint, a given correlation. For teaching a method or testing an analysis.
- Graph, network and optimisation generators
- You need an instance of a named problem — travelling salesman, knapsack, bin packing, minimum spanning tree — to solve, teach or benchmark against.
- Coordinate and geometry tools
- The output is a point, an angle, a polygon or a shape rather than a quantity.
- Practical calculators
- You have a real-world figure to work out — an age, a running cost, a tyre size — and the answer is one correct number rather than a random one.
Every tool in this category draws its results in your browser. How Generate Random works explains how the randomness is produced and what happens to anything you type in.