Lottery Number Generator
Generate combinations using the official number ranges for Lotto 6/45, US Powerball, and Mega Millions. Forced and excluded values apply only to the main-number pool and do not improve the draw odds.
Scope of Lottery Rules and Combination Odds
Reference date and last reviewed: August 19, 2026
Calculation Basis
Uses the current main-number and bonus-ball ranges published by Korea Lotto 6/45, Powerball, and Mega Millions, together with the combination formula C(n, r), to calculate filtered candidate lines and exact-match odds for one line.
Reference Limits
This tool generates random lines and explains the size of the combination space; it does not predict winning numbers or identify patterns with better odds. Forced values, exclusions, sums, and odd-even balance do not improve the official draw probability, and the tool does not sell tickets or verify prizes.
When to Confirm Officially
Lottery operators may change number matrices, prices, drawing schedules, or sales jurisdictions. Before buying or checking a ticket, confirm the latest rules and eligibility on the official sites below, and use a predetermined entertainment budget rather than treating a random line as an investment.
Usage Tips
Filters do not change the odds for a completed line
Forced and excluded numbers only change the pool available to the generator. Compare the candidate count with the exact-match odds shown in the result, and confirm the current rules on the official lottery site before playing.
What is Lottery Number Generator?
The Lottery Number Generator creates unique main-number combinations for Lotto 6/45, US Powerball, Mega Millions, or a custom range. Forced and excluded values apply to the main-number pool only; Powerball and Mega Ball numbers are generated from their separate bonus pools. The result distinguishes the number of candidate lines available under the selected filters from the exact-match odds for one completed line. Generation and saved history stay in the browser, and the tool does not predict winning numbers.
How to Use
- 1 Choose Lotto 6/45, Powerball, Mega Millions, or Custom Rules. The preset main-number and bonus-ball ranges use the rules verified on the displayed review date.
- 2 Select how many lines to generate. Under Custom Rules, enter the minimum, maximum, and number of main values to draw for each line.
- 3 Enter any forced main numbers and numbers to exclude. Separate values with commas or spaces; repeated entries are applied only once.
- 4 Press Generate Numbers to sample the remaining main-number pool without duplicates and sort each line. Powerball and Mega Millions add one bonus ball from the game's separate pool.
- 5 Compare the candidate-line count with the exact-match odds shown above the results. Copy a line or save it in this browser if you want to keep it.
How filters change candidate lines without changing draw odds
Last reviewed: August 19, 2026Number of lines available after filters
candidate lines = C(full range - excluded - forced, draw count - forced) Γ bonus outcomes
A forced number is already selected, so it is removed from both the remaining pool and the remaining draw count. Formats with a separate bonus pool multiply the main combinations by the number of possible bonus balls.
Forcing 7 and excluding 13 in Lotto 6/45
- β’ Main pool: choose 6 numbers from 1~45
- β’ Forced number: 7; excluded number: 13
- 1. Removing 7 and 13 leaves 43 selectable values, with 5 still needed.
- 2. Candidate lines matching the filters = C(43, 5) = 962,598
- 3. All Lotto 6/45 draw outcomes = C(45, 6) = 8,145,060
The generator can produce 962,598 filtered lines, while one completed line still has jackpot odds of 1 in 8,145,060.
How to read the result
- A smaller candidate count means the generator has fewer acceptable outputs; it does not mean the official draw became more favorable.
- Sum and odd-even balance describe a generated line but do not predict which independent combination will be drawn next.
Conditions that change the result
- If an operator changes a game's number matrix, the preset and its displayed odds must be reviewed again.
- Custom-format odds assume that every combination in the entered range is drawn with equal probability.
Common input mistakes
- Treating the Powerball or Mega Ball as part of the main-number range produces a different game from the official two-pool format.
- Using the same value as both forced and excluded, or excluding too much of the pool, leaves no valid line to generate.
Reference Knowledge
- β Korea Lotto 6/45 selects six main numbers from 1 through 45, giving one completed line jackpot odds of 1 in 8,145,060.
- β The current official matrices are 5 main numbers from 1~69 plus 1 Powerball from 1~26, and 5 main numbers from 1~70 plus 1 Mega Ball from 1~24.
- β The filtered candidate count uses the combination C(n, r) for the remaining main-number pool and multiplies it by the number of bonus-ball outcomes when a separate bonus pool applies.
- β Number selection uses uniform integer sampling backed by the Web Crypto API when the browser supports it, with a general browser-random fallback for older environments.
FAQ
Q. Do forced or excluded numbers improve the chance of winning?
No. Filters only reduce the set of lines that this generator can produce. Within the same lottery format, every completed line has the same chance of matching the actual draw.
Q. What is the difference between candidate lines and exact-match odds?
Candidate lines count the distinct results the generator can create under the current forced and excluded values. Exact-match odds compare one completed line with every possible official draw, regardless of the filters used to create it.
Q. Do the filters apply to the Powerball or Mega Ball?
No. The current filter fields apply only to the white main-number pool. The Powerball or Mega Ball is generated independently from its own official bonus range.
Q. Why does Mega Millions use Mega Ball numbers 1 through 24?
Mega Millions changed from 25 to 24 gold Mega Balls when its redesigned game began in April 2025. This tool uses the current 1~24 range as of the displayed review date.
Q. Are saved combinations sent to a server?
No. Generation and storage run in the current browser, and saved lines remain only in browser local storage. Clearing site data or closing a private window may remove them.
