Number Generators
Random Numbers That Sum To a Target
Generate a set of random numbers that add up to the exact total you specify.
Random Numbers That Sum To a Target
5 numbers · sum 100
How many numbers and target sum
The numbers will add up exactly to the target
Options
Sort resultsHow to use the sum to target generator
- Set how many numbers you want and the exact total they must reach.
- Optionally bound each number with a minimum and a maximum.
- Press Generate numbers. The set always lands exactly on the target.
How many ways a total can be split
Splitting a target into parts is a classic counting problem, and the number of possible ordered splits grows explosively. For a target of 100 with parts allowed from 0 to 100, the counts are:
| Parts | Possible ordered splits of 100 |
|---|---|
| 2 | 101 |
| 3 | 5,151 |
| 4 | 176,851 |
| 5 | 4,598,126 |
| 10 | 4,263,421,511,271 |
Combinatorics calls these figures compositions, counted by the stars and bars formula. Ten parts already allow over four trillion different splits of 100, which is why two presses of the button essentially never repeat.
When the target is impossible
The count and the per number bounds set hard limits: the smallest reachable total is the minimum times the count, and the largest is the maximum times the count. Ask for five numbers between 0 and 10 that total 100 and no answer exists, since five tens only reach 50. The tool checks this before drawing and tells you the reachable band, so you can widen the bounds or change the count instead of getting a silently wrong set.
Where a fixed total draw is used
This draw pattern appears wherever a whole must be shared randomly: splitting a marketing budget across five channels for a scenario test, sharing 100 quiz points across rounds, generating invoice lines that must reconcile to a known total, allocating a fixed stock across bins, or building spreadsheet test data whose sum column is already agreed. Each press gives a fresh split with the total guaranteed, and the per number bounds keep any single share from dominating.
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Frequently asked questions
How can random numbers add up to a set total
The tool shares the target across the count you ask for. Each number is drawn within its allowed range, and the last values are constrained so the set always lands exactly on the target.
Can I control how big each number is
Yes. Set a minimum and a maximum per number. If the target cannot be reached within those limits, the tool tells you the total range that is possible.
Why does it say the target is not possible
Because the count and the per number limits cannot reach it. For example five numbers each 0 to 10 can only total between 0 and 50.
Are the numbers whole
Yes, every value is a whole number and the set adds up to the exact target you set.
Is it free
Yes, free and with no sign up. Every draw runs in your browser and nothing you enter leaves your device.
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