Enter the total, choose between “Exact shares” and “Whole units”, and add one weight per line. Each weight can be a whole number, a fraction or a decimal, and its size only matters relative to the others. When you calculate, each group appears in the order of your list with its share and a check that the shares add up to the total.
Worked example: 10 items among three equal groups
10 items must be shared among groups A, B and C with weights 1 : 1 : 1. How much does each group get?
- Add the weights. 1 + 1 + 1 = 3.
- Find the exact share. Each group gets 10 × 1/3 = 10/3, which is 3 + 1/3.
- If the items can be cut, the answer is 10/3 for each group, and the three parts add up to 10.
- If they cannot be cut, each group first takes 3 items. One is left over, and the three remainders of 1/3 tie, so it goes to group A, the first in the list.
Result: 10/3 each with divisible parts; 4, 3 and 3 in whole units.
Check: 4 + 3 + 3 = 10, and no part is more than one unit away from its exact share.
How to share a total by a ratio
To share a total T in the ratio 2 : 3, add the weights, 2 + 3 = 5, and each group takes its fraction of that sum. With 100, the first group gets 100 × 2/5 = 40 and the second 100 × 3/5 = 60. Because the fractions 2/5 and 3/5 add up to 1, the parts always add up to the total.
Weights can be fractions. To share 48 with weights 1/2 and 1/3, the sum is 5/6. The first group gets 1/2 ÷ 5/6 = 3/5 of the total, and the second gets 2/5. The shares are 48 × 3/5 = 144/5 = 28.8 and 48 × 2/5 = 96/5 = 19.2, which add up to 48.
Before sharing, you can simplify the ratio by dividing out the common factor, because 4 : 6 and 2 : 3 give the same shares. The simplify ratios calculator reduces ratios with two or more terms, and the guide to proportional sharing with fractions explains how to set up the split when the problem is given in words.
Fractions and whole units in several cases
The whole-units mode uses the largest remainder method, which first assigns the whole part of each share and then gives the leftover units to the highest fractional remainders. The English Wikipedia article Largest remainder method describes this method for allocating seats: the groups with the largest remainders each get one additional unit (accessed October 17, 2026). The tie rule in this calculator is its own: the group that comes first in the list wins.
| Case | Exact shares | Whole units |
|---|---|---|
| 7 in the ratio 1 : 2 | 7/3 and 14/3 | 2 and 5 |
| 100 in the ratio 1 : 2 | 100/3 and 200/3 | 33 and 67 |
| 11 in the ratio 1 : 1 : 1 : 1 | 11/4 each | 3, 3, 3 and 2 |
| 50 in the ratio 3 : 2 | 30 and 20 | 30 and 20 |
When the sum of the weights divides the total, as in the last case, the shares are already whole numbers and both modes agree. In the case of 11, the four remainders of 3/4 tie, and the three leftover units go to the first three groups in the list.
Where it applies and where it does not
Proportional sharing works when each group should receive in proportion to a known quantity: profits by contribution, costs by usage or hours by time spent. It is the same calculation as the 17 camels puzzle, where the 17 camels are split in the ratio 9 : 6 : 2 and the result is 9, 6 and 2. If you only need one part of a total, such as 3/4 of 80, use fraction of a number; if you are looking for an unknown term of a proportion, the proportion calculator or the rule of three is more direct.
The calculator applies proportions and largest remainders, not legal or electoral rules, so an estate with forced shares or a seat apportionment by another method needs its own rules.
Frequently asked questions
How do I split an amount in inverse proportion, for example by ages?
Use the reciprocals of the data as weights: the youngest gets the most. To split 900 in inverse proportion to the ages 4, 5 and 20, enter the weights 1/4, 1/5 and 1/20. They add up to 1/2, so each person gets 1/2, 2/5 and 1/10 of the total, which is 450, 360 and 90.
Can I enter the weights as percentages?
Yes, but type only the number, without the % sign. To split 350 between two partners with 30% and 70%, use the weights 30 and 70: you get 105 and 245. Fractions, decimals and mixed numbers also work, as long as they are positive.
What happens with a zero total or a zero weight?
With a zero total, every share is zero. A zero or negative weight is not accepted, and the calculator says the weights must be positive. A group that gets nothing simply stays off the list.