# How to calculate size distribution of an object than has been divided into smaller pieces

I have an object that is broken into smaller pieces such that the sum of the pieces is the volume of the original object.

I have arranged the volumes from the smallest to largest and have calculated the cumulative volume starting at 0% and ending at 100%.

Initially I was thinking that this graph was the same as the probability of the size distribution but the more I think about it am not 100% sure.

**Vol       Cumm Vol    % of total**
0.002652009 0.004214928 100
0.00064838  0.001562919 37.08055596
0.000261065 0.000914539 21.69761768
0.000142893 0.000653474 15.50379186
9.25843E-05 0.00051058  12.11362071
6.63311E-05 0.000417996 9.917040157
5.06804E-05 0.000351665 8.343322696
4.05044E-05 0.000300985 7.140921227
3.34249E-05 0.00026048  6.179945411
2.82653E-05 0.000227055 5.386932085
2.4392E-05  0.00019879  4.716332593
2.13362E-05 0.000174398 4.137627787
1.89405E-05 0.000153062 3.631422336
1.69605E-05 0.000134121 3.182054867
1.53332E-05 0.000117161 2.77966324
1.39699E-05 0.000101828 2.415880905
1.27933E-05 8.78578E-05 2.084442725
1.17995E-05 7.50645E-05 1.780918818
1.09368E-05 6.32649E-05 1.500972549
1.01715E-05 5.23281E-05 1.241494728
9.49734E-06 4.21567E-05 1.000174814
8.9103E-06  3.26593E-05 0.774848551
8.38075E-06 2.3749E-05  0.563449821
7.90202E-06 1.53683E-05 0.364614847
7.46623E-06 7.46623E-06 0.177137873


So if I have this set of sizes is this how I calculate the size distribution?

If not then how do I do this?

## 1 Answer

Your percentages (the third column) are the probability that a point chosen uniformly from the object is in a piece of volume less than or equal to the value in the first column. For example, looking at the fourth row of numbers, there is a $15.50379186\%$ probability that a point chosen is in in a piece of volume less than or equal to $0.000142893$.

In that sense your data shows a cumulative distribution function.