# Ceph Erasure Code Overhead Mathematics

Posted on Sat 30 November 2019 in hints-and-kinks • 2 min read

So you’re running a Ceph cluster, and you want to create pools using erasure codes, but you’re not quite sure of exactly how much extra space you’re going to save, and whether or not that’s worth the performance penalty? Here’s a simple recipe for calculating that space overhead.

Suppose a RADOS object has a size of $$S$$, and because it’s in an EC pool using the jerasure or isa plugin,1 Ceph splits it into $$k$$ equally-sized chunks. Then the size of any of its $$k$$ chunks will be:

$$S \over k$$

In addition, we get $$m$$ more parity chunks, also of size $$S \over k$$.

Thus, the total amount of storage taken by an object of size $$S$$ is:

$$k \cdot {S \over k} + m \cdot {S \over k}$$

This of course we can rearrange and reduce to

$$S + S \cdot {m \over k}$$

or

$$S \cdot (1 + {m \over k})$$

In other words, the overhead (that is, the additional storage taken up by the EC parity data) is

$$S \cdot {m \over k}$$

or when expressed as a proportion to $$S$$, simply

$$m \over k$$

As an example, an EC profile with $$k = 8, m=3$$ comes with a storage overhead of $$3 \over 8$$ or 37.5%.

One with $$k=5, m=2$$ has an overhead of $$2 \over 5$$, or 40%.

And finally, a replicated (conventional, non-EC) pool with 3 replicas can be thought of as having a degenerate EC profile with $$k=1, m=2$$, resulting in an overhead of $$2 \over 1$$, or 200%.

On a parting note, you should realize that the space utilization overhead is only one factor by which you should weigh erasure code profiles against one another. The other is performance. Here, the general (deliberately oversimplified) rule is that the more chunks you define — in other words, the higher your $$k$$ — the higher the performance penalty you suffer, particularly on reads.2 This is due to the fact that in order to reconstruct the object and serve it to the application, your client must collect data from $$k$$ different OSDs and assemble it locally.3

1. Thanks to Lars Marowsky-Bree for reminding me that slightly different arithmetics apply to the lrc, shec, and clay plugins.

2. Thanks to Lenz Grimmer for pointing out that the post should make this clear.

3. If you want to know more about erasure codes and their history, not limited to their use in Ceph, Danny Abukalam did an interesting talk on the subject at OpenStack Days Nordic 2019.