# How many nines is 95%?

by Charlton Rose

In business, we often describe performance approaching perfection with a number of nines. For example, if a web server is 99.9% available, then we say that the server gives us 3 nines of availability.

That's all fine and dandy when we're dealing with mantissas that only involve nines, such as 90% or 99%. But just how many nines, exactly, is 95%? Is this 1½ nines?

It sounds good, but it's not quite right. This is because the nines scale is logarithmic. I'll spare you the derivation, but if you want a handy formula to compute the number of nines for performance measurements that don't always line up on the nines, try this:

$n = - log ( 1 - p )$

where $n$ is the number of nines, and $p$ is the performance (ranging from 0 to 1).

With this formula, we can answer our original question: A performance of 95% is 1.3 nines. You can verify this result using the "nines calculator," provided below.

## nines calculator

attribute range value
performance 0 - 100 %
number of nines 0 - +∞ nines
annual downtime 0 - 365.24d

In this interpretation of nines, 100% is equivalent to an infinite number of nines: 99.999999...%. Intuitively, this makes sense, don't you think?

And what about the case where your performance is only 75%? Is this 0 nines? For some, this might be one way of looking at it. But then again, those same people might also say there is one nine in 9%. From where I stand, however, 9% has only 0.04 nines.