Availability is a fraction of a period, and the downtime it permits is (1 − A) × period. Each further nine divides that downtime by ten while moving the percentage by less than a tenth of a point, which is why the two ways of quoting the same target sound so unlike each other. The period is part of the number: a downtime figure without one says nothing at all.
Core ideas
One equation read in both directions, and the convention that makes its answer reproducible from one page to the next.
A is the fraction of a period during which the service does its job, so 1 − A is the fraction during which it does not, and multiplying that by the length of the period gives the downtime the target permits. Nothing else is happening: downtime = (1 − A) × period is the whole of this lesson, and every other lesson on this course is what happens to A when several of them are put together.
Going from 99.9% to 99.99% moves the percentage by 0.09 points, which sounds like a rounding. It divides 1 − A by ten, and 1 − A is what you actually buy: 43 minutes and 48 seconds a month become 4 minutes and 22.8 seconds. The percentage is a bad scale for this quantity and the downtime is a good one, which is why the lab draws the ladder in minutes.
“Fifty-two minutes of downtime” is four nines over a year and barely three nines over a month; the same duration is a different promise on a different clock. This course fixes one table of periods, and a month in it is a twelfth of a 365-day year — 2 628 000 seconds — so every monthly figure on every page can be reconciled with every other.
The material
What an availability is, what a nine is worth, and why the period has to be written down before the arithmetic starts.
The availability A of a service over a period is the fraction of that period during which it is serving. It is a number in [0, 1]; the percentage is a presentation of it and never enters a calculation. The complementary fraction 1 − A is the unavailability, and the downtime permitted by A over a period of length T is (1 − A) × T.
Both directions of that equation are used constantly. A target hands you A and you want the minutes; a downtime budget hands you the minutes and you want the A it corresponds to. They are the same equation rearranged, and the lab does both.
Keep A as a fraction throughout. 999/1000 is exactly three nines and 0.999 is a double that is very slightly not; the differences this course cares about live in the fourth decimal place and further down, and a percentage rounded for display hides all of them. Every figure the lab prints is an exact fraction until the last digit.
At 99.9% you may be down 43 min 48 s a month and 8 h 45 min 36 s a year. At 99.99% those become 4 min 22.8 s and 52 min 33.6 s. The percentages differ by 0.09000%; the minutes differ by a factor of ten, and it is the minutes that get paid for — in redundancy, in deployment discipline and in how fast someone has to be woken up.
An availability has k nines when 1 − A ≤ 10⁻ᵏ, taking the largest such k. This is a statement about the unavailability and not about how many 9 characters appear in the printed percentage.
The two readings come apart immediately. 99.95% shows two nines in its digits, but 1 − A = 0.0005, which is smaller than 10⁻³ and larger than 10⁻⁴, so it has three nines — and it permits 21 min 54 s a month, half of what 99.9% permits. Nines are a logarithmic scale, so “three and a half nines” is not a category the definition contains.
A downtime is a duration and a duration only means something against a period. This course fixes one table and states it on every page: an hour is 3600 s, a day 86 400 s, a week 604 800 s, a month 2 628 000 s, a quarter 7 884 000 s and a year 31 536 000 s. The month is a twelfth of a 365-day year, which is the convention under which three nines is the 43.8 minutes quoted everywhere above.
Another convention is in circulation and it is also defensible: a 30-day month is 2 592 000 seconds, and three nines over that is 2592 s, or 43.2 minutes. Neither figure is wrong. What is wrong is quoting one of them beside an annual figure computed from the other, and that is why the period is written down first rather than assumed.
Start from what you are willing to be down and the same equation hands back the target. This is usually the more honest order, because a team can say how long an outage may last long before it can say which nine it wants, and the arithmetic converts one into the other without any negotiation.
Someone rounds 43.8 minutes up and writes “44 minutes a month” into a document. That budget is 1 − 2640/2 628 000 = 10939/10950, or 99.89954%, and by the definition above it has two nines rather than three. The rounding went the wrong way across a boundary. Set the lab to work from a budget and move the slider between 43 and 44 minutes to watch the count change.
Interactive
Downtime is (1 − A) × period, and each nine is a factor of ten
Method
Four lines, and the third one is the only arithmetic. The other three are what stop the arithmetic being done on the wrong number.
99.9% is 999/1000. Do not carry it as 0.999, and do not carry the percentage into the multiplication: the factor you need is 1 − A, and here that is exactly 1/1000.
Write down which period you are quoting and its length before anything else. A month on this course is 2 628 000 s. If a different convention is in use, say so in the same sentence as the answer.
(1/1000) × 2 628 000 = 2628 s. Convert once, at the end: 43 minutes and 48 seconds. Converting earlier introduces a rounding into a quantity whose interesting digits are at the far right.
One more nine must give a tenth of the downtime and one fewer must give ten times as much. If your answer does not sit on that ladder, the error is almost always a period mismatch — a monthly figure compared with an annual one.
A target that is not a round nine, so the fraction has to be carried rather than recognised.
The check at the end is the part worth keeping. Two digits of the percentage moved and the count of nines did not; the downtime halved. Anyone reading “99.95” as “two nines and a bit” has compared the printed characters instead of the unavailability.
For a faded rehearsal, take 99.5%. The supplied first move is 1 − A = 1/200. Produce the downtime per week and per quarter, say how many nines it has by the definition rather than by looking, and then state the monthly budget in minutes that would buy exactly one more nine. Check all three against the lab before opening the quiz, and say which period each of your figures belongs to.
You should be able to convert either into the other over any of the six periods without looking anything up, say how many nines an availability has by the definition rather than by eye, and state the period alongside every duration you quote.
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