

Ask HN: Do you know any useful "Back of the Envelope Calculations"? - ddoonie

Intrigued by the recent HN submission regarding estimating the revenues of a company, does anyone have any other useful back of the envelope calculations?  Anything that you find useful for quick mental calculations - preferably for financial applications (but any are welcome).<p>Thanks
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cperciva
One I use often is that 1 Mbps of IP packets ~~ 10 GB / day of data. (1 Mbps
is 10.8 GB/day, but TCP/IP overhead will typically eat up at least 0.4 GB and
usually close to 0.8 GB from that.)

Another, more often financial calculation: If you have X% growth, it takes
72/X time periods to double. (Accurate to within 1 time period for X% > 2%,
and accurate to within 10% for X% < 29%.)

~~~
porter
Using 70/X will also work just fine.

~~~
cperciva
Yes, and for small values of X, 70/X is more accurate, too. 72 has the
advantage of being a multiple of 2, 3, 4, 6, 8, 9, and 12, whereas 70 is a
multiple of 2, 5, 7, 10, and 14 -- knowing both of these gives you a whole-
number answer for any growth rate under 15% except 11% (correct answer is
6.64) and 13% (correct answer is 5.67).

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jonsen
Memorize powers of 2 up to 9

    
    
      0   1   2   3    4    5    6    7    8    9
      1   2   4   8   16   32   64  128  256  512
    

and

    
    
      2^10 = 1K,   2^20 = 1M,   2^30 = 1G  etc.  
    

then split anything else

    
    
      ex. 2^23 = 2^20 * 2^3 =   8M
      ex. 2^37 = 2^30 * 2^7 = 128G
    

Edit: Also useful in reverse

    
    
      ex. 400K: 256K < 400K < 512K <=> 2^18 < 400K < 2^19
    

At least memorize 2^4 = 16 (hex) and 2^8 = 256 (byte), then do doubling or
halving as necessary.

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gruseom
It's trivial but useful that an hourly rate multiplied by 2000 gives a year's
worth (for a standard working year).

~~~
cperciva
Yep, that one's good, subject to the caveat that the 2000 is really 1800 in
Europe (more holidays) and 1500 in France (lots of holidays AND a less hours
per week).

Related and very useful: Consulting rates should start at annual income /
1000.

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mchadwick
Not quite a mental calculation, but still in the spirit: One rough estimation
I often find myself using is that a US dollar bill is six inches long. Using
either folding or flipping, you can approximate most distances in the wave-
your-arms-about scale. Be it thinking about a new physical device or ball-
parking blinds at Home Depot, I use this all the time.

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mixu
I use revenue per employee as a rough guide to the type of company in question
(is it human-based or tech/marketing-based? is it a startup or an established
business?). It's simple to calculate, and revenue is usually less sensitive
information than net income per employee (so easier to get for non-public
companies). My feeling is that for the average (non-public, not particularly
successful but OK, non-automated) company the average salary is about 1/3 of
that (more or less). Actual net income per employee of course depends on the
degree of automation and success.

Example tables:

[http://www.jbryanscott.com/2009/02/07/nasdaq-100-revenue-
per...](http://www.jbryanscott.com/2009/02/07/nasdaq-100-revenue-per-
employee/)

[http://37signals.com/svn/posts/2283-ranking-tech-
companies-b...](http://37signals.com/svn/posts/2283-ranking-tech-companies-by-
revenue-per-employee)

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fauxfauxpas
I've always liked this page - <http://www.vendian.org/envelope/>

and the dots clock is interesting as well

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keyle
The rule of 72 for me is a classic that comes to my mind.

<http://en.wikipedia.org/wiki/Rule_of_72>

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nailer
Two:

* Golden ratio is also miles to ks. Which means you can use Fibonacci to convert miles to ks.

* Divide by square route of two for compound doubling time.

~~~
zalew
kilometer is km not ks. just sayin'

~~~
nailer
One is an abbreviation. The other is a coloquial term, pronounced 'kays' used
in most western speaking metric countries.

