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

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).

Thanks

cperciva 15y

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 15y

Using 70/X will also work just fine.

cperciva 15y

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).

jonsen 15y

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.

gruseom 15y

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

cperciva 15y

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.

mchadwick 15y

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.

mixu 15y

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://37signals.com/svn/posts/2283-ranking-tech-companies-b...

fauxfauxpas 15y

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

and the dots clock is interesting as well

keyle 15y

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

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

nailer 15y

Two:

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