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 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%.) Using 70/X will also work just fine. 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). Memorize powers of 2 up to 9 It's trivial but useful that an hourly rate multiplied by 2000 gives a year's worth (for a standard working year). 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. 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. 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... I've always liked this page - http://www.vendian.org/envelope/ and the dots clock is interesting as well The rule of 72 for me is a classic that comes to my mind. 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. kilometer is km not ks. just sayin' One is an abbreviation. The other is a coloquial term, pronounced 'kays' used in most western speaking metric countries.
and 0 1 2 3 4 5 6 7 8 9
1 2 4 8 16 32 64 128 256 512
then split anything else 2^10 = 1K, 2^20 = 1M, 2^30 = 1G etc.
Edit: Also useful in reverse ex. 2^23 = 2^20 * 2^3 = 8M
ex. 2^37 = 2^30 * 2^7 = 128G
At least memorize 2^4 = 16 (hex) and 2^8 = 256 (byte), then do doubling or halving as necessary. ex. 400K: 256K < 400K < 512K <=> 2^18 < 400K < 2^19