Password strength

52385 words in our dictionary
  Of average length 7.96
  With entropy content of 1.97 bits per character

We're using 63 characters
  With entropy content of 5.98 bits each
  Containing 303.44% the entropy content of single character in a random word

With 9,001,000,000 hashes per second:

Example passwords:
  12 random characters:
    9I6q3vWPnRTM  31dhplwF_Rtp
    NcjSg8tmX974  1Pv9VSC8I6xW
    yRVqiH0akVOE  JWZKFEX157VJ
    epNJ7XxmGVMd  x_gC3r1deEkV
    Rv_cP3LDr1ug  HLm85XFvZwAz
  4 random words:
    BDSO: BorderingDisbarredSluggingOverdid (33ch)
    CSCB: ColStenchCherryBamboozling (26ch)
    HAMC: HairstylistAngioplastyMammographyCommodore (42ch)
    BPTS: BilingualPoutedTampedSlacken (28ch)
    RTSE: RubyingTrobriandSoreheadExcitable (33ch)
  5 random words:
    IFTER: ImperiallyFretTrilledEagerRivaled (33ch)
    RAHBR: RestatementAmoralHalcyonBeheadedRetooling (41ch)
    ISHAS: IngratiatingSubsistenceHarpooningAdmissibleSharper (50ch)
    SOCUC: SupervisedObscuredChickadeeUnscrambledCataract (46ch)
    WREWH: WorriedReappraisingElbowingWarehousingHelena (44ch)
  15 random characters:
    dU6i9e06jxKbfkn  PJz67vXqfqrWeUf
    zVlc0AHlNSwaXUs  YhktUXWSniLqEDr
    BkO7rsKVmswMbqY  TqAdi1fmzY4CRbi
    AM9W2NTPkcE_sGY  uIDHJVUUyLIXeuW
    RP5OKjPlc6TV3QW  twb7qjpXmqvQCuq
==Starting from seconds==
1 words( 8ch): 5.24e+04 permutations, 3.64MiB disk space (0.00 seconds to brute force)
 4 chars:      1.58e+07 permutations, 1.01GiB disk space (0.00 seconds to brute force)
 5 chars:      9.92e+08 permutations, 64.70GiB disk space (0.11 seconds to brute force)
2 words(16ch): 2.74e+09 permutations, 206.80GiB disk space (0.30 seconds to brute force)
 6 chars:      6.25e+10 permutations, 4.04TiB disk space (6.95 seconds to brute force)
==Going into minutes==
 7 chars:      3.94e+12 permutations, 257.94TiB disk space (7.29 minutes to brute force)
==Going into hours==
3 words(24ch): 1.44e+14 permutations, 11.35PiB disk space (4.44 hours to brute force)
 8 chars:      2.48e+14 permutations, 16.09PiB disk space (7.66 hours to brute force)
==Going into days==
 9 chars:      1.56e+16 permutations, 1.00EiB disk space (20.10 days to brute force)
==Going into months==
==Going into years==
10 chars:      9.85e+17 permutations, 64.07EiB disk space (3.52 years to brute force)
4 words(32ch): 7.53e+18 permutations, 632.49EiB disk space (26.90 years to brute force)
==Going into centuries==
11 chars:      6.21e+19 permutations, 3.99ZiB disk space (2.22 centuries to brute force)
12 chars:      3.91e+21 permutations, 254.96ZiB disk space (139.63 centuries to brute force)
13 chars:      2.46e+23 permutations, 15.89YiB disk space (8796.71 centuries to brute force)
5 words(40ch): 3.94e+23 permutations, 34.20YiB disk space (14090.54 centuries to brute force)
14 chars:      1.55e+25 permutations, 1013.90YiB disk space (554192.56 centuries to brute force)
15 chars:      9.77e+26 permutations, much disk space (34914130.98 centuries to brute force)
==Going into ages of universe==
6 words(48ch): 2.07e+28 permutations, much disk space (5.39 ages of universe to brute force)
16 chars:      6.16e+28 permutations, much disk space (16.06 ages of universe to brute force)
17 chars:      3.88e+30 permutations, much disk space (1011.49 ages of universe to brute force)
18 chars:      2.44e+32 permutations, much disk space (63723.90 ages of universe to brute force)
7 words(56ch): 1.08e+33 permutations, much disk space (282241.63 ages of universe to brute force)
19 chars:      1.54e+34 permutations, much disk space (4014605.43 ages of universe to brute force)
20 chars:      9.70e+35 permutations, much disk space (252920142.00 ages of universe to brute force)
21 chars:      6.11e+37 permutations, much disk space (15933968945.83 ages of universe to brute force)
Disk usage is amount of space to store all hashes
Brute force assumes worst case, averages to half of the value

Notes:
  With disk usage, I am assuming no compression is used on words.
   Zipping my words file yielded decrease from 931 to 252 kilobytes
   Compressing would probably decrease size by ~2/3 of that,
   since hashes are pretty much incompressible
  Compressing random characters makes no significant difference
  I am not accounting for technological progress, but I assume
   that by time it becomes easy enough to crack these,
   most currently used algorithms will be irrelevant anyway

Verdict:
  While random characters contain way more entropy per character,
   a set of words is much easier to remember
  Inserting randomly a single number into 4 words increases
   amount of permutations 318 times (2 orders of magnitude)
   505.30% of how much adding a single char to a random sequence does
As such, I declare that using a sequence of 5 or even 4 random words
 is a superior alternative to random characters,
 since it is much easier for human brain to remember sequences
 that have a meaning, and acronyms help further