Useful conversions

These are handy mental conversions that don't take much math. I use them fairly often, for back-of-the-envelope calculations.

• Obvious but useful. An exit is coming up in 1/2 mile on the highway? That's 30 seconds away.
• It took you 30 minutes to go 15 miles? That's an average of 30 mi/hour (30 mph = 2 minutes per mile).

• 60 mph is 88 ft/sec. This converstion is linear, so roughly, FPS = MPH * 1.5
• A trick: just add 1/2 your speed to your current speed (easy way to do 1.5x)
• 100 mph? You're going 150 feet per second.
• 30 feet per second? You're going 20 mph. (Multiply by 2/3 to go the other way)

• This assumes you are working 40 hours/week for 50 weeks (or 2000 hours/year)
• Earn 20 bucks an hour? That's $40,000 a year.
• For part-time, use $1000/year for each dollar hour (20 hours/week).

• This follows from $20/week * 50 weeks/year = $1000/year
• Spend $10 a week on gas? That's $500 a year.
• Save $40 a week by bagging your lunch? That's 2000 clams.

• Actually, 2^10 = 1024. But 1000 is close enough.
• Thus, 2^20 is 1000 squared or 1 million.
• 2^30 is 1 billion.
• If you have 20 bits of address space, that is roughly one million possible locations (or exactly 1MB). Conversely, if you have 1 million possible addresses, you know you need roughly 20 bits to encode it.

• Given an annual interest rate of x%, your money will double in 72/x years
• With a 10% rate, doubles in 7.2 years
• With a 2% rate, doubles in 36 years
• The derivation indicates the rule of 69.3 would be better =). Reason for 72? It is divisible by many numbers, so it is good for rough estimates.
• Derivation: (1+x)^n = 2 (x is interest rate, n is years)
  • ln(1+x)^n = ln2
  • n*ln(1+x) = ln2
  • n = ln2/ln(1+x)
  • ln(1+x) ~ x so: n = ln2/x    [x is in terms of a percentage, mulitply by 100]
  • n = 69.3/x

• c ~ 300,000 km/s, or roughly 1 foot per nanosecond
• Useful when calculating speed of light delays
  • America is about 3000 miles across, roughly 5000 feet/mile
  • 3000 * 5000 = 15 * 10^6 or 15 million feet
  • About 15 million nanoseconds, or 15 milliseconds.
  • This is the minimum delay for any communications across the country (radio, satellite phone, tv broadcast)
  • The speed of electricity is even slower, so roughly 100 ms delay for network transmission