Mental Math Shortcuts

Time and Distance

• Going 60 mph and the exit is in 10 miles? That?s 10 minutes.
• Been driving a half hour? That?s about 30 miles at highway speeds.

• 60 mph is about 90 feet per second (88 exactly), so just multiply by 1.5. Or, just add half to itself (60 + 30 = 90).
• Going 100 mph? That?s 150 fps.
• Going 10 fps? That?s about 7 mph (10 * 2/3 is 6.666). Or, just take away 1/3 (10 - 3 = 7).

• The US is about 3000 miles long. There?s about 5000 feet/mile, so that?s about 3000 × 5000 or 15 million feet. 15 million feet takes 15 million nanoseconds, or 15/1000, or 15 milliseconds. That?s the minimum time for a signal to go across the country.
• Inside a microchip, if you have a clock cycle every nanosecond (1 GHz), your signal can only travel 1 foot at most (or less, depending on the material). Even light takes 30ns to cross a 30 foot room.

• Project takes 1000 man hours? That?s 6 months for 1 person.
• Daily commute of 1/2 hour? That?s .5 * 250 = 125 hours in the car each year.

Money and Finance

• Earn $25/hour? That?s about 50k/year.
• Make 200k/year? That?s about $100/hour. This assumes a 40-hour work week.

• Spend $20/week at Starbucks? That?s a cool grand a year.

• Have an investment growing at 10% interest? It will double in 7.2 years.
• Want your investment to double in 5 years? You need 72/5 or about 15% interest.
• Growing at 2% a week? You?ll double in 72/2 or 36 weeks. You can use this rule for any duration of time, not just years.
• Inflation at 4%? It will halve your money in 72/4 or 18 years.

Mental Arithmetic

• 1% of 10k is 100. The Dow is roughly 10k (it?s about 12k now). So if the dow drops 100, it?s about a 1% loss.
• What?s 5k x 50k? That?s 250 * thousand * thousand or 250 million.

• 12 days = 1 million seconds
• 1 year = 31 million seconds (about pi * 10 million)
• 30 years = 1 billion seconds
• 30,000 years = 1 trillion seconds

• One ?part per million? means an accuracy of 1 second every 12 days. One ?part per trillion? means an accuracy of 1 second every 30,000 years.

• Sure, 2 to the tenth = 1024, but 1000 is good enough for government work. (Read on about KB vs KiB).
• Have 32-bit color? That?s 2 + 30 bits, aka 2^2 billion, or 4 billion (4gb exactly).
• Have a 16-bit number? That?s 6 + 10 bits, or 2^6 thousand, or 64 thousand (64 kb).

• It?s not immediately clear, but it?s true: a% of b = .01 * a * b, which is the same as b% of a (.01 * b * a).
• What?s 16% of 25? The same as 25% of 16: 4
• What?s 43% of 200? Same as 200% of 43: 86.