Ask HN: What Back-of-the-Napkin Calculation Should Everyone learn? | Hacker News Reader

Ask HN: What Back-of-the-Napkin Calculation Should Everyone learn?

23 pointsThomPete17 comments

What are some of the most powerful and useful but easy calculations should more people know how to use?

Doubling rate based on percentage. Roughly: 72 / percentage = years to double. An investment returning 1%/year will double after 72, 6% will double after 12. And for debts, illustrates for people who aren't good with money why that 20% (or worse) CC rate is so bad.

I wish I could upvote this more than once.

Doubling your speed quadruples your stopping distance for most cars. This is useful for all drivers to understand from a conceptual level, even if they aren't crunching the numbers.

There is a similar one useful for RF - doubling your distance quadruples the signal loss. Probably only useful for hams or people setting up wireless networks. But I think it can be good to understand this so that you can reduce your RF exposure for health precautions.

I can't explain how incredibly satisfying it was to fully grasp KE=1/2mv2.

Twice as much initial velocity very clearly has 4x the area under the curve on a speed/time graph.

If something has a 1/n chance of happening and I try it n times, there's only a 63% chance of it happening.

(Approaches 63% as n gets larger)

The Pareto Principle, simple but important to know! https://en.wikipedia.org/wiki/Pareto_principle

15% of 33 is the same as 33% of 15. Sometimes you get an easier calculation by switching the numbers this way.

https://www.amazon.com/Back-Napkin-Expanded-Problems-Picture...

Quick way to get the median of some value - take 5 random samples. There will be a 92.5% chance the median is between the largest and the smallest value.

It blew my mind when somebody pointed out to me that pic is close enough to 3 that you can just consider it to be 3. You can figure out the area and circumference of any circle in your head for the most part.

So the Indiana legislator who wanted a simpler value for pi was on to something...

I mean, I'd still want engineers using the real value in important situations, but that margin of error is acceptable for any circle I need to measure.

1 year ~= PI 10^7 seconds

Earth's orbital diameter ~= 1000 light-seconds

The PIs cancel!

So Earth's orbital velocity ~= 0.0001c ~= 30 km/s

The Fibonacci sequence for approximately converting kilometres to miles.

X% of Y is Y% of X

Ex: 7% of 50?

50% of 7 = 3.5

7% of 50 = 3.5

Percentage change:

((New / Old) - 1) * 100

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