kitchen table math, the sequel: Street-Fighting Mathematics

## Monday, August 9, 2010

### Street-Fighting Mathematics

Freakonomics interview with Sanjay Mahajan:

Q.
I work on the 7th floor. How many additional calories will I expend if, for the next four years, I take the stairs instead of the elevator? – Jordan

A.
Time to estimate! The energy required to raise an object—pretend it is me—to a height is the object’s mass times the earth’s gravitational strength (“g”) times the height.

[snip]

Because the human “engine” is only about 25% efficient (internal-combustion engines are also about 25% efficient), the total energy required is a factor of 4 greater: 48,000 Joules. Each Calorie (with a capital C) is about 4,000 Joules, so the energy required to walk up the stairs is 12 Calories. I could use this value to answer the question, but it would give me just a very large number of Calories, and I would not immediately know whether that number is large or small.

To make this energy more meaningful, I compare it against another relevant energy. A useful estimation fact: a moderate-sized jelly doughnut provides 1 million Joules or about 250 Calories. That would be enough to climb the stairs 20 times. Thus, one jelly doughnut provides enough energy to climb the stairs (every weekday) for a month. Equivalently, climbing the stairs for a month will burn off the Calories from one jelly donut.

Calories with a capital C
The distinction between calories (1 calorie is roughly 4 Joules) and Calories (1 Calorie is roughly 4,000 Joules) is sometimes ignored.