Human Energy Units

We eat food to get energy, which we measure in terms of dietary Calories.

We use electricity to provide energy to our homes, which we measure in kilowatt-hours.

Physicists often measure energy in joules, which is the amount of energy needed to apply a newton of force across one meter of distance.

These different units of “energy” aren’t merely analogous; they’re all measuring the same thing. It’s totally sensible to talk about the Calories burned by your toaster, or to say that your bowl of pasta contains a kilowatt-hour of energy.

¶ Energy Conversion

¶ Ratios

We can use the following ratios to convert between various measures of energy:

• 1 dietary Calorie (Cal) = 4184 J ≈ 0.001162 kWh
• 1 kilowatt-hour (kWh) = 3,600,000 J ≈ 860.4 Cal
• 1 BTU ≈ 1055 J ≈ 0.252 Cal
• 1 metric ton of TNT = 4,184,000,000 J = 1,000,000 Cal¹

¶ Energy Comparisons

First of all, how expensive would your food bill be if you could eat electricity?

The “standard” adult needs 2000 dietary Calories per day,² which converts to about 2.3 kWh (or 8.4 megajoules or 7900 BTU). Let’s call this amount a “Day of Food Energy” or DoFE for short.

At 16 cents per kWh³, electricity costs only 37 cents per DoFE. Pretty cheap! Michael Phelps, in 2008, claimed to eat a whopping 10,000 dietary Calories per day, which would still be less than two dollars worth of electricity. Alas, man cannot live on voltage alone.

Gasoline would be an even cheaper source of food if you could eat it. (You cannot. Do not try. You will die.) A gallon of gas contains a bit over 15 DoFE.⁵ At /$3.62 per gallon,⁶ that works out to less than 25 cents per DoFE.

A single gram of uranium fuel produces over 172 DoFE of electricity in a typical reactor,⁷ and up to 9500 DoFE (26 years of food energy) could be theoretically produced. A single DoFE could be provided by a speck of Uranium the size of a grain of sand (in a reactor; do not eat uranium).

One gram of antimatter, reacting with one gram of matter, would release over 20 million DoFE.⁸ (Honestly, that’s less than I expected. Sci-fi has made me overestimate the power of antimatter.) If only people could eat neutrinos and gamma rays, then a mere pound of antimatter could feed the whole world.

Comparisons to explosions are the easiest to make, since a “ton of TNT”, as a unit of energy, is exactly equal to 500 DoFE (one million Cal). A megaton blast is equal to 500 million DoFE, which is roughly the amount of food energy consumed by Americans each day.⁹

Lazily pulling some examples from the wikipedia page on TNT equivalent:

• Mount Saint Helens: 24 Megatons days of American food consumption
• Tsar Bomba: 55 Megatons days of American food consumption
• Krakatoa: 200 Megatons days of American food consumption
• All nukes ever detonated, combined: 540 Megatons days of American food consumption

(I know I sound like a broken record here, but please don’t try to eat antimatter or atomic bombs,… or uh, volcanic eruptions.)

¶ Power usage

• A watt (W) is 1 joule per second.
• The “standard” adult needs 2000 dietary Calories per day.
• There are 86400 seconds in a day.

Combine these conversions to find that 2000 Cal per day is about the same as 97 watts. I’ll round that up to 100 watts, and call it 1 “Manpower”.¹⁰

We can then conceptualize the power use of appliances in terms of person-equivalents.

Note that these are comparisons of the rate of power usage. Not comparisons of the daily energy usage. Most people don’t leave their tea kettles running 24 hours a day.