List of facts useful for Fermi problems
A Fermi problem is the task of making a simple estimate of a real-world quantity based on little information. Usually, one is not supposed to look up any facts or perform any computations more difficult than basic arithmetic. Often, it's useful to have several facts memorized in order to answer these problems more easily. This article presents a list of numbers which will be useful for the most common types of Fermi problem, grouped by rough classification.
The goal of this article is to give round numbers which are easy to memorize, and not to serve as a reference for more accurate calculations.
Earth systems
- The average ocean depth is 4 km.
- The Earth's surface is about 70% water and 30% land.
- When the sun is directly overhead, the Earth receives about 1 kilowatt of light per square meter.
Population sizes
- There are 8 billion people alive today.
- About 100 billion humans have ever lived.
- A large city has about 10 million people.
| Location | Population |
|---|---|
| United States | 300 million |
| United Kingdom | 70 million |
| China | 1.4 billion |
| City | Population |
|---|---|
| Chicago | 3 million |
| New York City | 8 million |
| London | 9 million |
| Beijing | 22 million |
Sizes of vehicles
- A Boeing 747 seats about 500 people.
Unit conversion
- 1 mile equals 1.6 km, so there are about 3 km in 2 miles.
- A meter is about 3 feet.
- There are 2.54 cm in an inch, or about 5 cm in 2 inches.
- Light travels about one foot per nanosecond.
Fractional powers of 10
- 100.3 ≈ 2
- 100.5 ≈ 3
- 100.6 ≈ 4
Geometry
- Spheres of uniform size have a packing density of about 3/4.
- Spheres have the worst packing density of all shapes.
Astronomical
| Body | Radius | Mass |
|---|---|---|
| Earth[1] | 6×106 m | 6×1024 kg |
| The moon | 2×106 m | 7×1022 kg |
| The sun[1] | 7×108 m | 2×1030 kg |
- Surface temperature of the sun: 6000 K.
Energy
- Electricity in the US costs about 10 cents per kilowatt-hour.
- A household incandescent bulb uses about 100 watts, and an LED bulb of the same brightness uses about 20 watts.
- The human body emits about 100 watts of heat.
| Energy source | Efficiency |
|---|---|
| Solar | 0.2 |
| Wind | 0.5 |
| Nuclear | 0.9 |
| Fossil fuels | 0.4 |
References
- ↑ 1.0 1.1 Mamajek, E. E; Prsa, A; Torres, G; et al. (2015). "IAU 2015 Resolution B3 on Recommended Nominal Conversion Constants for Selected Solar and Planetary Properties". arXiv:1510.07674 [astro-ph.SR].
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