Orders of magnitude around us

A tool for comparing sizes

Orders of magnitude make it easy to compare very different objects, from the infinitely small to the infinitely large, without getting lost in the zeros.

Reference table

Object	Approximate size	Order of magnitude (m)
Atom	0.0000000001 m	10^-10
Virus	0.0000001 m	10^-7
Diameter of a hair	0.00005 m	10^-4
Ant	0.005 m	10^-3
Human being	1.7 m	10^0
Football field	100 m	10^2
Radius of the Earth	6400000 m	10^6
Earth-Sun distance	150000000000 m	10^11

Estimating without measuring

To estimate an order of magnitude, you can break a complex problem down into simple quantities. Example: how many grains of rice in a bowl? We estimate the volume of the bowl (about 10^-4 m^3) and the volume of a grain (about 10^-8 m^3), then divide: about 10^4 grains.

Classic pitfall

Don't confuse the order of magnitude of a length with that of a volume: the units change everything. A cube with side 10^2 m has a volume of the order of 10^6 m^3, because (10^2)^3 = 10^6, and not 10^2. Always check which quantity (length, area, volume, mass) is involved.