Order of Magnitude


Order of Magnitude

In performing rough calculations, estimates, or comparisons, we occasionally round off a number to zero significant figures - which is the nearest power of 10. A number rounded to the nearest power of 10 is called an order of magnitude. For example, let's say the average height of a human being is about 1.7 meters (about 5'7"). For the sake of simplicity, let's round off 1.7 meters to the nearest power of 10, which is 100 m (or 1 m). We are not saying that the average height of a person is a mere 1 meter, but rather the average height is closer to 1 meter (or 100 meters) than it is to 10 meters (or 101 meters). Similarly, rounding the height of an ant, which is about 8 x 10-4 meters, to the nearest power of ten results in 10-3 meters. Another way of saying this is that the order of magnitude of the height of an ant is 10-3 meters. Now, if we compare the height of a human being (100 meters) with the height of an ant (10-3 meters), we come up with the ratio human height/ant height = 100/10-3 = 100 - (-3) = 103 = 1000. A human being is roughly 1000 times (or 103 times) taller than an ant. In other words, a human being is 3 orders of magnitude (3 powers of 10) taller than an ant. The table below shows some interesting comparisons.

 Order of Magnitude of some Masses

 Order of Magnitude of some Lengths







 radius of proton




 radius of atom




 radius of virus




 radius of amoeba




 height of human being




 radius of earth


 human being


 radius of sun




 earth-sun distance




 radius of solar system




 distance of sun to nearest star


 milky way galaxy


 radius of milky way galaxy


 the Universe


 radius of visible Universe