Measuring & units

How tall are you? How far is it to school? How warm is it outside? As soon as you answer such questions with numbers, you are doing physics. Physics always starts with measuring, and for that you need units everyone can rely on.

Quantities and their units

A measurement always has two parts: a number and a unit. Just saying 5 is not enough, because 5 metres, 5 kilograms and 5 seconds are completely different things. The most important base units are the metre (m) for lengths, the kilogram (kg) for masses and the second (s) for times. Temperatures are given in degrees Celsius (°C) in everyday life, while physics often works in kelvin (K). To keep numbers handy there are prefixes: 1 km is 1000 m, 1 m is 100 cm, and 1 cm is 10 mm.

Converting without tripping up

When converting, first ask yourself: is my unit getting smaller or bigger? If you go to a smaller unit (from m to cm), the number gets bigger, so you multiply. If you go to a bigger unit (from m to km), the number gets smaller, so you divide. Example: 2.5 m is 2.5 x 100 = 250 cm, and 3500 m is 3500 / 1000 = 3.5 km.

Why everyone needs the same units

Shared units are no small matter. In 1999 the Mars Climate Orbiter probe was lost because one team calculated in newtons while the other used pound-force, an Anglo-American unit of force. As a result the probe came far too close to Mars: it passed at roughly 57 km altitude instead of the planned 226 km and burned up in the atmosphere. One single mix-up of units cost hundreds of millions of dollars. That is why you check in every calculation: do my units fit together?