Every physical equation must balance dimensionally. SI base units: m, kg, s, A, K, mol, cd.
Try this
10
kinetic energy KE = ½ · m · v² — units: kg · (m/s)² = kg·m²/s² = joules = 50.0 J
Every equation must balance its units
Both sides of a physical equation must carry the same dimensions. ½mv² works because kg × (m/s)² = kg·m²/s², which is exactly the joule. If a rearranged formula leaves you with 'metres = kg/s', you've slipped somewhere.
The seven SI base units
- metre (m) — length
- kilogram (kg) — mass
- second (s) — time
- ampere (A) — electric current
- kelvin (K) — temperature
- mole (mol) — amount of substance
- candela (cd) — luminous intensity
Your turn
Force is mass × acceleration. What combination of base units is one newton?
Dimensional analysis is a great error-checker. If your derivation gives metres = kg/s, something's wrong.