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SI units

A physical quantity is always a number times a unit. The SI system has seven base units (meter, kilogram, second, ampere, kelvin, mole and candela), and most other units are built from these. A unit error makes an otherwise correct calculation useless, so always check that the unit of your answer makes sense.

1 N=1 kg⋅m/s21\ \mathrm{N} = 1\ \mathrm{kg\cdot m/s^2}force, from Newton's second law
1 J=1 N⋅m1\ \mathrm{J} = 1\ \mathrm{N\cdot m}energy and work
1 W=1 J/s1\ \mathrm{W} = 1\ \mathrm{J/s}power

Symbols

mmmeter, base unit of length
kgkgkilogram, base unit of mass
sssecond, base unit of time

Example

A load has mass m=250m = 250 kg. Its weight is G=mg=250⋅9.81≈2453G = mg = 250\cdot 9.81 \approx 2453 N, about 2.452.45 kN – a force, not a mass.

Always write the unit together with the number at every step – without a unit, a number is meaningless in physics.
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Part of Foundations of Physics: Quantities, units and measurement.