MKS System: Meter-Kilogram-Second Explained

The MKS system uses the metre for length, kilogram for mass, and second for time. These three units provide a coherent foundation for mechanical quantities and form part of the modern International System of Units (SI).

The three base units

• Metre (m): the SI base unit of length.
• Kilogram (kg): the SI base unit of mass.
• Second (s): the SI base unit of time.

“Coherent” means that derived-unit equations need no extra numerical conversion factor when coherent units are used. For example, one newton is exactly one kilogram metre per second squared.

Common derived quantities

Worked force example

A 4 kg object accelerating at 3 m/s² has a net force of:

F = ma = 4 kg × 3 m/s² = 12 kg·m/s² = 12 N.

No extra conversion factor is needed because kilograms, metres, and seconds are coherent in this expression.

MKS, CGS, and SI

The centimetre-gram-second (CGS) system uses centimetres, grams, and seconds. Its force unit is the dyne rather than the newton. Converting between CGS and MKS therefore requires powers-of-ten factors: 1 N = 100,000 dyn.

SI is broader than MKS. In addition to metre, kilogram, and second, SI includes the ampere, kelvin, mole, and candela as base units. The 11th General Conference on Weights and Measures adopted the name International System of Units and abbreviation SI in 1960. Today all SI units are defined through fixed values of defining constants.

Practical rules

• Write a space between a number and unit symbol: 12 m, not 12m.
• Unit symbols are case-sensitive: m is metre, while M is the prefix mega.
• Use kg as the coherent mass unit; prefixes for mass attach to gram, as in mg.
• State units at every step when converting from CGS, U.S. customary, or natural units.

For the full set of base units and decimal prefixes, continue with Metric System Basics.

Primary Sources

• BIPM: The International System of Units (SI Brochure)
• BIPM: The International System of Units
• NIST Special Publication 811: Guide for the Use of SI