Units & dimensions

Every measurement in physics needs a unit and a dimension. This track builds from why we standardise units all the way to using dimensional analysis to check equations and even find a formula.

Physics turns the world into numbers, and a number means nothing without a unit. This track starts with why standard units exist, works through the SI system of base and derived quantities, then separates a quantity's dimension (the kind of thing it is, like length or time) from its unit (the amount, like metres or seconds).

From there you use the homogeneity principle and dimensional analysis to check whether an equation is even possible, and to reconstruct the shape of a formula from the dimensions alone.

What you will learn:

  • Why we need standard units, and measuring length, area and derived quantities
  • Base quantities and the seven SI units
  • Dimension versus unit, and the dimensional fingerprint of a quantity
  • The homogeneity principle and dimensional analysis
  • Finding a formula from its dimensions

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Frequently asked questions

What is the difference between a unit and a dimension?
A dimension is the kind of quantity, such as length, mass or time. A unit is the specific amount used to measure it, such as the metre, kilogram or second. Speed has the dimension length over time and can be measured in metres per second or kilometres per hour.
What is dimensional analysis used for?
It checks whether an equation is consistent, since both sides must share the same dimensions, and it can help reconstruct the form of a formula from the dimensions of the quantities involved.