Equation field guide
Units and dimensions: a formula’s consistency check
Units describe how a quantity is measured. A valid physical equation must combine compatible dimensions.
Multiply and divide units
Speed has units of distance divided by time. Multiplying speed by time gives distance. Dividing distance by time gives speed.
Power is energy per unit time, so power × time gives energy. The units of factors tell you the units of a product even when the article gives no numerical example.
Addition requires matching kinds
Two distances can be added after conversion to the same unit. Adding a distance directly to a duration has no physical meaning.
All terms in a sum and both sides of an equality must share compatible dimensions. This is a necessary check, but it is not sufficient to prove an equation is scientifically correct.
Dimensionless quantities
A ratio of two quantities with the same units can be dimensionless. Probabilities, proportions, and normalized scores are examples, though their numerical domains can still differ.
The symbol itself never establishes a unit: E can mean energy, expectation, or an event. The article and its sources determine which.