Order of magnitude

Physical Quantities & Units - OCR A-Level Physics

Key Definition

Order of magnitude
The power of ten closest to the value of a quantity. Used for rough comparisons and estimation.

An order of magnitude estimateA rough calculation to the nearest power of 10, used to check whether a value is reasonable. gives a value to the nearest powerThe rate of energy transfer. Measured in watts (W). of 10.
Useful for checking whether a calculated answer is reasonable.
Mass of a human: $\sim 10^{2}$ kg (order of magnitudeThe powerThe rate of energy transfer. Measured in watts (W). of ten closest to the value of a quantity. Used for rough comparisons and estimation. 2).
Diameter of an atom: $\sim 10^{-10}$ m.
Diameter of a nucleus: $\sim 10^{-15}$ m.
Speed of light: $\sim 10^{8}$ $m s^{-1}$.
Speed of sound in air: $\sim 10^{2}$ $m s^{-1}$.
Height of a person: $\sim 10^{0}$ m (i.e. ~1-2 m).
Mass of a proton: $\sim 10^{-27}$ kg.

Examiner Tips and Tricks

OCR loves estimation questions.
You must know key orders of magnitude: atom diameter ($\sim 10^{-10}$ m), nucleus diameter ($\sim 10^{-15}$ m), human mass (~70 kg), walking speed (~1.5 $m s^{-1}$).
You are expected to justify your estimate with a brief calculation.