Order of magnitude

An order of magnitude is a factor of ten in scale, commonly used to describe a quantity approximately by its nearest power of ten. The difference between two orders of magnitude corresponds to a factor of one hundred.

Power of ten: An integer power of ten, such as 10³ or 10⁻², used to express scale compactly. Each step between adjacent powers of ten marks one order of magnitude.
Fermi problem: An estimation problem solved by breaking an unknown quantity into manageable factors. Fermi estimates use powers of ten to keep uncertain calculations tractable.
Factor of ten: A multiplicative ratio of ten between two quantities. It is the numerical change represented by one order of magnitude.
Avogadro constant: The number of specified elementary entities in one mole, exactly 6.02214076 × 10²³ mol⁻¹. Its exponent gives the scale of the number of particles in a mole.
Scientific notation: A way to write numbers as a coefficient multiplied by a power of ten. Its exponent makes a number’s approximate order of magnitude visible.
Dimensional analysis: A method for checking physical equations by comparing the dimensions of their quantities. Magnitude estimates can expose equations that produce implausibly large or small results.
Order of magnitude estimate: An approximate numerical value expressed at the scale of a nearby power of ten. This estimate is a common use of the broader idea of an order of magnitude.
Speed of light: The speed of light in vacuum, exactly 299,792,458 metres per second. Its value is about 3 × 10⁸ metres per second, illustrating power-of-ten notation.
Base-10 logarithm: The logarithm that gives the exponent to which ten must be raised to produce a number. Taking this logarithm turns multiplicative scale changes into additive magnitude steps.
Back-of-the-envelope calculation: A rough calculation using simplified assumptions to estimate a quantity quickly. Rounding values to powers of ten makes such estimates easier to perform mentally.

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