Order of magnitude

An order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value, usually ten, interpreted as the base of the logarithm and the representative of values of magnitude one. Logarithmic distributions are common in nature and considering the order of magnitude of values sampled from such a distribution can be more intuitive. When the reference value is ten, the order of magnitude can be understood as the number of digits in the base-10 representation of the value. Similarly, if the reference value is one of certain powers of two, the magnitude can be understood as the amount of computer memory needed to store the exact integer value.

If two numbers have the same order of magnitude, they are about the same size.

But if one would compare the surface of an orange with that of the earth, one would say the surface of the earth is many orders of magnitude larger than that of the orange.

Orders of magnitude are used to make approximate comparisons. If numbers differ by one order of magnitude, x is about ten times different in quantity than y. If values differ by two orders of magnitude, they differ by a factor of about 100. Two numbers of the same order of magnitude have roughly the same scale: the larger value is less than ten times the smaller value.

List

In words (long scale)	In words (short scale)	Prefix (Symbol)	Decimal	Power of ten	Order of magnitude
quintillionth	nonillionth	quecto- (q)	0.000000000000000000000000000001	10−30	−30
quadrilliardth	octillionth	ronto- (r)	0.000000000000000000000000001	10−27	−27
quadrillionth	septillionth	yocto- (y)	0.000000000000000000000001	10−24	−24
trilliardth	sextillionth	zepto- (z)	0.000000000000000000001	10−21	−21
trillionth	quintillionth	atto- (a)	0.000000000000000001	10−18	−18
billiardth	quadrillionth	femto- (f)	0.000000000000001	10−15	−15
billionth	trillionth	pico- (p)	0.000000000001	10−12	−12
milliardth	billionth	nano- (n)	0.000000001	10−9	−9
millionth	millionth	micro- (µ)	0.000001	10−6	−6
thousandth	thousandth	milli- (m)	0.001	10−3	−3
hundredth	hundredth	centi- (c)	0.01	10−2	−2
tenth	tenth	deci- (d)	0.1	10−1	−1
one	one	uni- (no symbol)	1	100	0
ten	ten	deca- (da)	10	101	1
hundred	hundred	hecto- (h)	100	102	2
thousand	thousand	kilo- (k)	1000	103	3
million	million	mega- (M)	1000000	106	6
milliard	billion	giga- (G)	1000000000	109	9
billion	trillion	tera- (T)	1000000000000	1012	12
billiard	quadrillion	peta- (P)	1000000000000000	1015	15
trillion	quintillion	exa- (E)	1000000000000000000	1018	18
trilliard	sextillion	zetta- (Z)	1000000000000000000000	1021	21
quadrillion	septillion	yotta- (Y)	1000000000000000000000000	1024	24
quadrilliard	octillion	ronna- (R)	1000000000000000000000000000	1027	27
quintillion	nonillion	quetta- (Q)	1000000000000000000000000000000	1030	30
In words (long scale)	In words (short scale)	Prefix (Symbol)	Decimal	Power of ten	Order of magnitude

Related pages

• Magnitude (mathematics)

Other websites

• Powers of 10, a graphic animated illustration that starts with a view of the Milky Way at 10²³ meters and ends with subatomic particles at 10^-16 meters.
• Orders of Magnitude - Distance
• What is Order of Magnitude?