Orders of magnitude

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Orders of magnitude
Length – Mass – Time – Area – Volume – Power – Temperature – Density – Numbers – Data – U.S. money
Related articles
SI – SI base units – SI derived units – SI prefixes – conversion of units

An order of magnitude is a factor of ten. For example, two numbers are said to differ by "three orders of magnitude" if they differ by three factors of ten, that is one is approximately 1000 times larger than other.

The order of magnitude of a number is, intuitively speaking, the number of powers of 10 contained in the number or a close approximation to it. More precisely, the order of magnitude of a number can be defined in terms of the logarithm of the number to the base of 10, usually as the integer part of the logarithm. Thus the order of magnitude of 400 is 2. The order of magnitude of a number may also be defined as the exponent of the power of 10 when the number is represented using scientific notation.

An order of magnitude estimate of a variable whose precise value is unknown is an estimate rounded in some way to the nearest power of 10. For example, an accurate order of magnitude estimate for the human population of the Earth in the year 2000 is 10 billion. An order of magnitude estimate is sometimes also called a zeroth order approximation.

One way of categorising things in the physical world is by their size. The pages below contain lists of items that are of the same order of magnitude in time, length, area, volume, mass, energy or temperature. This is useful for getting an intuitive sense of the comparative size of things and the overall scale of the universe. SI units are used together with SI prefixes: these were devised with orders of magnitude in mind. Each individual page also gives other units; see also conversion of units.

Table of contents

1 Orders of magnitude of various quantities 2 Units used in the table 3 See also 4 External links

Orders of magnitude of various quantities

In the following table the different quantities are lined up so that the following are in the same row:

• length and the approximate time taken by light to cross that length
• area of a square and the length of one side
• volume of a cube and the area of one face
• mass of some water and its volume at 4 degrees Celsius or 277.16 K

See also the separate tables for time, length, area, volume, mass, energy, power, temperature and dimensionless numbers.

Time	Length	Area	Volume	Mass	Energy	Temperature
(x 3)*	(m)	(m2)	(m3)	(kg)	(J)	(K)
(second)	(metre)	(square metre)	(cubic metre)	(kilogram)	(joule)	(kelvin)**
10-44 s	10-35 m
...
10-28 s	100 zm
10-27 s	1 am					1 nK
10-26 s	10 am				1 peV	1 �K
10-25 s	100 am					1 mK
10-24 s	1 fm				0.001 meV 0.01 meV 0.1 meV	1 K
10-23 s	10 fm				1 meV 10 meV 100 meV	10 K 100 K 1000 K
10-22 s	100 fm	10-28 m2			1 eV 10 eV 100 eV	10,000 K 100,000 K 106 K
10-21 s	1 pm			10-33 kg 10-32 kg 10-31 kg	1000 eV 104 eV 105 eV	109 K
10-20 s	10pm			10-30 kg 10-29 kg 10-28 kg	1 MeV 10 MeV 100 MeV	109 K
10-20 s	10pm			10-30 kg 10-29 kg 10-28 kg	1 MeV 10 MeV 100 MeV	1012 K
10-19 s	100 pm	10-20 m2 10-19 m2		10-27 kg 10-26 kg 10-25 kg	1 GeV 10 GeV 100 GeV	1015 K
10-18 s	1 nm	10-18 m2 10-17 m2		10-24 kg 10-23 kg 10-22 kg	1 TeV 10 TeV 100 TeV	1018 K
10-17 s	10 nm	10-16 m2 10-15 m2		10-21 kg 10-20 kg 10-19 kg	0.0001 J 0.001 J 0.01 J	1021 K
10-16 s	100 nm	10-14 m2 10-13 m2	10-21 m3 10-20 m3 10-19 m3	10-18 kg 10-17 kg 10-16 kg	0.1 J 1 J 10 J	1024 K
1 fs	1 μm	10-12 m2 10-11 m2	10-18 m3 10-17 m3 10-16 m3	10-15 kg 10-14 kg 10-13 kg	100 J 1000 J 10000 J	1027 K
10 fs	10 μm	10-10 m2 10-9 m2	10-15 m3 10-14 m3 10-13 m3	10-12 kg 10-11 kg 10-10 kg	100000 J 0.001 kWh 0.01 kWh	1030 K
100 fs	100 μm	10-8 m2 10-7 m2	10-12 m3 10-11 m3 10-10 m3	10-9 kg 10-8 kg 10-7 kg	0.1 kWh 1 kWh 10 kWh
1 ps	1 mm	10-6 m2 10-5 m2	10-9 m3 10-8 m3 10-7 m3	10-6 kg 10-5 kg 10-4 kg	100 kWh 1000 kWh 10000 kWh
10 ps	1 cm	1 cm2 10 cm2	1 ml 10 ml 100 ml	1 g 10 g 100 g	100000 kWh 1 GWh 10 GWh
100 ps	10 cm	0.01 m2 0.1 m2	1 l 10 l 100 l	1 kg 10 kg 100 kg	100 GWh 1000 GWh 10000 GWh
1 ns	1 m	1 m2 10 m2	1 m3 10 m3 100 m3	1 t 10 t 100 t	100000 GWh 106 GWh 107 GWh
10 ns	10 m	100 m2 1,000 m2	1,000 m3 10,000 m3 105 m3	106 kg 107 kg 108 kg	108 GWh 109 GWh
100 ns	100 m	1 ha 10 ha	106 m3 107 m3 108 m3	109 kg 1010 kg 1011 kg	1012 GWh
1 μs	1 km	1 km2 10 km2	1 km3 10 km3 100 km3	1012 kg 1013 kg 1014 kg	1015 GWh
10 μs	10 km	108 m2 109 m2	1012 m3	1015 kg 1016 kg 1017 kg	1018 GWh
100 μs	100 km	1010 m2 1011 m2	1015 m3	1018 kg 1019 kg 1020 kg	1021 GWh
1 ms	1000 km	1012 m2 1013 m2	1018 m3	1021 kg 1022 kg 1023 kg	1024 GWh
10 ms	104 km	1014 m2 1015 m2	1021 m3	1024 kg	1027 GWh
100 ms	105 km	1016 m2 1017 m2	1024 m3	1027 kg	1030 GWh
1 s	106 km	1018 m2 1019 m2	1027 m3	1030 kg	1033 GWh
10 s	107 km	1020 m2 1021 m2		1033 kg	1036 GWh
100 s	1 AU			1036 kg	1039 GWh
1 h	10 AU			1039 kg	1042 GWh
10 h	100 AU			1042 kg	1045 GWh
1 day	1000 AU			1045 kg	1048 GWh
10 day	104 AU			1048 kg	1051 GWh
1 yr	1 LY			1051 kg	1054 GWh
10 yr	10 LY
100 yr	100 LY
1000 yr	1000 LY
104 yr	104 LY	1040 m2 1041 m2
105 yr	105 LY
106 yr	106 LY
107 yr	107 LY
108 yr	108 LY
109 yr	109 LY
1010 yr	1010 LY
1011 yr
1012 yr and more

* Each time shown is linked to that time. However, the time taken for light to cross the corresponding length is 3 times the time shown.

** These are the standard units but this table uses a variety of units, which can make it harder to read.

Units used in the table

The table uses units and prefixes that are commonly recognized:

• Time:
  • femtosecond (fs)
  • nanosecond (ns)
  • microsecond (μs)
  • millisecond (ms)
  • second (s)
  • hour (h)
  • day (d)
  • year (yr)
• Length:
  • attometre (am)
  • femtometre (fm)
  • picometre (pm)
  • nanometre (nm)
  • micrometre (�m)
  • millimetre (mm)
  • centimetre (cm)
  • metre (m)
  • kilometre (km)
  • astronomical unit (AU)
  • light year (LY)
• Area:
  • square metre (m²)
  • hectare (ha)
  • square kilometre (km²)
• Mass:
  • gram (g)
  • kilogram (kg)
  • tonne (t)
• Volume:
  • millilitre (ml)
  • litre (l)
  • cubic metre (m³)
• Energy:
  • millielectronvolt (meV),
  • electronvolt (eV)
  • megaelectronvolt (MeV)
  • gigaelectronvolt (GeV)
  • teraelectronvolt (TeV)
  • erg
  • joule (J)
  • kilowatthour kWh
  • megawatthour MWh
  • gigawatthour GWh
• Temperature:
  • nanokelvin (nK)
  • microkelvin (�K)
  • millikelvin (mK)
  • kelvin (K)

See also

• Orders of approximation
• Orders of magnitude (area)
• Orders of magnitude (data)
• Orders of magnitude (density)
• Orders of magnitude (energy)
• Orders of magnitude (length)
• Orders of magnitude (mass)
• Orders of magnitude (numbers)
• Orders of magnitude (power)
• Orders of magnitude (temperature)
• Orders of magnitude (time)
• Orders of magnitude (U.S. money)
• Orders of magnitude (volume)
• Powers of Ten
• SI base units
• SI derived units
• Complete list of SI prefixes
• Timeline of the Big Bang
• Timeline of the Universe

External links

• Powers of 10 (http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/index.html), 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.
• Calculation: Orders of Magnitude (http://www.sengpielaudio.com/ConvPref.htm)
• Orders of Magnitude - Distance (http://www.alcyone.com/max/physics/orders/metre.html)

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