Orders Of Magnitude

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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.

1 Orders of magnitude of various quantities

2 Units used in the table

3 See also

4 External links

Table of contents

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.

 
  0.01 meV
0.1 meV10 meV
100 meV100 K
1000 K10 eV
100 eV100,000 K
106 K10-32kg
10-31 kg104 eV
105 eV10-29 kg
10-28 kg10 MeV
100 MeV10-29 kg
10-28 kg10 MeV
100 MeV10-19m210-26 kg
10-25 kg10 GeV
100 GeV10-17m210-23 kg
10-22 kg10 TeV
100 TeV10-15m210-20 kg
10-19 kg0.001 J
0.01 J10-13m210-20m3
10-19m310-17 kg
10-16 kg1 J
10 J10-11m210-17m3
10-16m310-14 kg
10-13 kg1000 J
10000 J10-9m210-14m3
10-13m310-11 kg
10-10 kg0.001 kWh
0.01 kWh10-7m210-11m3
10-10m310-8 kg
10-7 kg1 kWh
10 kWh10-5m210-8m3
10-7m310-5 kg
10-4 kg1000 kWh
10000 kWh10 cm210 ml
100 ml 10 g
100 g1 GWh
10 GWh0.1 m210 l
100 l 10 kg
100 kg1000 GWh
10000 GWh10 m210 m3
100 m310 t
100 t106 GWh
107 GWh1,000 m210,000 m3
105m3107 kg
108 kg109 GWh
10 ha 107m3
108m31010 kg
1011 kg10 km210 km3
100 km31013 kg
1014 kg109m21016 kg
1017 kg1011m21019 kg
1020 kg1013m21022 kg
1023 kg1015m21017m21019m21021m21041m2
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 µK
10-25 s 100 am        

1 mK
10-24 s 1 fm       0.001 meV


1 K
10-23 s 10 fm       1 meV
10 K
10-22 s 100 fm 10-28 m2     1 eV
10,000 K
10-21 s 1 pm     10-33 kg
1000 eV


109 K
10-20 s 10pm     10-30 kg
1 MeV


109 K
10-20 s 10pm     10-30 kg
1 MeV


1012 K
10-19 s 100 pm 10-20 m2
  10-27 kg
1 GeV


1015 K
10-18 s 1 nm 10-18 m2
  10-24 kg
1 TeV


1018 K
10-17 s 10 nm 10-16 m2
  10-21 kg
0.0001 J


1021 K
10-16 s 100 nm 10-14 m2
10-21 m3
10-18 kg
0.1 J


1024 K
1 fs 1 μm 10-12 m2
10-18 m3
10-15 kg
100 J


1027 K
10 fs 10 μm 10-10 m2
10-15 m3
10-12 kg
100000 J


1030 K
100 fs 100 μm 10-8 m2
10-12 m3
10-9 kg
0.1 kWh
 
1 ps 1 mm 10-6 m2
10-9 m3
10-6 kg
100 kWh
 
10 ps 1 cm 1 cm2
1 ml
1 g
100000 kWh
 
100 ps 10 cm 0.01 m2
1 l
1 kg
100 GWh
 
1 ns 1 m 1 m2
1 m3
1 t
100000 GWh
 
10 ns 10 m 100 m2
1,000 m3
106 kg
108 GWh
 
100 ns 100 m 1 ha
106 m3
109 kg

1012 GWh
 
1 μs 1 km 1 km2
1 km3
1012 kg

1015 GWh
 
10 μs 10 km 108 m2
1012 m3

1015 kg

1018 GWh
 
100 μs 100 km 1010 m2
1015 m3

1018 kg

1021 GWh
 
1 ms 1000 km 1012 m2
1018 m3

1021 kg

1024 GWh
 
10 ms 104 km 1014 m2
1021 m3

1024 kg


1027 GWh
 
100 ms 105 km 1016 m2
1024 m3

1027 kg

 

1030 GWh
 
1 s 106 km 1018 m2
1027 m3

1030 kg


1033 GWh
 
10 s 107 km 1020 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
       
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:

See also

External links