Orders of magnitude
Orders of magnitude |
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Length - Mass - Time - Area - Volume - Power - Temperature - Numbers - Data - U.S. money |
Related articles |
SI base units - SI derived units - SI prefixes |
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 |
2 Units used in the table 3 See also 4 External links |
Orders of magnitude of various quantities
- 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
Time | Length | Area | Volume | Mass | Energy | Temperature |
---|---|---|---|---|---|---|
(x 3)* | (m) | (m^{2}) | (m^{3}) | (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 E-9 K>1 nK | ||||
10^{-26} s | 10 am | 1 peV | 1 E-6 K>1 µK | |||
10^{-25} s | 100 am | 1 E-3 K>1 mK | ||||
10^{-24} s | 1 fm | 0.001 meV 0.01 meV 0.1 meV | 1 E0 K>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} m^{2} | 1 eV 10 eV 100 eV | 10,000 K 100,000 K 10^{6} K | ||
10^{-21} s | 1 pm | 10^{-33} kg 10^{-32} kg 10^{-31} kg | 1000 eV 10^{4} eV 10^{5} eV | 1 E9 K>10^{9} K | ||
10^{-20} s | 10pm | 10^{-30} kg 10^{-29} kg 10^{-28} kg | 1 MeV 10 MeV 100 MeV | 1 E9 K>10^{9} K | ||
10^{-20} s | 10pm | 10^{-30} kg 10^{-29} kg 10^{-28} kg | 1 MeV 10 MeV 100 MeV | 1 E12 K>10^{12} K | ||
10^{-19} s | 100 pm | 10^{-20} m^{2} 10^{-19} m^{2} | 10^{-27} kg 10^{-26} kg 10^{-25} kg | 1 GeV 10 GeV 100 GeV | 1 E15 K>10^{15} K | |
10^{-18} s | 1 nm | 10^{-18} m^{2} 10^{-17} m^{2} | 10^{-24} kg 10^{-23} kg 10^{-22} kg | 1 TeV 10 TeV 100 TeV | 1 E18 K>10^{18} K | |
10^{-17} s | 10 nm | 10^{-16} m^{2} 10^{-15} m^{2} | 10^{-21} kg 10^{-20} kg 10^{-19} kg | 0.0001 J 0.001 J 0.01 J | 1 E21 K>10^{21} K | |
10^{-16} s | 100 nm | 10^{-14} m^{2} 10^{-13} m^{2} | 10^{-21} m^{3} 10^{-20} m^{3} 10^{-19} m^{3} | 10^{-18} kg 10^{-17} kg 10^{-16} kg | 0.1 J 1 J 10 J | 1 E24 K>10^{24} K |
1 fs | 1 μm | 10^{-12} m^{2} 10^{-11} m^{2} | 10^{-18} m^{3} 10^{-17} m^{3} 10^{-16} m^{3} | 10^{-15} kg 10^{-14} kg 10^{-13} kg | 100 J 1000 J 10000 J | 1 E27 K>10^{27} K |
10 fs | 10 μm | 10^{-10} m^{2} 10^{-9} m^{2} | 10^{-15} m^{3} 10^{-14} m^{3} 10^{-13} m^{3} | 10^{-12} kg 10^{-11} kg 10^{-10} kg | 100000 J 0.001 kWh 0.01 kWh | 1 E30 K>10^{30} K |
100 fs | 100 μm | 10^{-8} m^{2} 10^{-7} m^{2} | 10^{-12} m^{3} 10^{-11} m^{3} 10^{-10} m^{3} | 10^{-9} kg 10^{-8} kg 10^{-7} kg | 0.1 kWh 1 kWh 10 kWh | |
1 ps | 1 mm | 10^{-6} m^{2} 10^{-5} m^{2} | 10^{-9} m^{3} 10^{-8} m^{3} 10^{-7} m^{3} | 10^{-6} kg 10^{-5} kg 10^{-4} kg | 100 kWh 1000 kWh 10000 kWh | |
10 ps | 1 cm | 1 cm^{2} 10 cm^{2} | 1 ml 10 ml 100 ml | 1 g 10 g 100 g | 100000 kWh 1 GWh 10 GWh | |
100 ps | 10 cm | 0.01 m^{2} 0.1 m^{2} | 1 l 10 l 100 l | 1 kg 10 kg 100 kg | 100 GWh 1000 GWh 10000 GWh | |
1 ns | 1 m | 1 m^{2} 10 m^{2} | 1 m^{3} 10 m^{3} 100 m^{3} | 1 t 10 t 100 t | 100000 GWh 10^{6} GWh 10^{7} GWh | |
10 ns | 10 m | 100 m^{2} 1,000 m^{2} | 1,000 m^{3} 10,000 m^{3} 10^{5} m^{3} | 10^{6} kg 10^{7} kg 10^{8} kg | 10^{8} GWh 10^{9} GWh | |
100 ns | 100 m | 1 ha 10 ha | 10^{6} m^{3} 10^{7} m^{3} 10^{8} m^{3} | 10^{9} kg 10^{10} kg 10^{11} kg | 1 E27 J>10^{12} GWh | |
1 μs | 1 km | 1 km^{2} 10 km^{2} | 1 km^{3} 10 km^{3} 100 km^{3} | 10^{12} kg 10^{13} kg 10^{14} kg | 1 E30 J>10^{15} GWh | |
10 μs | 10 km | 10^{8} m^{2} 10^{9} m^{2} | 10^{12} m^{3} | 10^{15} kg 10^{16} kg 10^{17} kg | 1 E33 J>10^{18} GWh | |
100 μs | 100 km | 10^{10} m^{2} 10^{11} m^{2} | 10^{15} m^{3} | 10^{18} kg 10^{19} kg 10^{20} kg | 1 E36 J>10^{21} GWh | |
1 ms | 1000 km | 10^{12} m^{2} 10^{13} m^{2} | 10^{18} m^{3} | 10^{21} kg 10^{22} kg 10^{23} kg | 1 E39 J>10^{24} GWh | |
10 ms | 10^{4} km | 10^{14} m^{2} 10^{15} m^{2} | 10^{21} m^{3} | 10^{24} kg | 1 E42 J>10^{27} GWh | |
100 ms | 10^{5} km | 10^{16} m^{2} 10^{17} m^{2} | 10^{24} m^{3} | 10^{27} kg | 1 E45 J>10^{30} GWh | |
1 s | 10^{6} km | 10^{18} m^{2} 10^{19} m^{2} | 10^{27} m^{3} | 10^{30} kg | 1 E48 J>10^{33} GWh | |
10 s | 10^{7} km | 10^{20} m^{2} 10^{21} m^{2} | 10^{33} kg | 1 E51 J>10^{36} GWh | ||
100 s | 1 AU | 10^{36} kg | 1 E54 J>10^{39} GWh | |||
1 h | 10 AU | 10^{39} kg | 1 E57 J>10^{42} GWh | |||
10 h | 100 AU | 10^{42} kg | 1 E60 J>10^{45} GWh | |||
1 day | 1000 AU | 10^{45} kg | 1 E63 J>10^{48} GWh | |||
10 day | 10^{4} AU | 10^{48} kg | 1 E66 J>10^{51} GWh | |||
1 yr | 1 LY | 10^{51} kg | 1 E69 J>10^{54} GWh | |||
10 yr | 10 LY | |||||
100 yr | 100 LY | |||||
1000 yr | 1000 LY | |||||
10^{4} yr | 10^{4} LY | 10^{40} m^{2} 10^{41} m^{2} | ||||
10^{5} yr | 10^{5} LY | |||||
10^{6} yr | 10^{6} LY | |||||
10^{7} yr | 10^{7} LY | |||||
10^{8} yr | 10^{8} LY | |||||
10^{9} yr | 10^{9} LY | |||||
10^{10} yr | 10^{10} LY | |||||
10^{11} yr | ||||||
10^{12} yr and more |
** 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 (µm)
- millimetre (mm)
- centimetre (cm)
- metre (m)
- kilometre (km)
- astronomical unit (AU)
- light year (LY)
- Area:
- square metre (m^{2})
- hectare (ha)
- square kilometre (km^{2})
- Mass:
- Volume:
- millilitre (ml)
- litre (l)
- cubic metre (m^{3})
- Energy:
- Temperature:
- nanokelvin (nK)
- microkelvin (µK)
- millikelvin (mK)
- kelvin (K)
See also
- Orders of approximation
- Orders of magnitude (time)
- Orders of magnitude (length)
- Orders of magnitude (area)
- Orders of magnitude (volume)
- Orders of magnitude (mass)
- Orders of magnitude (energy)
- Orders of magnitude (power)
- Orders of magnitude (temperature)
- Orders of magnitude (numbers)
- Orders of magnitude (U.S. money)
- Orders of magnitude (data)
- 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, a graphic animated illustration that starts with a view of the Milky Way at 10^{23} meters and ends with subatomic particles at 10^{-16} meters.
- Orders of magnitude - Distance