# Centimetre

A centimetre (international spelling as used by the International Bureau of Weights and Measures; symbol cm) or centimeter (American spelling) is a unit of length in the metric system, equal to one hundredth of a metre, centi being the SI prefix for a factor of 1/100.[1] The centimetre was the base unit of length in the now deprecated centimetre–gram–second (CGS) system of units.

Though for many physical quantities, SI prefixes for factors of 103—like milli- and kilo-—are often preferred by technicians, the centimetre remains a practical unit of length for many everyday measurements. A centimetre is approximately the width of the fingernail of an average adult person.

Centimetre
A carpenter's ruler with centimetre divisions
General information
Unit systemmetric
Unit oflength
Symbolcm
Conversions
1 cm in ...... is equal to ...
SI units   10 mm
imperial & US system   ~0.3937 in

## Equivalence to other units of length

 1 centimetre = 10 millimetres = 0.01 metres = 0.393700787401574803149606299212598425196850 inches (There are exactly 2.54 centimetres in one inch.)

One millilitre is defined as one cubic centimetre, under the SI system of units.

## Other uses

In addition to its use in the measurement of length, the centimetre is used:

• sometimes, to report the level of rainfall as measured by a rain gauge [2]
• in the CGS system, the centimetre is used to measure capacitance, where 1 cm of capacitance = 1.113×10−12 farads[3]
• in maps, centimetres are used to make conversions from map scale to real world scale (kilometres)
• to represent second moment of areas (cm4)
• as the inverse of the kayser, a CGS unit, and thus a non-SI metric unit of wavenumber: 1 kayser = 1 wave per centimetre; or, more generally, (wavenumber in kaysers) = 1/(wavelength in centimetres). The SI unit of wavenumber is the inverse metre, m−1.

## Unicode symbols

For the purposes of compatibility with Chinese, Japanese and Korean (CJK) characters, Unicode has symbols for:[4]

• centimetre (㎝) – code 339D
• square centimetre (㎠) – code 33A0
• cubic centimetre (㎤) – code 33A4

They are mostly used only with East Asian fixed-width CJK fonts, because they are equal in size to one Chinese character.

## References

1. ^ "Decimal multiples and submultiples of SI units". Bureau International des Poids et Mesures. 2014. Retrieved 5 July 2015.
2. ^ Rain Measurement, Rain Gauge, Wireless Rain Gauge, Rain Gage, Rain Gauge Data
3. ^ Capacitance - from Eric Weisstein's World of Physics
4. ^ CJK Compatibility excerpt from The Unicode Standard, Version 10.0.
5 Centimeters per Second

5 Centimeters per Second (Japanese: 秒速5センチメートル, Hepburn: Byōsoku Go Senchimētoru) is a 2007 Japanese animated coming-of-age romantic drama film produced, written and directed by Makoto Shinkai. Finished on 22 January 2007, the first part streamed on Yahoo! Japan to Yahoo! Premium members from 16 to 19 February 2007. On 3 March 2007, the full-length film had its theatrical premiere at Cinema Rise in Shibuya, Tokyo. The film consists of three segments: "Cherry Blossom" (桜花抄, Ōkashō), "Cosmonaut" (コスモナウト, Kosumonauto), and "5 Centimeters per Second" (秒速5センチメートル, Byōsoku Go Senchimētoru), totaling about an hour of runtime. As in Shinkai's previous works, Tenmon composed this film's soundtrack. The film's ending theme was "One More Time, One More Chance" by Masayoshi Yamazaki. The film was awarded Best Animated Feature Film at the 2007 Asia Pacific Screen Awards. The DVD was released on 19 July 2007.

A novelization of 5 Centimeters per Second was released in November 2007, expanding on the film. In the July 2010 issue of the manga anthology Afternoon, a manga adaptation started serialization, illustrated by Seike Yukiko.

Centimetre–gram–second system of units

The centimetre–gram–second system of units (abbreviated CGS or cgs) is a variant of the metric system based on the centimetre as the unit of length, the gram as the unit of mass, and the second as the unit of time. All CGS mechanical units are unambiguously derived from these three base units, but there are several different ways of extending the CGS system to cover electromagnetism.The CGS system has been largely supplanted by the MKS system based on the metre, kilogram, and second, which was in turn extended and replaced by the International System of Units (SI). In many fields of science and engineering, SI is the only system of units in use but there remain certain subfields where CGS is prevalent.

In measurements of purely mechanical systems (involving units of length, mass, force, energy, pressure, and so on), the differences between CGS and SI are straightforward and rather trivial; the unit-conversion factors are all powers of 10 as 100 cm = 1 m and 1000 g = 1 kg. For example, the CGS unit of force is the dyne which is defined as 1 g⋅cm/s2, so the SI unit of force, the newton (1 kg⋅m/s2), is equal to 100,000 dynes.

On the other hand, in measurements of electromagnetic phenomena (involving units of charge, electric and magnetic fields, voltage, and so on), converting between CGS and SI is more subtle. Formulas for physical laws of electromagnetism (such as Maxwell's equations) need to be adjusted depending on which system of units one uses. This is because there is no one-to-one correspondence between electromagnetic units in SI and those in CGS, as is the case for mechanical units. Furthermore, within CGS, there are several plausible choices of electromagnetic units, leading to different unit "sub-systems", including Gaussian units, "ESU", "EMU", and Lorentz–Heaviside units. Among these choices, Gaussian units are the most common today, and "CGS units" often used specifically refers to CGS-Gaussian units.

Cubic centimetre

A cubic centimetre (or cubic centimeter in US English) (SI unit symbol: cm3; non-SI abbreviations: cc and ccm) is a commonly used unit of volume that extends the derived SI-unit cubic metre, and corresponds to the volume of a cube that measures 1 cm × 1 cm × 1 cm. One cubic centimetre corresponds to a volume of 1/1,000,000 of a cubic metre, or 1/1,000 of a litre, or one millilitre; thus, 1 cm3 ≡ 1 mL. The mass of one cubic centimetre of water at 3.98 °C (the temperature at which it attains its maximum density) is closely equal to one gram. SI supports only the use of symbols and deprecates the use of any abbreviations for units. Hence cm3 is preferred to cc or ccm.

Many scientific disciplines have replaced cubic centimeter measurements with milliliters, but the medical and automotive fields in the United States still use the term cubic centimetre. Much of the automotive industry outside the U.S. has switched to litres. The United Kingdom uses millilitres in preference to cubic centimetres in the medical field, but not the automotive. Most other English-speaking countries follow the UK example.[citation needed]

There is currently a movement within the medical field to discontinue the use of cc in prescriptions and on medical documents, as it can be misread as "00". This could cause a hundredfold overdose of medication, which could be dangerous or even lethal. In the United States, such confusion accounts for 12.6% of all errors associated with medical abbreviations.

In automobile engines, "cc" refers to the total volume of its engine displacement in cubic centimetres. The displacement can be calculated using the formula

${\displaystyle d={\pi \over 4}\times b^{2}\times s\times n}$

where d is engine displacement, b is the bore of the cylinders, s is length of the stroke and n is the number of cylinders.

Conversions

Dyne

The dyne (symbol dyn, from Greek δύναμις, dynamis, meaning power, force) is a derived unit of force specified in the centimetre–gram–second (CGS) system of units, a predecessor of the modern SI.

Ecchymosis

An ecchymosis is a subcutaneous spot of bleeding with diameter larger than 1 centimetre (0.39 in). It is similar to (and sometimes indistinguishable from) a hematoma, commonly called a bruise, though the terms are not interchangeable in careful usage. Specifically, bruises are caused by trauma whereas ecchymoses, which are the same as the spots of purpura except larger, are not necessarily caused by trauma, often being caused by pathophysiologic cell function, and some diseases such as Marburg virus disease.

A broader definition of ecchymosis is the escape of blood into the tissues from ruptured blood vessels. The term also applies to the subcutaneous discoloration resulting from seepage of blood within the contused tissue.

Erg

The erg is a unit of energy and work equal to 10−7 joules. It originated in the centimetre–gram–second (CGS) system of units. It has the symbol erg. The erg is not an SI unit. Its name is derived from ergon (ἔργον), a Greek word meaning work or task.An erg is the amount of work done by a force of one dyne exerted for a distance of one centimeter. In the CGS base units, it is equal to one gram centimeter-squared per second-squared (g⋅cm2/s2). It is thus equal to 10−7 joules or 100 nanojoules (nJ) in SI units. An erg is approximately the amount of work done (or energy consumed) by one common house caterpillar performing one "push up", the leg-bending dip that brings its mouth to the surface on which it stands and back up.

1 erg = 10−7 J = 100 nJ

1 erg = 10−10sn⋅m = 100 psn⋅m = 100 picosthène-metres

1 erg = 624.15 GeV = 6.2415×1011 eV

1 erg = 1 dyn⋅cm = 1 g⋅cm2/s2

Gauss (unit)

The gauss, abbreviated as G or Gs, is the cgs unit of measurement of magnetic flux density (or "magnetic induction") (B). It is named after German mathematician and physicist Carl Friedrich Gauss. One gauss is defined as one maxwell per square centimeter. The cgs system has been superseded by the International System of Units (SI), which uses the tesla (symbol T) as the unit of magnetic flux density. One gauss equals 1×10−4 tesla (100 μT), so 1 tesla = 10,000 gauss.

Gram

The gram (alternative spelling: gramme; SI unit symbol: g) (Latin gramma, from Greek γράμμα, grámma) is a metric system unit of mass.

Originally defined as "the absolute weight of a volume of pure water equal to the cube of the hundredth part of a metre [1 cm3], and at the temperature of melting ice" (later at 4 °C, the temperature of maximum density of water). However, in a reversal of reference and defined units, a gram is now defined as one thousandth of the SI base unit, the kilogram, or 1×10−3 kg, which itself is now defined by the International Bureau of Weights and Measures, not in terms of grams, but by "the amount of electricity needed to counteract its force"

Hydrogen line

The hydrogen line, 21-centimeter line or H I line refers to the electromagnetic radiation spectral line that is created by a change in the energy state of neutral hydrogen atoms. This electromagnetic radiation is at the precise frequency of 1420405751.7667±0.0009 Hz, which is equivalent to the vacuum wavelength of 21.1061140542 cm in free space. This wavelength falls within the microwave region of the electromagnetic spectrum, and it is observed frequently in radio astronomy, since those radio waves can penetrate the large clouds of interstellar cosmic dust that are opaque to visible light.

The microwaves of the hydrogen line come from the atomic transition of an electron between the two hyperfine levels of the hydrogen 1s ground state that have an energy difference of ≈ 5.87433 µeV. It is called the spin-flip transition. The frequency, ν, of the quanta that are emitted by this transition between two different energy levels is given by the Planck–Einstein relation E = hν. According to that relation, the photon energy of a 1,420,405,751.7667 Hz photon is ≈ 5.87433 µeV. The constant of proportionality, h, is known as the Planck constant.

Maxwell (unit)

The maxwell (symbol: Mx) is the CGS (centimetre-gram-second) unit of magnetic flux (Φ).

Millimetre

The millimetre (international spelling as used by the International Bureau of Weights and Measures; SI unit symbol mm) or millimeter (American spelling) is a unit of length in the metric system, equal to one thousandth of a metre, which is the SI base unit of length. Therefore, there are one thousand millimetres in a metre. There are ten millimetres in a centimetre.

One millimetre is equal to 1000 micrometres or 1000000 nanometres. A millimetre is equal to exactly ​5⁄127 (approximately 0.039370) of an inch.

Newton metre

The newton metre (also newton-metre, symbol N m or N⋅m) is a unit of torque (also called moment) in the SI system. One newton metre is equal to the torque resulting from a force of one newton applied perpendicularly to the end of a moment arm that is one metre long.

It is also used less commonly as a unit of work, or energy, in which case it is equivalent to the more common and standard SI unit of energy, the joule. In this usage the metre term represents the distance travelled or displacement in the direction of the force, and not the perpendicular distance from a fulcrum as it does when used to express torque. This usage is generally discouraged, since it can lead to confusion as to whether a given quantity expressed in newton metres is a torque or a quantity of energy. However, since torque represents energy transferred or expended per angle of revolution, one newton metre of torque is equivalent to one joule per radian.

Newton metres and joules are dimensionally equivalent in the sense that they have the same expression in SI base units:

${\displaystyle 1\,{\text{N}}{\cdot }\mathrm {m} =1{\frac {{\text{kg}}{\cdot }{\text{m}}^{2}}{{\text{s}}^{2}}}\quad ,\quad 1\,\mathrm {J} =1{\frac {\mathrm {kg} {\cdot }\mathrm {m} ^{2}}{\mathrm {s} ^{2}}}}$

Again, N⋅m and J are distinguished in order to avoid misunderstandings where a torque is mistaken for an energy or vice versa. Similar examples of dimensionally equivalent units include Pa versus J/m3, Bq versus Hz, and ohm versus ohm per square.

Oersted

The oersted (symbol Oe) is the unit of the auxiliary magnetic field H in the centimetre–gram–second system of units (CGS). It is equivalent to 1 dyne per maxwell.

Pixel density

Pixels per inch (ppi) or pixels per centimeter (ppcm) are measurements of the pixel density (resolution) of an electronic image device, such as a computer monitor or television display, or image digitizing device such as a camera or image scanner. Horizontal and vertical density are usually the same, as most devices have square pixels, but differ on devices that have non-square pixels.

Pixels per inch (or pixels per centimeter) can also describe the resolution, in pixels, of an image file. A 100×100 pixel image printed in a 1 inch square has a resolution of 100 pixels per inch. Used this way, the measurement is meaningful when printing an image. It has become commonplace to refer to PPI as DPI, even though PPI refers to input resolution. Industry standard, good quality photographs usually require 300 pixels per inch, at 100% size, when printed onto coated paper stock, using a printing screen of 150 lines per inch (lpi). This delivers a quality factor of 2, which is optimum. The lowest acceptable quality factor is considered 1.5, which equates to printing a 225 ppi image using a 150 lpi screen onto coated paper.Screen frequency is determined by the type of paper the image is printed on. An absorbent paper surface, uncoated recycled paper for instance, lets ink droplets spread (dot gain)—so requires a more open printing screen. Input resolution can therefore be reduced to minimize file size without loss in quality, as long as the quality factor of 2 is maintained. This is easily determined by doubling the line frequency. For example, printing on an uncoated paper stock often limits printing screen frequency to no more than 120 lpi, therefore, a quality factor of 2 is achieved with images of 240 ppi.

Poise (unit)

The poise (symbol P; /pɔɪz, pwɑːz/) is the unit of dynamic viscosity (absolute viscosity) in the centimetre–gram–second system of units. It is named after Jean Léonard Marie Poiseuille (see Hagen–Poiseuille equation).

${\displaystyle 1~{\text{P}}=0.1~{\text{kg}}{\cdot }{\text{m}}^{-1}{\cdot }{\text{s}}^{-1}=1~{\text{g}}{\cdot }{\text{cm}}^{-1}{\cdot }{\text{s}}^{-1}=1~{\text{dyne}}{\cdot }{\text{s}}{\cdot }{\text{cm}}^{-2}.}$

The analogous unit in the International System of Units is the pascal-second (Pa⋅s):

${\displaystyle 1~{\text{Pa}}{\cdot }{\text{s}}=1~{\text{N}}{\cdot }{\text{s}}{\cdot }{\text{m}}^{-2}=1~{\text{kg}}{\cdot }{\text{m}}^{-1}{\cdot }{\text{s}}^{-1}=10~{\text{P}}.}$

The poise is often used with the metric prefix centi- because the viscosity of water at 20 °C (NTP) is almost exactly 1 centipoise. A centipoise is one hundredth of a poise, or one millipascal-second (mPa⋅s) in SI units (1 cP = 10−3 Pa⋅s = 1 mPa⋅s).

The CGS symbol for the centipoise is cP. The abbreviations cps, cp, and cPs are sometimes seen.

Liquid water has a viscosity of 0.00890 P at 25 °C at a pressure of 1 atmosphere (0.00890 P = 0.890 cP = 0.890 mPa⋅s).

Primeval Structure Telescope

The Primeval Structure Telescope (PaST), also called 21 Centimetre Array (21CMA), is a Chinese radio telescope array designed to detect the earliest luminous objects in the universe, including the first stars, supernova explosions, and black holes. All of these objects were strong sources of ultraviolet radiation, so they ionised the material surrounding them. The structure of this reionisation reflects the overall density structure at the redshift of luminous-object formation.

Square metre

The square metre (international spelling as used by the International Bureau of Weights and Measures) or square meter (American spelling) is the SI derived unit of area with symbol m2.Adding and subtracting SI prefixes creates multiples and submultiples; however, as the unit is exponentiated, the quantities grow geometrically by the corresponding power of 10. For example, a kilometre is 103 (a thousand) times the length of a metre, but a square kilometre is 1032 (106, a million) times the area of a square metre, and a cubic kilometre is 1033 (109, a billion) cubic metres.

Super high frequency

Super high frequency (SHF) is the ITU designation for radio frequencies (RF) in the range between 3 and 30 gigahertz (GHz). This band of frequencies is also known as the centimetre band or centimetre wave as the wavelengths range from one to ten centimetres. These frequencies fall within the microwave band, so radio waves with these frequencies are called microwaves. The small wavelength of microwaves allows them to be directed in narrow beams by aperture antennas such as parabolic dishes and horn antennas, so they are used for point-to-point communication and data links and for radar. This frequency range is used for most radar transmitters, wireless LANs, satellite communication, microwave radio relay links, and numerous short range terrestrial data links. They are also used for heating in industrial microwave heating, medical diathermy, microwave hyperthermy to treat cancer, and to cook food in microwave ovens.

Frequencies in the SHF range are often referred to by their IEEE radar band designations: S, C, X, Ku, K, or Ka band, or by similar NATO or EU designations.

Torque

Torque, moment, or moment of force is the rotational equivalent of linear force. The concept originated with the studies of Archimedes on the usage of levers. Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object. The symbol for torque is typically ${\displaystyle {\boldsymbol {\tau }}}$, the lowercase Greek letter tau. When being referred to as moment of force, it is commonly denoted by M.

In three dimensions, the torque is a pseudovector; for point particles, it is given by the cross product of the position vector (distance vector) and the force vector. The magnitude of torque of a rigid body depends on three quantities: the force applied, the lever arm vector connecting the origin to the point of force application, and the angle between the force and lever arm vectors. In symbols:

${\displaystyle {\boldsymbol {\tau }}=\mathbf {r} \times \mathbf {F} \,\!}$
${\displaystyle \tau =\|\mathbf {r} \|\,\|\mathbf {F} \|\sin \theta \,\!}$

where

${\displaystyle {\boldsymbol {\tau }}}$ is the torque vector and ${\displaystyle \tau }$ is the magnitude of the torque,
r is the position vector (a vector from the origin of the coordinate system defined to the point where the force is applied)
F is the force vector,
× denotes the cross product, which is defined as magnitudes of the respective vectors times ${\displaystyle \sin \theta }$.
${\displaystyle \theta }$ is the angle between the force vector and the lever arm vector.

The SI unit for torque is N⋅m. For more on the units of torque, see Units.

Metric units of length

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