Units

Objective

This module defines how physical units are attached to dimensionful H5MD elements.

Module name and version

The name of this module is units. The module version is 1.0.0.

Unit system definition

The units group possesses, in addition to the version attribute, a system attribute that defines the unit system in use. system is of scalar dataspace and fixed-length string datatype.

Unit attribute

The datasets of any H5MD element that have a physical dimension may carry an attribute unit to indicate the physical unit of the respective data. In general, this refers to the dataset itself for time-independent elements, or to the datasets value and time in the time-dependent case:

<element>
 \-- step: Integer[variable]
 \-- time: Float[variable]
 |    +-- (unit: String[])
 \-- value: <type>[variable][...]
      +-- (unit: String[])

The attribute unit is of scalar dataspace and fixed-length String datatype using the ASCII character set.

Unit string

The unit string consists of a sequence of unit factors separated by a space. A unit factor is either a number (an integer or a decimal fraction) or a unit symbol optionally followed by a non-zero, signed integer indicating the power to which this factor is raised. Each unit symbol may occur only once. There may also be at most one numeric factor, which must be the first one.

Examples:

  • “nm+3” stands for cubic nanometers
  • “um+2 s-1” stands for micrometers squared per second
  • “60 s” stands for a minute
  • “10+3 m” stands for a kilometer

The “SI” unit system

The “SI” unit system (“The International System of Units (SI)” 2006) defines SI base units (§2.1), SI derived units (§2.2), and SI prefixes (§3.1).

dimension symbol unit name
length m meter
mass kg kilogram
time s second
electric current A ampere
temperature K kelvin
amount of substance mol mole
luminous intensity cd candela

Table: SI base unit symbols and names.

dimension symbol unit name conversion
plane angle rad radian 1 rad = 1 m m⁻¹
solid angle sr steradian 1 sr = 1 m² m⁻²
frequency Hz hertz 1 Hz = 1 s⁻¹
force N newton 1 N = 1 m kg s⁻²
pressure/stress Pa pascal 1 Pa = 1 N m⁻²
energy/work J joule 1 J = 1 N m
power W watt 1 W = 1 J s⁻¹
electric charge C coulomb 1 C = 1 A s
voltage V volt 1 V = W A⁻¹
capacitance F farad 1 F = C V⁻¹
electric resistance ohm ohm 1 Ω = V A⁻¹
electric conductance S siemens 1 S = 1 A V⁻¹
magnetic flux Wb weber 1 Wb = 1 V s
magnetic flux density T tesla 1 T = 1 Wb m⁻²
inductance H henry 1 H = 1 Wb A⁻¹
Celsius temperature degC degree Celsius 0 °C = 273.15 K
luminous flux lm lumen 1 lm = 1 cd sr
illuminance lx lux 1 lx = 1 lm m⁻²
radioactivity Bq becquerel 1 Bq = 1 s⁻¹
absorbed dose Gy gray 1 Gy = 1 J kg⁻¹
dose equivalent Sv sievert 1 Sv = 1 J kg⁻¹
catalytic activity kat katal 1 kat = 1 mol s⁻¹

Table: SI derived unit symbols, names and conversion rules.

prefix symbol factor
exa- E 10¹⁸
peta- P 10¹⁵
tera- T 10¹²
giga- G 10⁹
mega- M 10⁶
kilo- k 10³
hecto- h 10²
deca- da 10¹
deci- d 10⁻¹
centi- c 10⁻²
milli- m 10⁻³
micro- u 10⁻⁶
nano- n 10⁻⁹
pico- p 10⁻¹²
femto- f 10⁻¹⁵
atto- a 10⁻¹⁸

Table: SI prefixes.

References

“The International System of Units (SI).” 2006. 8th ed. Paris: Bureau International des Poids et Mesures. http://www.bipm.org/en/publications/si-brochure/.