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).

SI base unit symbols and names.

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

SI derived unit symbols, names and conversion rules.

dimension

symbol

unit name | conversio

n

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 W

b m⁻²

inductance

H

henry | 1 H = 1 W

b A⁻¹

Celsius temperature

degC

degree Celsius | 0 °C = 27

3.15 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

SI prefixes.

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

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/.