The table of units defines new units in terms of previously defined units. A term of units is expressed according to the ISO standard 2955 using the following operators:
The exponentiation is expressed by writing an (integer) number directly behind the units symbol, e.g. a cubic meter is expressed as `m2'. Negative exponents are allowed by writing a `-' in front of the number. The use of parentheses to overcome left to right association is not allowed. Thus, the Newton is defined as `kg/m/s2'. Note that because there are no parentheses and operators strictly associate left to right, `kg/m.s2' is not a correct representation for the Newton. Using negative exponents `kg.m-1.s-2' is again the Newton. Parentheses in units are a part of the unit symbol itself. Thus, `m(H2O)' is an allowed unit symbol that can be defined distinct from `m(Hg)' and the base unit of length `m'.
The following basic units are predefined:
SYMBOL BASE UNIT VECTOR M E -------- ---------------------- -- -- m [ 1, 0, 0, 0, 0, 0, 0] 1 0 s [ 0, 1, 0, 0, 0, 0, 0] 1 0 g [ 0, 0, 1, 0, 0, 0, 0] 1 0 c [ 0, 0, 0, 1, 0, 0, 0] 1 0 k [ 0, 0, 0, 0, 1, 0, 0] 1 0 cd [ 0, 0, 0, 0, 0, 1, 0] 1 0 circ [ 0, 0, 0, 0, 0, 0, 1] 1 0 1 [ 0, 0, 0, 0, 0, 0, 0] 1 0 10* [ 0, 0, 0, 0, 0, 0, 0] 1 1
In the above table the attribute `M' is the mantissa and `E' is the exponent of logarithmical representation of the coefficient to the base 10. A unit symbol may be prepended by a prefix symbol. However, it is important that the combination of prefix and unit does not interfere with another combination of a prefix and a unit. The symbols are interpreted case insensitive according to ISO 2955. This is the reason, why the symbols for prefices as well as for the units slightly differ from the normal SI symbols. The following prefices may be used:
Beside the proportional conversions, i.e. those where conversion is performed simply by multiplication with a conversion coefficient, a limited set of non-proportional conversions is supported. This is used for logarithmic units like pH or db as well as for conversions of temperature scales of Celsius, Kelvin and Fahrenheit.
Proportional conversions are defined as
new_unit = number known_unit
while non-proportional conversions are defined as
new_unit = function_name(number known_unit)
where function_name must be a name known at compile time. Working with functions is a bit tricky and limits the applicability of the unit in conversions. Therefore the general rule is to avoid functions where possible. If not avoidable define new functions as follows:
unitmgr to remake the database
Functions are applied as follows: If the table states:
foo = foo_f(12.3 bar)
a given foo (F) is converted to bar (B) as:
B = foo_from(F) * ( 12.3 bar )
and if a bar (B) is given, we get the foo (F) by:
F = foo_to(B / ( 12.3 bar ))
Comment lines starting with a number sign (`#') are allowed as well as blank lines.
The following is the current contents of the file `units.tab'.
# Pseudo Units, i.e. those whose dimension is 1 % = 1 10*-2 # percent # Angle rad = 1.5915494309189533577 10*-1.circ # radian sr = 4.0528473456935108578 10*-1.circ+2 # steradian deg = 2.7777777777777777778 10*-3.circ # degree (angular) mnt = 1.6666666666666666667 10*-2.deg # angular minute # Space l = 1 dm3 # liter # Time hr = 3.6 10*3.s # hour min = 6 10*1.s # minute d = 8.64 10*4.s # day ann = 3.1536 10*7.s # year hz = 1 /s # Herz # Mechanics n = 1 kg.m/s2 # Newton p = 9.80665 g.m/s2 # pond j = 1 n.m # Joule cal = 4.1868 j # calorie w = 1 j/s # Watt pal = 1 n/m2 # Pascal bar = 1 10*5.pal # bar m(h2o) = 9.806650 kpal # meter of water column m(hg) = 133.3220 kpal # meter of mercury column # Temperature cel = cel_f(1 k) # degree Celsius degf = degf_f(0.5555555555555555556 k) # degree Fahrenheit # Electromagnetism a = 1 c/s # Ampere v = 1 j/c # Volt ohm = 1 v/a # Ohm sie = 1 a/v # Siemens f = 1 c/v # Farad wb = 1 v.s # Weber (magnetic flux) t = 1 wb/m2 # Tesla (magnetic inductance) hy = 1 wb/a # Henry (inductance) # Nuclear/Atomic/Molecular/Chemical mol = 6.022137 10*23 # mole -- Avogadro's number val = 6.022137 10*23 # val -- equivalents eq = 6.022137 10*23 # equivalents ph = ph_f(1 mol/l) # pH e = 1.6021892 10*-19.c # elementary charge ev = 1.602177 10*-19.j # electronvolt u = 1.6605655 10*-24.g # atomic mass unit bq = 1 1/s # Bequerel (activity) gy = 1 j/s # Gray (energy dose) # Biological/Biochemical/Medical Units sv(a) = 0.04 gy # Sievert (alpha rays) sv(b) = 1 gy # Sievert (beta rays) sv(g) = 1 gy # Sievert (gamma rays) sv(x) = 1 gy # Sievert (X-rays) sv(n) = 0.2 gy # Sievert (neutrons) sv(p) = 0.1 gy # Sievert (protons) tot = 1 1 # particles total count cfu = 1 1 # colony forming units ppm = 1 10*-6 # parts per million ppb = 1 10*-9 # parts per billion iu = 1 1 # international units kat = 1 mol/s # katal # Photometric Units lm = 1 cd/sr # lumen (luminous flux) lx = 1 lm/m2 # lux # Levels bel = f_ln(1 1) # bel db(spl) = f_20_lg(2 10*-5.pal) # decibel sound pressure db(v) = f_20_lg(1 v) # decibel volts db(mv) = f_20_lg(1 mv) # decibel millivolts db(uv) = f_20_lg(1 uv) # decibel mycrovolts db(w) = f_10_lg(1 w) # decibel watts db(kw) = f_10_lg(1 kw) # decibel kilowatts
section Managing the Database of Units