Units of measurement
 >>fast Notation Arithmetic Functions convert conversion factor coefficient unit Tables Basic units of the SI Units derived from SI Units from other systems Prefixes for the SI System of Units

Units of measurement are the basic tools of physics and also some aspects of mathematics.

Units of measurement that WIRIS allows us to represent include all of those in the International System of units (SI) and some others, such as the litre and the bar (atmospheric pressure), which have a practical relevance. It also allows users to define their own units with the command unit.

In addition to the principal units, the SI system includes decimal multiples and submultiples, denoted using the prefixes deka, hecto, kilo, deci, centi, milli... The complete list of units in the SI, along with their prefixes, names, abbreviations and the corresponding conversion factors with respect to basic units, can be found in the tables at the end of the chapter. The icons on the tab Units of measurement can be used to create units and measurements. For example, to express the metre, use the icon to express the decimetre, select the icon deci from the drop-down menu on the left, and then click on the icon .

Some of the more common units we can use, from the SI or other systems, are:

meter, gram, amper, kelvin, mol, liter, hour, minute, second, coulomb, henry, newton, joule, volt, ohm, hertz, pascal, bar, radian, siemens, farad, tesla, watt, weber
You will find the complete list of units included in WIRIS in the tables at the end of the chapter.

Units can be multiplied and divided together to define new units. If a unit of measurement is multiplied by a number we obtain a quantity, which can represent the value of a measurement. Quantities corresponding to measurements of the same magnitude can be summed, multiplied or divided together even if not expressed in the same units. The units in which they are represented can be changed.

To express a complex quantity in a single unit, use the command convert with the quantity as the first argument and the unit in which we wish the express the result as the second argument. Let's look at some examples:

Notation

Physical quantities can be added, subtracted, multiplied and divided. In general, to add or subtract quantities we use the notation we refer to as complex. That is, we separate the quantities (remember that a quantity is a number followed by a unit) with spaces. WIRIS understands complex notation. Nonetheless, when in doubt it is advisable to use the usual symbols for addition and subtraction.

Arithmetic

When adding and subtracting physical quantities, negative quantities can arise. When possible, WIRIS transforms these into the positive equivalent. Let’s look at some examples:

Functions

The functions to convert quantities to different units are:

convert:  command convert

The command convert can take one or two arguments. In the first case, we get the quantity that was entered, expressed in SI basic units. In the second case, the second argument is the unit of measurement in which the specified quantity should be expressed.

conversion factor:  command conversion_factor

This command can take one or two units of measurement as arguments. If it is given two arguments, it returns the factor by which the quantities expressed should be multiplied in the first unit to obtain the equivalent in the second unit. If it is given only one argument, which we assume is a unit of measurement, it calculates the factor to convert quantities expressed in this unit into SI basic units.

coefficient:  command coefficient

Given one quantity this returns its coefficient if there is only one summand. If there is more than one summand, it returns the coefficient of the quantity transformed into SI units.

unit:  command unit

Given one quantity this returns its unit of measurement if there is only one summand. If there are more summands it returns the equivalent SI unit.

Basic units of the SI

Besides these, other units are defined:

Magnitude SI unit
Name Symbol
length meter m
mass kilogram kg
time second s
electric current amper A
thermodynamic temperature kelvin K
quantity of substance mol mol
luminous intensity candela cd

Units derived from SI

Defined from the basic units:

Magnitude SI unit Expression in other units Expression in basic units
Name Symbol
frequency hertz Hz   s-1
force newton N   kg·m·s-2
pressure, strain pascal Pa N/m2 m-1·kg·s-2
energy, work, quantity of heat joule J N·m m2·kg·s-2
power, radiant flux watt W J/s m2·kg·s-3
electric potential difference, electromotive force volt V W/A m2·kg·s-3·A-1
electrical resistance ohm W V/A m2·kg·s-3·A-2
electrical charge coulomb C F·V A·s
electrical conductivity siemens S A/V m-2·kg-1·s3·A2
magnetic flux weber Wb V·s m2·kg·s-2·A-1
magnetic flux density tesla T Wb/m2 kg·s-2·A-1
inductance henry H Wb/A m2·kg·s-2·A-2
luminous flux lumen lm cd·sr m2·m-2·cd=cd
illuminance lux lx lm/m2 m2·m-4·cd=m-2·cd
absorbed dose gray Gy J/kg m2·s-2
equivalent dose sievert Sv J/kg m2·s-2
catalytic activity katal Kat   s-1·mol

Units from other systems

Magnitude Unit
Name Symbol
time hour h
time minute min
time second s
volume liter l
pressure, strain bar b

Prefixes for the SI System of Units

Factor Prefix Symbol
101 deka da
102 hecto h
103 kilo k
106 mega M
109 giga G
1012 tera T
1015 peta P
1018 exa E
1021 zetta Z
1024 yotta Y

Factor Prefix Symbol
10-1 deci d
10-2 centi c
10-3 milli m
10-6 micro µ
10-9 nano n
10-12 pico p
10-15 femto f
10-18 atto a
10-21 zepto z
10-24 yocto y

The nomenclature in this chapter is based on the standard of the European Standards Committee.