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--- manual:chapter3:units [2018/10/25 09:34]
claudio
+++ manual:chapter3:units [2019/11/19 13:34] (current)
claudio [Custom Units]
@@ Line 22: / Line 22: @@
 Exponents within a unit expression can be integer numbers, real numbers or fractional exponents. The use of fractional exponents is always preferred over real numbers because they can be simplified in an exact way. \\
 ''3_[m^(2/3)]'' is always preferred to ''3_[m^0.666667]'' \\
+==== Multiples and Submultiples ====
+Multiples and submultiples of many units are obtained by prefixing them with the standard SI prefixes. Therefore, ''1_dal'' is equivalent to ''10_l'' and ''3.5_MHz'' is equivalent to ''3500000_Hz''.
+SI prefixes can be used with all SI units and many non-SI units where SI prefixes are common usage. Other non-SI units do not accept prefixes.
+^  SI Prefix  ^  Factor  ^  Name  ^
+|  Y   |   $10^{24}$    |  yotta-  |
+|  Z   |   $10^{21}$    |  zetta-  |
+|  E   |   $10^{18}$    |  exa-    |
+|  P   |   $10^{15}$    |  peta-   |
+|  T   |   $10^{12}$    |  tera-   |
+|  G   |   $10^{9}$     |  giga-   |
+|  M   |   $10^{6}$     |  mega-   |
+|  k   |   $10^{3}$     |  kilo-   |
+|  h   |   $10^{2}$     |  hecto-  |
+|  da  |   $10^{1}$     |  deka-   |
+|  d   |   $10^{-1}$    |  deci-   |
+|  c   |   $10^{-2}$    |  centi-  |
+|  m   |   $10^{-3}$    |  milli-  |
+|  µ   |   $10^{-6}$    |  micro-  |
+|  n   |   $10^{-9}$    |  nano-   |
+|  p   |   $10^{-12}$   |  pico-   |
+|  f   |   $10^{-15}$   |  femto-  |
+|  a   |   $10^{-18}$   |  atto-   |
+|  z   |   $10^{-21}$   |  zepto-  |
+|  y   |   $10^{-24}$   |  yocto-  |
 ==== Operating with Units ====
@@ Line 29: / Line 57: @@
 Results of an addition or subtraction between consistent units will produce a result with the units of the first argument (argument in level 2 of the stack at the time of the operation, or the left argument in an algebraic expression).
-This is a list of the units available in the ''Units'' menu on newRPL:
+Unit conversions can be performed directly using the ''CONVERT'' command, which is accessible directly from the keyboard (**LS-6**). For example to convert 100 ml into m^3 simply place the original unit and the new unit on the stack: ''100_ml'' ''1_m^3'' ''CONVERT''.
-| **Length** ||||
+To reduce a unit to its base components, use the command ''UBASE''. For example ''1_N'' ''UBASE'' will return ''1_kg*m/s^2''.
-| Unit | Unit name | Definition | Description |
-| 1_m | metre | 1_m  | Base SI unit of length |
+To extract the value part of a unit object, use the ''UVAL'' command, which will return the object without its unit.
-| 1_cm | centimetre | 1_cm = 0.01_m | SI length |
-| 1_mm | millimetre | 1_mm = 0.001_m | SI length |
+==== Custom Units ====
-| 1_yd | yard | 1_yd = 3_ft | US customary length |
-| 1_ft | foot | 1_ft = 12_in | US customary length |
+Units in newRPL can be arbitrary symbols, not just the ones predefined in the system. For example, adding ''3_apples'' and ''2_apples'' will produce ''5_apples'' as expected. In this case, ''apples'' is a custom unit without a definition. Units without a definition are considered base units. The system already includes base units for mass, length, time, etc. but any number of new base units can be added simply by using new symbols.
-| 1_in | inch | 1_in = 0.0254_m | US customary length |
-| 1_Mpc | megaparsec | 1_Mpc = 1000000_pc | Astronomical length |
+Custom units can also be defined as derived units, in terms of other base units. This is done with the ''UDEFINE'' command. For example typing ''750_ml'' ''%%'mug'%%'' ''UDEFINE'' would define a unit named ''mug'' as 750 ml. From that moment ''mug'' can be used in the exact same way as any system-defined unit, and it will be considered consistent with all other volume units.
-| 1_pc | parsec | 1_pc = (648000/π)_au | Astronomical length |
-| 1_lyr | light year | 1_lyr = 365.25_d*c | Astronomical length |
+Custom units may also accept SI prefixes, but this needs to be explicitly enabled during the unit definition. To create a custom unit that accepts SI prefixes, the name of the unit needs to be preceded by a question mark ''?'' when the unit is defined. For example, following the previous example, for the unit ''mug'' to accept SI prefixes, the definition should be done typing ''750_ml'' ''%%'?mug'%%'' ''UDEFINE'' creates a unit ''mug'' exactly as before, except now ''1_[Mmug]'' ''UBASE'' will produce ''750_m^3'', as expected.
-| 1_au | astronomical unit | 1_au = 149597870700_m | SI astronomical length |
-| 1_km | kilometre | 1_km = 1000_m | SI length |
+New units can also be defined in terms of new (unknown) base units. For example typing ''3_apples'' ''%%'oranges'%%'' ''UDEFINE'' will define ''oranges'' as equivalent to 3 ''apples'', where ''apples'' is a base unit (amount of fruit?) that may or may not have been explicitly defined before.
-| 1_mi | mile | 1_mi = 5280_ft | US customary length |
+From that moment the addition ''2_[oranges]+3_[apples]'' will result in ''3_oranges'' since the units of the result will match the units of the left operand, and the 3 apples were automatically converted to 1 orange.
-| 1_nmi | nautical mile | 1_nmi = 1852_m | non-SI length |
-| 1_miUS | surveying mile | 1_miUS = 5280_ftUS | US surveying length |
+Custom units work systemwide, the command ''ULIST'' returns a list of all the custom units that are defined in the system. To remove a unit definition use the ''UPURGE'' command. Following the previous example, typing ''%%'oranges'%%'' ''UPURGE'' will undefine the unit. Notice that the unit ''oranges'' definition was removed, which means this symbol now represents an unknown base unit, then ''2_[oranges]+3_[apples]'' cannot proceed since oranges and apples are now considered as unrelated base units.
-| 1_chain | surveying chain | 1_chain = 66_ftUS | US surveying length |
-| 1_rd | rod | 1_rd =16.5_ft | US customary length |
-| 1_rdUS | surveying rod | 1_rdUS =16.5_ftUS | US surveying length |
+==== Available Units ====
-| 1_fath | surveying fathom | 1_fath =6_ftUS | US surveying length |
-| 1_ftUS | surveying foot | 1_ftUS = 1200/3937_m | US surveying length |
+This is a list of the units available in the ''Units'' menu on newRPL. All the conversion factors are meant to be exact, not approximated.
-| 1_mil | thousandth of inch | 1_mil = 0.001_in | US customary length |
-| 1_µ | micron or micrometre | 1_µ = 1_µm | SI length |
+=== Length ===
-| 1_Å | Ångström | 1_Å = 0.1_nm | non-SI length |
-| 1_fermi | fermi or femtometre | 1_fermi = 1_fm | SI length |
+^ Unit ^ Unit name ^ Definition ^ Description ^ Prefixable ^
+| 1_m | metre | 1_m  | Base SI unit of length | {{fa>check?lg&color=green}} |
+| 1_cm | centimetre | 1_cm = 0.01_m | SI, metric | {{fa>times?lg&color=red}} |
+| 1_mm | millimetre | 1_mm = 0.001_m | SI, metric | {{fa>times?lg&color=red}} |
+| 1_yd | yard | 1_yd = 3_ft | US Customary | {{fa>times?lg&color=red}} |
+| 1_ft | foot | 1_ft = 12_in | US Customary | {{fa>times?lg&color=red}} |
+| 1_in | inch | 1_in = 0.0254_m | US Customary | {{fa>times?lg&color=red}} |
+| 1_Mpc | megaparsec | 1_Mpc = 1000000_pc | Astronomical length | {{fa>times?lg&color=red}} |
+| 1_pc | parsec | 1_pc = (648000/π)_au | Astronomical length | {{fa>times?lg&color=red}} |
+| 1_lyr | light year | 1_lyr = 9460730472580800_m | Astronomical length | {{fa>times?lg&color=red}} |
+| 1_au | astronomical unit | 1_au = 149597870700_m | SI astronomical length | {{fa>times?lg&color=red}} |
+| 1_km | kilometre | 1_km = 1000_m | SI, metric | {{fa>times?lg&color=red}} |
+| 1_mi | mile | 1_mi = 5280_ft | US Customary | {{fa>times?lg&color=red}} |
+| 1_nmi | nautical mile | 1_nmi = 1852_m | non-SI length | {{fa>times?lg&color=red}} |
+| 1_miUS | surveying mile | 1_miUS = 5280_ftUS | US surveying length | {{fa>times?lg&color=red}} |
+| 1_chain | surveying chain | 1_chain = 66_ftUS | US surveying length | {{fa>times?lg&color=red}} |
+| 1_rd | rod | 1_rd =16.5_ft | US customary length | {{fa>times?lg&color=red}} |
+| 1_rdUS | surveying rod | 1_rdUS =16.5_ftUS | US surveying length | {{fa>times?lg&color=red}} |
+| 1_fath | surveying fathom | 1_fath =6_ftUS | US surveying length | {{fa>times?lg&color=red}} |
+| 1_ftUS | surveying foot | 1_ftUS = 1200/3937_m | US surveying length | {{fa>times?lg&color=red}} |
+| 1_mil | thousandth of inch | 1_mil = 0.001_in | US customary length | {{fa>times?lg&color=red}} |
+| 1_µ | micron | 1_µ = 1_µm | SI length | {{fa>times?lg&color=red}} |
+| 1_Å | ångström | 1_Å = 0.1_nm | non-SI length | {{fa>times?lg&color=red}} |
+| 1_fermi | fermi  | 1_fermi = 1_fm | SI length | {{fa>times?lg&color=red}} |
 | **Area** ||||
@@ Line 87: / Line 138: @@
 | 1_cu | cup | 1_cu = 1/16_gal | US customary volume |
 | 1_ozfl | fluid ounce | 1_ozfl = 1/128_gal | US customary volume |
-| 1_tbsp | table spoon | 1_tbsp = 1/2_ozfl | US customary volume |
+| 1_tbsp | tablespoon | 1_tbsp = 1/2_ozfl | US customary volume |
-| 1_tsp | tea spoon | 1_tsp = 1/6_ozfl | US customary volume |
+| 1_tsp | teaspoon | 1_tsp = 1/6_ozfl | US customary volume |
 | 1_fbm | board foot | 1_fbm = 144_in%%^%%3 | US customary volume |
 | 1_galUK | gallon (UK) | 1_galUK = 0.00454609_m%%^%%3 | Imperial volume |
@@ Line 108: / Line 159: @@
 | **Time** ||||
 | Unit | Unit name | Definition | Description |
-| 1_yr | tropical year | 1_yr = 31556925.9747_sper  | 1952 Ephemeris Time |
+| 1_yr | tropical year | 1_yr = 31556925.9747_s  |  per 1952 Ephemeris Time |
 | 1_d | day | 1_d = 86400_s | SI time |
 | 1_h | hour | 1_h = 3600_s | SI time |
 | 1_min | minute | 1_min = 60_s | SI time |
 | 1_s | second | 1_s | Base SI unit of time |
-| 1_Hz | Hertz | 1_Hz = 1_1/s | SI frequency |
+| 1_Hz | hertz | 1_Hz = 1_1/s | SI frequency |
 | **Speed** ||||
@@ Line 139: / Line 190: @@
 | Unit | Unit name | Definition | Description |
 | 1_kg | kilogram | 1_kg | Base SI unit of mass |
-| 1_g | kilogram | 1_g = 0.001_kg | SI mass |
+| 1_g | gram | 1_g = 0.001_kg | SI mass |
 | 1_lb | pound | 1_lb = 7000_grain | US customary mass |
 | 1_oz | ounce | 1_oz = 1/16_lb | US customary mass |
@@ Line 146: / Line 197: @@
 | 1_ton | tonne | 1_ton = 2000_lb | US customary mass |
 | 1_tonUK | tonne (UK) | 1_tonUK = 2240_lb | Imperial mass |
-| 1_t | Metric tonne | 1_t = 1000_kg | non-SI mass |
+| 1_t | metric tonne | 1_t = 1000_kg | non-SI mass |
 | 1_ozt | troy ounce | 1_ozt = 480_grain | Imperial mass |
-| 1_ct | Metric carat | 1_ct = 200_mg | Metric System mass |
+| 1_ct | metric carat | 1_ct = 200_mg | Metric System mass |
 | 1_grain | grain | 1_grain = 64.79891_mg | Imperial mass |
 | 1_u | unified atomic mass | 1_u = 1.660539040E-27_kg | non-SI mass |
 | 1_mol | mole | 1_mol | Base SI amount of substance |
 | 1_gmol | gram mole | 1_gmol = 1_mol | non-SI amount of substance |
-| 1_lbmol | pound mole | 1_lbmol = 453.59237_mol | US customary substance |
+| 1_lbmol | pound mole | 1_lbmol = 453.59237_mol | US customary amount of substance |
 | **Force** ||||
 | Unit | Unit name | Definition | Description |
-| 1_N | Newton | 1_N = 1_kg*m/s%%^%%2 | SI force |
+| 1_N | newton | 1_N = 1_kg*m/s%%^%%2 | SI force |
 | 1_dyn | dyne | 1_dyn = 1_g*cm/s%%^%%2 | non-SI force |
 | 1_gf | gram-force | 1_gf = 1_g*ga | non-SI force |
 | 1_kip | kip | 1_kip = 1000_lbf | US customary force |
 | 1_lbf | pound-force | 1_lbf = 1_lb*ga | US customary force |
-| 1_pdl | poundal | 1_pdl = = 1_lb*ft/s%%^%%2 | US customary force |
+| 1_pdl | poundal | 1_pdl = 1_lb*ft/s%%^%%2 | US customary force |
 | **Energy** ||||
 | Unit | Unit name | Definition | Description |
-| 1_J | Joule | 1_J = 1_N*m | SI energy |
+| 1_J | joule | 1_J = 1_N*m | SI energy |
 | 1_kW*h | kilowatt-hour | 1_kW*h = 3.6_MJ | non-SI energy |
 | 1_erg | erg | 1_erg = 1_dyn*cm | non-SI energy |
-| 1_kcal | kilo calorie | 1_kcal = 1000_cal | non-SI energy |
+| 1_kcal | kilocalorie (thermochemical) | 1_kcal = 1000_cal | non-SI energy |
-| 1_cal | calorie | 1_cal = 4.184_J | non-SI energy |
+| 1_cal | calorie (thermochemical) | 1_cal = 4.184_J | non-SI energy |
 | 1_Btu | british thermal unit | 1_Btu = =1055.056_J | Imperial energy |
 | 1_ft*lbf | foot-pound | 1_ft*lbf = 1_lb*ft*ga | US customary energy |
 | 1_therm | therm | 1_therm = 100000_Btu | Imperial energy |
-| 1_MeV | mega electronvolt | 1_MeV = 1E6_eV | non-SI energy |
+| 1_MeV | megaelectronvolt | 1_MeV = 1E6_eV | non-SI energy |
 | 1_eV | electronvolt | 1_eV = 1.6021766208E-19_J | non-SI energy |
 | **Power** ||||
 | Unit | Unit name | Definition | Description |
-| 1_W | Watt | 1_W = 1_J/s | SI power |
+| 1_W | watt | 1_W = 1_J/s | SI power |
 | 1_kW | kilowatt | 1_kW = 1000_W | SI power |
 | 1_MW | megawatt | 1_MW = 1000000_W | SI power |
@@ Line 187: / Line 238: @@
 | **Pressure** ||||
 | Unit | Unit name | Definition | Description |
-| 1_Pa | Pascal | 1_Pa = 1_N/m%%^%%2 | SI pressure |
+| 1_Pa | pascal | 1_Pa = 1_N/m%%^%%2 | SI pressure |
 | 1_atm | atmospheric pressure | 1_atm = 101325_Pa | non-SI pressure |
 | 1_bar | bar | 1_bar = 100000_Pa | non-SI pressure |
 | 1_psi | pound per square inch | 1_psi = 1_lbf/in%%^%%2 | US customary pressure |
-| 1_Torr | Torricelli | 1_Torr = 1/760_atm | non-SI pressure |
+| 1_Torr | torr | 1_Torr = 1/760_atm | non-SI pressure |
 | 1_mmHg | millimetres of mercury (at 0°C) | 1_mmHg = 13595.1_kg/m%%^%%3*mm*ga | non-SI pressure |
 | 1_inHg | inches of mercury (at 0°C) | 1_inHg = 13595.1_kg/m%%^%%3*in*ga | non-SI pressure |
@@ Line 198: / Line 249: @@
 | **Temperature** ||||
 | Unit | Unit name | Definition | Description |
-| 1_°C | celsius (or degree celsius) | 1_°C Zero: 0_°C → 273.15_K | Base SI temperature (rel. scale) |
+| 1_°C | celsius (or degree Celsius) | 1_°C Zero: 0_°C → 273.15_K | Base SI temperature (rel. scale) |
 | 1_Δ°C | celsius temperature change | 1_Δ°C = 1_ΔK | Change of temperature |
-| 1_°F | farenheit (or degree farenheit) | 1_°F Zero: 0_°F → 459.67_°R | US cust. temp. (rel. scale) |
+| 1_°F | farenheit (or degree Farenheit) | 1_°F Zero: 0_°F → 459.67_°R | US cust. temp. (rel. scale) |
 | 1_Δ°F | farenheit temperature change | 1_Δ°F = 1_Δ°R | Change of temperature |
 | 1_K | kelvin | 1_K | Base SI temperature (abs. scale) |
@@ Line 217: / Line 268: @@
 | 1_Fdy | faraday | 1_Fdy = 96485.33289_C | non-SI electrical charge |
 | 1_H | henry | 1_H = 1_Wb/A | SI inductance |
-| 1_mho | mho (Siemens) | 1_mho = 1_S | non-SI conductance |
+| 1_mho | mho | 1_mho = 1_S | non-SI conductance |
 | 1_S | siemens | 1_S = 1_1/Ω | SI conductance |
 | 1_T | tesla | 1_T = 1_Wb/m%%^%%2 | SI magnetic flux density |
@@ Line 250: / Line 301: @@
 | 1_Bq | becquerel | 1_Bq = 1_1/s | SI radiation |
 | 1_Ci | curie | 1_Ci = 3.7E10_Bq | non-SI radiation |
-| 1_R | rontgen | 1_R = 2.58E-4_C/kg | non-SI radiation |
+| 1_R | roentgen | 1_R = 2.58E-4_C/kg | non-SI radiation |
 | **Viscosity** ||||