manual:chapter3:units

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manual:chapter3:units [2018/10/25 10:13]
claudio [Operating with Units] 		manual:chapter3:units [2019/09/18 16:55]
jojo1973 First steps of review
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 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. \\ 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]'' \\ ''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''.
 +
 +There is only one exception: prefixes can't be used if the resulting name matches an already existing unit. For example, it's not possible use ''_[min]'' to mean milliinches because ''_[min]'' is already defined and corresponds to the time unit "minute".
 +
 +^  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 ==== ==== Operating with Units ====
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 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''. 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''.
 +
 +To reduce a unit to its base components, use the command ''UBASE''. For example ''1_N'' ''UBASE'' will return ''1_kg*m/s^2''.
 +
 +To extract the value part of a unit object, use the ''UVAL'' command, which will return the object without its unit.
  
 ==== Custom Units ==== ==== Custom Units ====
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 ==== Available Units ==== ==== Available Units ====
  
-This is a list of the units available in the ''Units'' menu on newRPL:+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.
  
-| **Length** |||| +=== Length === 
-| Unit | Unit name | Definition | Description | + 
-| 1_m | metre | 1_m  | Base SI unit of length |  +^ Unit ^ Unit name ^ Definition ^ Description ^ Prefixable ^ 
-| 1_cm | centimetre | 1_cm = 0.01_m | SI length |  +| 1_m | metre | 1_m  | Base SI unit of length | {{fa>check?lg&color=green}} | 
-| 1_mm | millimetre | 1_mm = 0.001_m | SI length |  +| 1_cm | centimetre | 1_cm = 0.01_m | SI, metric | {{fa>times?lg&color=red}} | 
-| 1_yd | yard | 1_yd = 3_ft | US customary length |  +| 1_mm | millimetre | 1_mm = 0.001_m | SI, metric | {{fa>times?lg&color=red}} | 
-| 1_ft | foot | 1_ft = 12_in | US customary length |  +| 1_yd | yard | 1_yd = 3_ft | US Customary | {{fa>times?lg&color=red}} | 
-| 1_in | inch | 1_in = 0.0254_m | US customary length |  +| 1_ft | foot | 1_ft = 12_in | US Customary | {{fa>times?lg&color=red}} |  
-| 1_Mpc | megaparsec | 1_Mpc = 1000000_pc | Astronomical length |  +| 1_in | inch | 1_in = 0.0254_m | US Customary | {{fa>times?lg&color=red}} | 
-| 1_pc | parsec | 1_pc = (648000/π)_au | Astronomical length |  +| 1_Mpc | megaparsec | 1_Mpc = 1000000_pc | Astronomical length | {{fa>times?lg&color=red}} | 
-| 1_lyr | light year | 1_lyr = 365.25_d*c | Astronomical length |  +| 1_pc | parsec | 1_pc = (648000/π)_au | Astronomical length | {{fa>times?lg&color=red}} | 
-| 1_au | astronomical unit | 1_au = 149597870700_m | SI astronomical length |  +| 1_lyr | light year | 1_lyr = 9460730472580800_m | Astronomical length | {{fa>times?lg&color=red}} | 
-| 1_km | kilometre | 1_km = 1000_m | SI length |  +| 1_au | astronomical unit | 1_au = 149597870700_m | SI astronomical length | {{fa>times?lg&color=red}} | 
-| 1_mi | mile | 1_mi = 5280_ft | US customary length |  +| 1_km | kilometre | 1_km = 1000_m | SI, metric | {{fa>times?lg&color=red}} | 
-| 1_nmi | nautical mile | 1_nmi = 1852_m | non-SI length |  +| 1_mi | mile | 1_mi = 5280_ft | US Customary | {{fa>times?lg&color=red}} | 
-| 1_miUS | surveying mile | 1_miUS = 5280_ftUS | US surveying length | +| 1_nmi | nautical mile | 1_nmi = 1852_m | non-SI length | {{fa>times?lg&color=red}} | 
-| 1_chain | surveying chain | 1_chain = 66_ftUS | US surveying length |  +| 1_miUS | surveying mile | 1_miUS = 5280_ftUS | US surveying length | {{fa>times?lg&color=red}} | 
-| 1_rd | rod | 1_rd =16.5_ft | US customary length |  +| 1_chain | surveying chain | 1_chain = 66_ftUS | US surveying length | {{fa>times?lg&color=red}} | 
-| 1_rdUS | surveying rod | 1_rdUS =16.5_ftUS | US surveying length |  +| 1_rd | rod | 1_rd =16.5_ft | US customary length | {{fa>times?lg&color=red}} | 
-| 1_fath | surveying fathom | 1_fath =6_ftUS | US surveying length |  +| 1_rdUS | surveying rod | 1_rdUS =16.5_ftUS | US surveying length | {{fa>times?lg&color=red}} | 
-| 1_ftUS | surveying foot | 1_ftUS = 1200/3937_m | US surveying length |  +| 1_fath | surveying fathom | 1_fath =6_ftUS | US surveying length | {{fa>times?lg&color=red}} | 
-| 1_mil | thousandth of inch | 1_mil = 0.001_in | US customary length |  +| 1_ftUS | surveying foot | 1_ftUS = 1200/3937_m | US surveying length | {{fa>times?lg&color=red}} | 
-| 1_µ | micron or micrometre | 1_µ = 1_µm | SI length |  +| 1_mil | thousandth of inch | 1_mil = 0.001_in | US customary length | {{fa>times?lg&color=red}} | 
-| 1_Å | Ångström | 1_Å = 0.1_nm | non-SI length |  +| 1_µ | micron | 1_µ = 1_µm | SI length | {{fa>times?lg&color=red}} | 
-| 1_fermi | fermi or femtometre | 1_fermi = 1_fm | SI length | +| 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** |||| | **Area** ||||
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 | 1_cu | cup | 1_cu = 1/16_gal | US customary volume |  | 1_cu | cup | 1_cu = 1/16_gal | US customary volume | 
 | 1_ozfl | fluid ounce | 1_ozfl = 1/128_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_fbm | board foot | 1_fbm = 144_in%%^%%3 | US customary volume | 
 | 1_galUK | gallon (UK) | 1_galUK = 0.00454609_m%%^%%3 | Imperial volume |  | 1_galUK | gallon (UK) | 1_galUK = 0.00454609_m%%^%%3 | Imperial volume | 
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 | **Time** |||| | **Time** ||||
 | Unit | Unit name | Definition | Description | | 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_d | day | 1_d = 86400_s | SI time |
 | 1_h | hour | 1_h = 3600_s | SI time |  | 1_h | hour | 1_h = 3600_s | SI time | 
 | 1_min | minute | 1_min = 60_s | SI time |  | 1_min | minute | 1_min = 60_s | SI time | 
 | 1_s | second | 1_s | Base SI unit of 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** |||| | **Speed** ||||
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 | Unit | Unit name | Definition | Description | | Unit | Unit name | Definition | Description |
 | 1_kg | kilogram | 1_kg | Base SI unit of mass |  | 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_lb | pound | 1_lb = 7000_grain | US customary mass | 
 | 1_oz | ounce | 1_oz = 1/16_lb | US customary mass |  | 1_oz | ounce | 1_oz = 1/16_lb | US customary mass | 
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 | 1_ton | tonne | 1_ton = 2000_lb | US customary mass |  | 1_ton | tonne | 1_ton = 2000_lb | US customary mass | 
 | 1_tonUK | tonne (UK) | 1_tonUK = 2240_lb | Imperial 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_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_grain | grain | 1_grain = 64.79891_mg | Imperial mass | 
 | 1_u | unified atomic mass | 1_u = 1.660539040E-27_kg | non-SI 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_mol | mole | 1_mol | Base SI amount of substance | 
 | 1_gmol | gram mole | 1_gmol = 1_mol | non-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** |||| | **Force** ||||
 | Unit | Unit name | Definition | Description | | 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_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_gf | gram-force | 1_gf = 1_g*ga | non-SI force | 
 | 1_kip | kip | 1_kip = 1000_lbf | US customary force |  | 1_kip | kip | 1_kip = 1000_lbf | US customary force | 
 | 1_lbf | pound-force | 1_lbf = 1_lb*ga | 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** |||| | **Energy** ||||
 | Unit | Unit name | Definition | Description | | 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_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_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_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_ft*lbf | foot-pound | 1_ft*lbf = 1_lb*ft*ga | US customary energy | 
 | 1_therm | therm | 1_therm = 100000_Btu | Imperial 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 | | 1_eV | electronvolt | 1_eV = 1.6021766208E-19_J | non-SI energy |
  
 | **Power** |||| | **Power** ||||
 | Unit | Unit name | Definition | Description | | 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_kW | kilowatt | 1_kW = 1000_W | SI power |
 | 1_MW | megawatt | 1_MW = 1000000_W | SI power |  | 1_MW | megawatt | 1_MW = 1000000_W | SI power | 
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 | **Pressure** |||| | **Pressure** ||||
 | Unit | Unit name | Definition | Description | | 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_atm | atmospheric pressure | 1_atm = 101325_Pa | non-SI pressure | 
 | 1_bar | bar | 1_bar = 100000_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_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_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 |  | 1_inHg | inches of mercury (at 0°C) | 1_inHg = 13595.1_kg/m%%^%%3*in*ga | non-SI pressure | 
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 | **Temperature** |||| | **Temperature** ||||
 | Unit | Unit name | Definition | Description | | 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_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_Δ°F | farenheit temperature change | 1_Δ°F = 1_Δ°R | Change of temperature | 
 | 1_K | kelvin | 1_K | Base SI temperature (abs. scale) |  | 1_K | kelvin | 1_K | Base SI temperature (abs. scale) | 
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 | 1_Fdy | faraday | 1_Fdy = 96485.33289_C | non-SI electrical charge |  | 1_Fdy | faraday | 1_Fdy = 96485.33289_C | non-SI electrical charge | 
 | 1_H | henry | 1_H = 1_Wb/A | SI inductance |  | 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_S | siemens | 1_S = 1_1/Ω | SI conductance | 
 | 1_T | tesla | 1_T = 1_Wb/m%%^%%2 | SI magnetic flux density |  | 1_T | tesla | 1_T = 1_Wb/m%%^%%2 | SI magnetic flux density | 
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 | 1_Bq | becquerel | 1_Bq = 1_1/s | SI radiation |  | 1_Bq | becquerel | 1_Bq = 1_1/s | SI radiation | 
 | 1_Ci | curie | 1_Ci = 3.7E10_Bq | non-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** |||| | **Viscosity** ||||
  • manual/chapter3/units.txt
  • Last modified: 2019/11/19 13:34
  • by claudio