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manual:chapter3:units [2018/10/25 09:08] claudio |
manual:chapter3:units [2019/11/19 13:34] claudio [Custom Units] |
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Units are objects that have 2 separate parts: the value and the unit per se. The value is usually a real number, but units may be attached to other numerical objects as well, for example complex numbers and vectors or matrices can have associated units. The unit part is entered using the underscore '' | Units are objects that have 2 separate parts: the value and the unit per se. The value is usually a real number, but units may be attached to other numerical objects as well, for example complex numbers and vectors or matrices can have associated units. The unit part is entered using the underscore '' | ||
+ | |||
The unit is an algebraic expression combining one or more unit symbols, and may be optionally surrounded by square brackets. The brackets are optional for stack input, but mandatory when units are used within a symbolic expression (to separate the unit from other algebraic operations). The '' | The unit is an algebraic expression combining one or more unit symbols, and may be optionally surrounded by square brackets. The brackets are optional for stack input, but mandatory when units are used within a symbolic expression (to separate the unit from other algebraic operations). The '' | ||
+ | |||
Examples of valid unit objects are: \\ | Examples of valid unit objects are: \\ | ||
'' | '' | ||
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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. \\ | ||
'' | '' | ||
+ | |||
+ | ==== Multiples and Submultiples ==== | ||
+ | |||
+ | Multiples and submultiples of many units are obtained by prefixing them with the standard SI prefixes. Therefore, '' | ||
+ | |||
+ | 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 | ||
+ | | Y | ||
+ | | Z | ||
+ | | E | ||
+ | | P | ||
+ | | T | ||
+ | | G | ||
+ | | M | ||
+ | | k | ||
+ | | h | ||
+ | | da | $10^{1}$ | ||
+ | | d | ||
+ | | c | ||
+ | | m | ||
+ | | µ | ||
+ | | n | ||
+ | | p | ||
+ | | f | ||
+ | | a | ||
+ | | z | ||
+ | | y | ||
+ | |||
+ | ==== Operating with Units ==== | ||
Unit objects can be operated upon normally, and the system will perform all the necessary unit conversions in the background. Unit consistency is strictly enforced for addition and subtraction, | Unit objects can be operated upon normally, and the system will perform all the necessary unit conversions in the background. Unit consistency is strictly enforced for addition and subtraction, | ||
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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). | 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). | ||
+ | Unit conversions can be performed directly using the '' | ||
- | This is a list of the units available in the '' | + | To reduce |
- | | **Length** |||| | + | To extract the value part of a unit object, use the '' |
- | | Unit | Unit name | Definition | + | |
- | | 1_m | metre | 1_m | Base SI unit of length | | + | ==== Custom Units ==== |
- | | 1_cm | centimetre | 1_cm = 0.01_m | SI length | + | |
- | | 1_mm | millimetre | 1_mm = 0.001_m | SI length | + | Units in newRPL can be arbitrary symbols, not just the ones predefined in the system. For example, adding '' |
- | | 1_yd | yard | 1_yd = 3_ft | US customary length | + | |
- | | 1_ft | foot | 1_ft = 12_in | US customary length | + | Custom units can also be defined as derived units, in terms of other base units. This is done with the '' |
- | | 1_in | inch | 1_in = 0.0254_m | US customary length | + | |
- | | 1_Mpc | megaparsec | 1_Mpc = 1000000_pc | 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 ''?'' |
- | | 1_pc | parsec | 1_pc = (648000/ | + | |
- | | 1_lyr | light year | 1_lyr = 365.25_d*c | + | New units can also be defined in terms of new (unknown) base units. For example typing '' |
- | | 1_au | astronomical unit | 1_au = 149597870700_m | SI astronomical length | | + | From that moment the addition '' |
- | | 1_km | kilometre | 1_km = 1000_m | SI length | + | |
- | | 1_mi | mile | 1_mi = 5280_ft | US customary length | + | Custom units work systemwide, the command '' |
- | | 1_nmi | nautical mile | 1_nmi = 1852_m | non-SI length | | + | |
- | | 1_miUS | surveying mile | 1_miUS = 5280_ftUS | US surveying length | | + | |
- | | 1_chain | surveying chain | 1_chain = 66_ftUS | US surveying length | | + | ==== Available Units ==== |
- | | 1_rd | rod | 1_rd =16.5_ft | US customary length | | + | |
- | | 1_rdUS | surveying rod | 1_rdUS =16.5_ftUS | US surveying length | | + | This is a list of the units available in the '' |
- | | 1_fath | surveying fathom | 1_fath =6_ftUS | US surveying length | | + | |
- | | 1_ftUS | surveying foot | 1_ftUS = 1200/3937_m | US surveying length | | + | === Length |
- | | 1_mil | thousandth of inch | 1_mil = 0.001_in | US customary length | | + | |
- | | 1_µ | micron | + | ^ Unit ^ Unit name ^ Definition |
- | | 1_Å | Ångström | + | | 1_m | metre | 1_m | Base SI unit of length |
- | | 1_fermi | fermi or femtometre | + | | 1_cm | centimetre | 1_cm = 0.01_m | SI, metric | {{fa> |
+ | | 1_mm | millimetre | 1_mm = 0.001_m | SI, metric | {{fa> | ||
+ | | 1_yd | yard | 1_yd = 3_ft | US Customary | {{fa> | ||
+ | | 1_ft | foot | 1_ft = 12_in | US Customary | {{fa> | ||
+ | | 1_in | inch | 1_in = 0.0254_m | US Customary | {{fa> | ||
+ | | 1_Mpc | megaparsec | 1_Mpc = 1000000_pc | Astronomical length | ||
+ | | 1_pc | parsec | 1_pc = (648000/ | ||
+ | | 1_lyr | light year | 1_lyr = 9460730472580800_m | ||
+ | | 1_au | astronomical unit | 1_au = 149597870700_m | SI astronomical length | ||
+ | | 1_km | kilometre | 1_km = 1000_m | SI, metric | {{fa> | ||
+ | | 1_mi | mile | 1_mi = 5280_ft | US Customary | {{fa> | ||
+ | | 1_nmi | nautical mile | 1_nmi = 1852_m | non-SI length | ||
+ | | 1_miUS | surveying mile | 1_miUS = 5280_ftUS | US surveying length | ||
+ | | 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 | ||
+ | | 1_fath | surveying fathom | 1_fath =6_ftUS | US surveying length | ||
+ | | 1_ftUS | surveying foot | 1_ftUS = 1200/3937_m | US surveying length | ||
+ | | 1_mil | thousandth of inch | 1_mil = 0.001_in | US customary length | ||
+ | | 1_µ | micron | 1_µ = 1_µm | SI length | ||
+ | | 1_Å | ångström | ||
+ | | 1_fermi | fermi | 1_fermi = 1_fm | SI length | ||
| **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_tsp | tea spoon | 1_tsp = 1/6_ozfl | US customary volume | | + | | 1_tsp | teaspoon |
| 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 | + | | 1_yr | tropical year | 1_yr = 31556925.9747_s |
| 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 | 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 | + | | 1_t | metric |
| 1_ozt | troy ounce | 1_ozt = 480_grain | Imperial mass | | | 1_ozt | troy ounce | 1_ozt = 480_grain | Imperial mass | | ||
- | | 1_ct | Metric | + | | 1_ct | metric |
| 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 |
| **Force** |||| | | **Force** |||| | ||
| Unit | Unit name | Definition | Description | | | Unit | Unit name | Definition | Description | | ||
- | | 1_N | Newton | + | | 1_N | newton |
| 1_dyn | dyne | 1_dyn = 1_g*cm/ | | 1_dyn | dyne | 1_dyn = 1_g*cm/ | ||
| 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/ | + | | 1_pdl | poundal | 1_pdl = 1_lb*ft/ |
| **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 | kilocalorie (thermochemical) |
- | | 1_cal | calorie | 1_cal = 4.184_J | non-SI energy | | + | | 1_cal | calorie |
| 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 | megaelectronvolt |
| 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 | pascal |
| 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/ | | 1_psi | pound per square inch | 1_psi = 1_lbf/ | ||
- | | 1_Torr | Torricelli | + | | 1_Torr | torr | 1_Torr = 1/760_atm | non-SI pressure | |
| 1_mmHg | millimetres of mercury (at 0°C) | 1_mmHg = 13595.1_kg/ | | 1_mmHg | millimetres of mercury (at 0°C) | 1_mmHg = 13595.1_kg/ | ||
| 1_inHg | inches of mercury (at 0°C) | 1_inHg = 13595.1_kg/ | | 1_inHg | inches of mercury (at 0°C) | 1_inHg = 13595.1_kg/ | ||
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| **Temperature** |||| | | **Temperature** |||| | ||
| Unit | Unit name | Definition | Description | | | Unit | Unit name | Definition | Description | | ||
- | | 1_°C | celsius (or degree | + | | 1_°C | celsius (or degree |
| 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 | + | | 1_°F | farenheit (or degree |
| 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 | 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/ | | 1_T | tesla | 1_T = 1_Wb/ | ||
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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 | roentgen |
| **Viscosity** |||| | | **Viscosity** |||| |