Quantities

functions related to Quantities, physical units and constants

Functions

Predicates

Constants

The Quantities module provides comprehensive support for physical quantities and units. It includes a wide range of physical properties, SI units, derived units, and constants, with automatic unit conversion and dimensional analysis.

Key Concepts

  • Physical quantities with units (like "5 meters" or "72 kilometers per hour")
  • Support for all SI base units and derived units
  • Automatic unit conversion and compatibility checking
  • Physical constants
  • Dimensional analysis
  • Support for currency units

Basic Usage

Creating Quantities

; basic quantities
distance: 100`m         ; 100 meters
time: 9.5`s             ; 9.5 seconds
mass: 75`kg             ; 75 kilograms

; derived units
speed: 60`km/h          ; 60 kilometers per hour
force: 10`N             ; 10 newtons
energy: 50`kWh          ; 50 kilowatt-hours

Unit Conversions

dist: 5`km
print convert dist `m           ; 5000 m

; or using the infix operator
print dist --> `m               ; 5000 m

speed: 90`km/h
print speed --> `m/s            ; 25 m/s

temp: 25`degC
print temp --> `degF            ; 77°F

Unit Compatibility

length1: 5`m
length2: 3`km

; compatible units can be used in calculations
total: length1 + (length2 --> `m)
print total                    ; 3005 m

speed: 100`km/h
time: 2.5`h

; dimensional analysis works automatically
distance: speed * time
print distance                 ; 250 km

Working with Currencies

price: 50`USD
euros: price --> `EUR
print euros                    ; 47.77 € (depends on the current
                               ;          exchange rate, obviously...)

salary: 5000`USD/mo
yearly: salary * 12
print yearly                   ; 60000 $/mo

Common Patterns

Complex Unit Calculations

; calculating power
voltage: 220`V
current: 5`A
power: voltage * current
print power                    ; 1100 V·A

; calculating energy cost
time: 2`h
energy: power * time
price: 0.15`USD/kWh
cost: price * (energy --> `kWh)
print cost                     ; 0.33 $

Using Physical Constants

; gravitational force
G: gravitationalConstant
m1: 5.97e24`kg                  ; mass of Earth
m2: 75`kg                       ; mass of a person
r: 6371000`m                    ; Earth's radius
force: G * m1 * m2 / (r * r)
print to :floating force        ; 736.2513565961324

Available Properties

Physical quantities in Arturo are classified by their properties. Here are some key properties and their dimensions:

Property Dimensions Example
Length L 5m
Time T 10s
Mass M 75kg
Current I 5A
Temperature K 20degC
Amount N 2mol
Luminosity J 100cd
Speed L·T⁻¹ 60km/h
Acceleration L·T⁻² 9.81m/s2
Force L·M·T⁻² 10N
Energy L²·M·T⁻² 100J
Power L²·M·T⁻³ 1000W

Note
There are many more properties available. Use property to inspect any quantity's dimensional formula.

Prefixes

Metric prefixes are supported for most units:

Prefix Symbol Factor
atto a 10⁻¹⁸
femto f 10⁻¹⁵
pico p 10⁻¹²
nano n 10⁻⁹
micro μ 10⁻⁶
milli m 10⁻³
kilo k 10³
mega M 10⁶
giga G 10⁹
tera T 10¹²
peta P 10¹⁵
exa E 10¹⁸

Note
Most units that allow prefixes can use any SI prefix (from atto- to exa-). Prefixes change the unit by the corresponding power of 10.

Supported Units

Base SI Units

Unit Symbol Property Example
meter m Length 5m
second s Time 10s
kelvin K Temperature 300K
gram g Mass 500g
ampere A Current 2A
mole mol Substance 1mol
candela cd Luminosity 100cd

Length Units

Unit Symbol Definition Note
inch in 127/5000 m
foot ft 12 in
yard yd 3 ft
mile mi 5280 ft
nautical mile nmi 1852 m
angstrom Å 10⁻¹⁰ m
light year ly 9.461e15 m
astronomical unit au 1.496e11 m
pixel px 1/96 in
point pt 1/72 in

Area Units

Unit Symbol Definition
acre ac 4840 yd²
hectare ha 10000 m²
barn b 100 ftm²

Volume Units

Unit Symbol Definition
liter L 1000 cm³
gallon gal 231 in³
barrel bbl 42 gal
quart qt 1/4 gal
pint p 1/2 qt
cup cup 1/2 p
fluid ounce floz 1/8 cup
bushel bu 2150.42 in³
cord cord 128 ft³

Mass Units

Unit Symbol Definition
pound lb 0.45359237 kg
ounce oz 1/16 lb
stone st 14 lb
ton ton 2000 lb
metric ton t 1000 kg
carat ct 0.2 g
grain gr 64.79891 mg

Time Units

Unit Symbol Definition
minute min 60 s
hour h 60 min
day day 24 h
week wk 7 day
month mo 2629746 s
year yr 31556952 s

Speed Units

Unit Symbol Definition
kilometers per hour km/h 1000/3600 m/s
miles per hour mph 5280/3600 ft/s
knot kn 1852/3600 m/s
mach mach 340.29 m/s

Force Units

Unit Symbol Definition
newton N 1 kg·m/s²
dyne dyn 10⁻⁵ N
pound-force lbf 4.44822 N

Pressure Units

Unit Symbol Definition
pascal Pa 1 N/m²
bar bar 100000 Pa
atmosphere atm 101325 Pa
torr Torr 133.3224 Pa
psi psi 6894.76 Pa

Energy Units

Unit Symbol Definition
joule J 1 N·m
watt-hour Wh 3600 J
calorie cal 4.184 J
electron volt eV 1.602e-19 J
BTU BTU 1055.06 J

Power Units

Unit Symbol Definition
watt W 1 J/s
horsepower hp 745.7 W

Electric Units

Unit Symbol Definition
volt V 1 W/A
ohm Ω 1 V/A
farad F 1 C/V
henry H 1 V·s/A
weber Wb 1 V·s
tesla T 1 Wb/m²

Angle Units

Unit Symbol Definition
radian rad base unit
degree ° π/180 rad
arcminute ' π/10800 rad
arcsecond " π/648000 rad

Radiation Units

Unit Symbol Definition
becquerel Bq 1/s
gray Gy 1 J/kg
sievert Sv 1 J/kg

Information Units

Unit Symbol Definition
byte B base unit
bit b 1/8 B
kibibyte KiB 1024 B
mebibyte MiB 1024 KiB
gibibyte GiB 1024 MiB
tebibyte TiB 1024 GiB

Tip
Arturo supports many world currencies including: AED, ALL, ARS, AUD, BGN, BHD, BND, BOB, BRL, BWP, CAD, CHF, CLP, CNY, COP, CRC, CZK, DKK, DOP, DZD, EGP, ETB, EUR, FJD, GBP, HKD, HNL, HRK, HUF, IDR, ILS, INR, IRR, ISK, JMD, JOD, JPY, KES, KRW, KWD, KYD, KZT, LBP, LKR, MAD, MDL, MKD, MXN, MUR, MYR, NAD, NGN, NIO, NOK, NPR, NZD, OMR, PAB, PEN, PGK, PHP, PKR, PLN, PYG, QAR, RON, RSD, RUB, SAR, SCR, SEK, SGD, SLL, SOS, SVC, THB, TND, TRY, TTD, TWD, TZS, UAH, UGX, UYU, UZS, VES, VND, XAF, XOF, YER, ZAR, ZMW.

Cryptocurrency codes are also supported: BTC (Bitcoin), ETH (Ethereum), BNB (Binance Coin).