Conversions
Unit conversions
Basic conversions
The conversion operator -> can be used to convert the physical quantity on its left hand side
to a different unit. For example:
> 120 km/h -> mph
= 74.5645 mph [Velocity]
> 1600 kcal / day -> W
= 77.4815 W [Power]
> 4 million ฿ -> €
= 109066 € [Money]
The right hand side can also be a more complex expression:
Grandpa Simpson
Quote
"The metric system is the tool of the devil! My car gets 40 rods to the hogshead and that's the way I likes it." — Grandpa Simpson, A Star Is Burns (S06E18)
To convert the mileage of Grandpa's car to miles per gallon, you can write:
Seeing this, we might actually want to convert to feet per gallon instead:
Supporters of Marge's side may instead want to convert to liters per 100 km:
By the way, if you are curious why fuel economy is inferred as having a physical dimension of an (inverse) area, you might enjoy reading (the latter half of) this "what if?" article. The first half of that article is also available as a Numbat program.
Advanced conversions
When the right hand side expression has a magnitude other than 1, the result shows how many times the right hand side fits into the left hand side. For example, to find out how many 45-minute slots fit into 6 hours, you can write:
Concorde's Mach number
Concorde flew at a speed of 2180 km/h and had a cruising altitude of 17,000 m where the air temperature is around -60 °C. We can convert Concorde's velocity to the speed of sound at that temperature to find out that it cruised at Mach 2:
If you want to convert a quantity to the same unit as another quantity, you can use the unit_of(…) function:
Temperature conversions
Temperature units like °C (degree Celsius) and °F (degree Fahrenheit) are special because they are not just scaled versions of the base unit (Kelvin), but also have an offset.
In Numbat, only the base unit Kelvin (K, kelvin) is an actual unit of type Temperature. The other temperature units can only be used to enter temperature values, and as
the target of a conversion. When you enter an expression like 25 °C, it is immediately converted to 298.15 K, and when °C and °F are used on the right hand side of a
unit conversion, you will only get the plain number as a result (without the unit). You can still do useful computations and conversions with these units. For example:
If your keyboard layout doesn't contain the ° symbol, you can also use celsius/fahrenheit or degree_celsius/degree_fahrenheit instead of °C/°F.
Alternatively, you can also use Numbat's Unicode input feature and type \degree<tab> to get the ° symbol.
Computations with °C and °F
You need to be extra careful when doing computations with °C and °F. Numbat does currently not prevent you from
doing something like 10 °C + 1 °C, even if the result is probably not what you expect. Since each of these
values will be converted to Kelvin before the addition, the result will be 557.3 K (or 284.15 °C), and not
11 °C. If you really want to add two temperatures, one of them should be a temperature difference expressed
in K (e.g. 10 °C + 1 K). Subtracting two temperatures is always fine, since any offsets will cancel out.
For example, 20 °C - 10 °C will correctly give a result of 10 K.
Conversion functions
The conversion operator -> (or to) can not just be used for unit conversions, but also for other types of conversions.
The way this is set up in Numbat is that you can call x -> f for any function f that takes a single argument of the same type as x.
The following functions are available for this purpose:
# Convert a date and time to a Unix timestamp
now() -> unixtime_s
# Convert a date and time to a different timezone
now() -> tz("Asia/Kathmandu")
# Convert a duration to years, months, days, hours, minutes, seconds
10 million seconds -> human
# Convert an angle to degrees, minutes, seconds (48° 46′ 32″)
48.7756° -> DMS
# Convert an angle to degrees, decimal minutes (48° 46.536′)
48.7756° -> DM
# Convert a length to feet and inches
1.75 m -> feet_and_inches
# Convert a mass to pounds and ounces
70 kg -> pounds_and_ounces
# Convert a number to its binary representation
42 -> bin
# Convert a number to its octal representation
42 -> oct
# Convert a number to its hexadecimal representation
2^31-1 -> hex
# Convert a code point number to a character
0x2764 -> chr
# Convert a character to a code point number
"❤" -> ord
# Convert a string to upper/lower case
"numbat is awesome" -> uppercase
"vier bis elf weiße Querbänder" -> lowercase
Note that the tz(…) call above returns a function, i.e. the right hand side of
the conversion operator is still a function.
Alternative syntax
You can also use the to keyword instead of the -> operator for conversions. Instead of the
ASCII arrow, you can also use Unicode arrows (x → y or x ➞ y).