Unit Parser

Unit Parser

This library is primarily for parsing strings representing physical quantities, like “5 feet” or “88 miles_per_hour”. It can also be used for converting between compatible units and doing basic arithmetic operations.

Install from PyPI:

$ pip install unit_parser

Or grab the source from Github.


When I worked at Boeing, I was working on this computer program that did something with satellites. There were hundreds of inputs to the program, that were managed via input files in “key: value” format. Some of the inputs had to be in kilometers, and some in nautical miles because people in the Aerospace industry love nautical miles. It was hard to keep it straight, so we starting using keys like, “key_km: value”. This is a form of Hungarian notation. If the key had a suffix of km, you knew the input had to be in kilometers.

This resolved the confusion, but sometimes we knew what an input needed to be in nautical miles, and so I had to convert before typing the value, multiplying by 1.852 (this number is forever burned in my brain). That doesn’t seem that bad, but it did introduce a failure point. What if I mistyped “1.852”? To double check the input, I’d have to re-copy the number from my email into the calculator and re-multiply by 1.852, which was kind of a hassle.

Fast-forward a few years to when I was developing some command line utilities for brewing and planning beer recipes. Like satellites, this involves handling physical quantities like water volumes, grain and hop masses, and temperatures. (Unlike satellites, nautical miles are nowhere in sight.) I wanted a more flexible approach to specifying the inputs, so I hatched upon an idea to turn the Hungarian notation on its head. Instead of including the unit in the key, I would include it in the value. So instead of specifying “water_volume_gallons: 3”, I would do “water_volume: 3 gallons”. Instead of requiring the input to be in liters, the volume could be specified in whatever units are most convenient, and the parser could do the conversion.


The parsing function does double duty as a method for converting between units and is thus called “convert”.

  >>> from unit_parser import unit_parser
  >>> up = unit_parser()
  >>> up.convert("3 gallons", "liters")

It may seem a little strange to have the number as part of the string, but keep in mind this function is used in the context of converting text inputs. For convenience, the—perhaps more intuitive—syntax works as well:

  >>> up.convert(3, "gallons", "liters")

Note the unit parser must be initialized before being used by calling the unit_parser() function without any arguments. That uses the built-in unit specification file to define the units recognized by this library. If a unit is not supported, you can create your own unit specification file and provide the file name to this function.

The next thing we see is that physical quantities and units are represented by strings. I find this to be the most intuitive way of interacting with physical quantities. (Aside, something like “3 gallons” is a physical quantity, while “liters” is a unit.)

Since we represent physical quantities by strings, it is trivial to use the convert function to parse an input in unknown units, but ensure it is in the appropriate units for the needs of the program. For example, suppose we have a program that does calculations on volumes of water. Suppose there is an input (e.g. from a JSON file) representing how much volume of water is to be used. The user is free to specify the input in whatever units are most convenient, e.g. “2 gallons”. The code that is parsing this input might call:

  >>> import json
  >>> from unit_parser import unit_parser
  >>> up = unit_parser()
  >>> config = json.load(open('example.json', 'r'))
  >>> water_volume = config['water_volume']
  >>> water_volume_liters = up.convert(water_volume, "liters")

In this way, no assumptions need to be made about what units the input is in. The code requires the water volume to be expressed in liters, but it doesn’t need to know or care how it was specified.

Although the above example seems trivial, perhaps the most interesting feature is the flexible unit specification parsing. Units may be specified by a definition file (built-in, or provide your own!), or by combinations of units defined in that file.

For example, if ‘second’, ‘meter’, and ‘kilogram’ are defined by the file, the specification ‘kilogram_meter_per_second_squared’ is valid and parsed as expected. These compound specifications consist of tokens separated by underscores. Tokens include previously defined units like ‘kilogram’ as well as the special keywords ‘per’, ‘squared’, and ‘cubed’.

The keyword ‘per’ may be used at most once per specification and directs that all subsequent tokens belong in the denominator of the unit.

The keywords ‘squared’ and ‘cubed’ indicate that the preceding token should be repeated once or twice more, respectively. They cannot be daisy chained, for example: ‘meters_squared_squared’ is not permitted, but ‘meters_squared_meters_squared’ or ‘meters_cubed_meters’ would be. They also only apply to the preceding token, so ‘second_second_meter_meter’ is equivalent to ‘second_squared_meter_squared’ but not ‘second_meter_squared’.

Finally, ‘second’, ‘seconds’, and ‘sec’ are not automatically treated as equivalent units, but the unit definition file can and does create these as if they were aliases. For example, ‘seconds’ is defined as ‘1 second’.

We also permit simple arithmetic operations on units. There are functions “add”, “subtract”, “multiply”, and “divide”. Each function takes three arguments: two physical quantities, and the desired units of the answer.

  >>> from unit_parser import unit_parser
  >>> up = unit_parser()
  >>> up.add("5 meters", "2 feet", "yards")
  >>> up.subtract("5 meters", "2 feet", "yards")
  >>> up.multiply("5 meters_per_sec_squared", "2 kg", "pounds")
  >>> up.divide("5 meters", "2 sec", "mph")

As mentioned above, this library ships with a unit specification file. It contains many of the most common units, but you may find some glaring omissions. For your particular use case, you may prefer to create your own unit specification file and include that with your application. The unit specification file syntax is simple, if not intuitive. The file is plain-text, with key-value pairs separated by a colon. Comments may be included and begin with “#blessed”. Units are either specified as primitives, or in terms of other units. A primitive definition consists of specifying the signature of the unit, which is represented as a vector of non-negative integers. For example:

second: [1 0 0]

The entries of this vector correspond to the exponents of units in an arbitrary order that nonetheless needs to be consistent throughout the application. We might arbitrarily decide that time units go first, then length, then mass. Then since force has dimension mass times length divided by time squared, all units of force have signature [-2 1 1]. The way we define the second really just tells the program which index (the first) corresponds to a particular primitive. A more complete specification might look like this:

second:   [1 0 0]
meter:    [0 1 0]
kilogram: [0 0 1]
minute:   60 second
hour:     60 minute
#blessed  We can define a newton either like this:
newton:   1 kilogram_meter_per_second_squared
#blessed  or like this:
#blessed  newton: [-2 1 1]
#blessed  (first way preferred).

Once we have defined the “primitive” units, it is simple and intuitive to define other units recursively in terms of previously specified units. For example, the newton could have been defined in terms of its signature, but it is better to define it in terms of kilograms, meters, and seconds. A pound (of force) could not have been defined in terms of its signature, because although it has the same signature, it has a different quantity. Meaning, a pound is not equal to one kilogram meter per second squared, and defining units in terms of signatures implicitly assumes the quantity is one.

The included unit specification file uses MKS (meters, kilograms, seconds) as the base, but as long as the internal specification is consistent, that is transparent to the user of such a file. A unit specification file using imperial units as the base would be just as valid, and the end user would never even notice.

If you are the sort of person that enjoys reading esoteric Wikipedia pages, the flexible syntax gives the fun opportunity to look up the official definitions of units, and using that in the file. For example, it turns out the slug, which is a unit of mass in the imperial system, is actually defined as one pound of force times one second squared per foot. So this unit of mass is actually defined in terms of a unit of force, even though conceptually mass seems like the more primitive notion! The included unit file tries to be faithful to these definitions. The reader may quite reasonably ask if it makes any difference. The answer is no, except perhaps for the fun of it. (If you are not the sort of person who enjoys reading esoteric Wikipedia articles, this whole paragraph makes me sound like a weirdo. The “#blessed” thing above doesn’t reflect well on me either.)

Finally, this library ships with a command line utility called “convert”. This can be run from the command line like so:

$ convert 5 feet to meters

(The “to” is optional syntactic sugar, but I find it more intuitive to include it.)

Bob Wilson
Bob Wilson
Data Scientist

The views expressed on this blog are Bob’s alone and do not necessarily reflect the positions of current or previous employers.