Ruby Units

Kevin C. Olbrich, Ph.D.

Project page: http://github.com/olbrich/ruby-units

Introduction

Many technical applications make use of specialized calculations at some point. Frequently, these calculations require unit conversions to ensure accurate results. Needless to say, this is a pain to properly keep track of, and is prone to numerous errors.

Solution

The 'Ruby units' gem is designed to simplify the handling of units for scientific calculations. The units of each quantity are specified when a Unit object is created and the Unit class will handle all subsequent conversions and manipulations to ensure an accurate result.

Installation

This package requires Ruby 3.2 or later.

This package may be installed using:

gem install ruby-units

or add this to your Gemfile

gem 'ruby-units'

Usage

unit = Unit.new("1")                 # constant only
unit = Unit.new("mm")                # unit only (defaults to a scalar of 1)
unit = Unit.new("1 mm")              # create a simple unit
unit = Unit.new("1 mm/s")            # a compound unit
unit = Unit.new("1 mm s^-1")         # in exponent notation
unit = Unit.new("1 kg*m^2/s^2")      # complex unit
unit = Unit.new("1 kg m^2 s^-2")     # complex unit
unit = Unit.new("1 mm")              # shorthand
unit = "1 mm".to_unit                # convert string object
unit = object.to_unit                # convert any object using object.to_s
unit = Unit.new('1/4 cup')           # Rational number
unit = Unit.new('1+1i mm')           # Complex Number
unit = Unit.new(scalar: 1.5, numerator: ["<meter>"], denominator: ["<second>"])  # keyword arguments

Rules

1. only 1 quantity per unit (with 2 exceptions... 6'5" and '8 lbs 8 oz')
2. use SI notation when possible
3. spaces in units are allowed, but ones like '11/m' will be recognized as '11 1/m'.

Unit compatibility

Many methods require that the units of two operands are compatible. Compatible units are those that can be easily converted into each other, such as 'meters' and 'feet'.

unit1 =~ unit2                  #=> true if units are compatible
unit1.compatible?(unit2)        #=> true if units are compatible

Unit Math

Unit#+()      # Add. only works if units are compatible
Unit#-()      # Subtract. only works if units are compatible
Unit#*()      # Multiply.
Unit#/()      # Divide.
Unit#**()     # Exponentiate.  Exponent must be an integer, can be positive,  negative, or zero
Unit#inverse  # Returns 1/unit
Unit#abs      # Returns absolute value of the unit quantity.  Units are preserved
Unit#ceil     # rounds quantity to next highest integer
Unit#floor    # rounds quantity down to next lower integer
Unit#round    # rounds quantity to nearest integer
Unit#truncate # truncates quantity to an integer
Unit#to_int   # returns the quantity as an integer
Unit#divmod   # divide and return quotient and remainder
Unit#remainder# returns remainder of division
Unit#quo      # returns quotient as a float or complex

Unit will coerce other objects into a Unit if used in a formula. This means...

Unit.new("1 mm") + "2 mm"  == Unit.new("3 mm")

This will work as expected so long as you start the formula with a Unit object.

Conversions & Comparisons

Units can be converted to other units in a couple of ways.

unit.convert_to('ft')             # convert
unit1 = unit >> "ft"              # convert to 'feet'
unit >>= "ft"                     # convert and overwrite original object
unit3 = unit1 + unit2             # resulting object will have the units of unit1
unit3 = unit1 - unit2             # resulting object will have the units of unit1
unit1 <=> unit2                   # does comparison on quantities in base units, throws an exception if not compatible
unit1 === unit2                   # true if units and quantity are the same, even if 'equivalent' by <=>
unit1 + unit2 >> "ft"             # converts result of math to 'ft'
(unit1 + unit2).convert_to('ft')  # converts result to 'ft'

Any object that defines a to_unit method will be automatically coerced to a unit during calculations.

Text Output

Units will display themselves nicely based on the display_name for the units and prefixes. Since Unit implements a Unit#to_s, all that is needed in most cases is:

"#{Unit.new('1 mm')}"  #=> "1 mm"

The to_s also accepts some options.

Unit.new('1.5 mm').to_s("%0.2f")  # "1.50 mm".  Enter any valid format
                                  #   string.  Also accepts strftime format
Unit.new('10 mm').to_s("%0.2f in")# "0.39 in". can also format and convert in
                                  # the same time.
Unit.new('1.5 mm').to_s("in")     # converts to inches before printing
Unit.new("2 m").to_s(:ft)         # returns 6'7"
Unit.new("100 kg").to_s(:lbs)     # returns 220 lbs, 7 oz
Unit.new("100 kg").to_s(:stone)   # returns 15 stone, 10 lb

You can also use Ruby's standard string formatting operator (%) with units:

'%0.2f' % '1 mm'.to_unit          # "1.00 mm"
'%0.2f in' % '1 mm'.to_unit       # "0.04 in" - format and convert
'%.2e' % '1000 m'.to_unit         # "1.00e+03 m" - scientific notation

Strings can be converted to units using the convert_to method:

'10 mm'.convert_to('cm')          # converts directly to centimeters
'100 km/h'.convert_to('m/s')      # converts compound units

Time Helpers

Ruby-units extends the Time, Date, and DateTime classes to support unit-based arithmetic, allowing you to add or subtract durations from time objects naturally.

Adding and Subtracting Durations

Time.now + Unit.new("10 min")   #=> 10 minutes from now
Time.now - Unit.new("2 hours")  #=> 2 hours ago

Date.today + Unit.new("1 week")  #=> 7 days from today
Date.today - Unit.new("30 days") #=> 30 days ago

Important: When adding or subtracting large time units (years, decades, centuries), the duration is first converted to days and rounded to maintain calendar accuracy. This means 1 year is treated as approximately 365 days rather than an exact number of seconds.

Time.now + Unit.new("1 year")    #=> Approximately 365 days from now
Time.now - Unit.new("1 decade")  #=> Approximately 3650 days ago

For more precise durations, use smaller units (hours, minutes, seconds):

Time.now + Unit.new("24 hours")  #=> Exactly 24 hours from now

Converting Time and Date to Units

You can convert Time objects to units representing the duration since the Unix epoch:

Time.now.to_unit              #=> Duration in seconds since epoch
Time.now.to_unit('hours')     #=> Duration in hours since epoch
Time.now.to_unit('days')      #=> Duration in days since epoch

You can convert Date objects to units representing days since the Julian calendar start:

Date.today.to_unit            #=> Duration in days since Julian calendar start
Date.today.to_unit('week')    #=> Duration in weeks since Julian calendar start
Date.today.to_unit('year')    #=> Duration in years since Julian calendar start

Creating Time from Units

Use Time.at to create a Time object from a duration unit:

Time.at(Unit.new("1000 seconds"))           #=> Time 1000 seconds after epoch
Time.at(Unit.new("1 hour"), 500, :ms)       #=> Time 1 hour + 500 milliseconds after epoch

Convenience Methods

The Time.in method provides a shorthand for calculating future times:

Time.in('5 min')    #=> 5 minutes from now
Time.in('2 hours')  #=> 2 hours from now

Duration Formats

Durations may be entered as 'HH:MM:SS, usec' and will be returned in 'hours'.

Unit.new('1:00')     #=> 1 h
Unit.new('0:30')     #=> 0.5 h
Unit.new('0:30:30')  #=> 0.5 h + 30 sec

If only one ":" is present, it is interpreted as the separator between hours and minutes.

Compatibility with Chronic

Several helpers are available for working with natural language time parsing. Note: If you include the 'Chronic' gem, you can specify times in natural language.

Unit.new('min').since(DateTime.parse('9/18/06 3:00pm'))

Range Errors and DateTime Fallback

If time arithmetic would result in a date outside the valid range for the Time class (typically 1970-2038 on 32-bit systems), ruby-units automatically falls back to using DateTime objects to handle the calculation.

Ranges

[Unit.new('0 h')..Unit.new('10 h')].each {|x| p x}

works so long as the starting point has an integer scalar

Math Functions

Ruby-units extends the Math module to support Unit objects seamlessly. All trigonometric and mathematical functions work with units, handling conversions automatically.

Supported Functions

Trigonometric Functions (angles converted to radians automatically):

• sin, cos, tan - Standard trigonometric functions
• sinh, cosh, tanh - Hyperbolic trigonometric functions

Inverse Trigonometric Functions (return angles in radians as Unit objects):

• asin, acos, atan - Inverse trigonometric functions
• atan2 - Two-argument arctangent for full quadrant determination

Root Functions (preserve dimensional analysis):

• sqrt - Square root (e.g., √(4 m²) = 2 m)
• cbrt - Cube root (e.g., ³√(27 m³) = 3 m)

Other Functions:

• hypot - Euclidean distance calculation with units
• log, log10 - Logarithmic functions (extract scalar from units)

Examples

# Trigonometric functions with angle units
Math.sin(Unit.new("90 deg"))        #=> 1.0
Math.cos(Unit.new("180 deg"))       #=> -1.0
Math.tan(Unit.new("45 deg"))        #=> 1.0

# Works with different angle units
Math.sin(Unit.new("1.571 rad"))     #=> 1.0 (approximately π/2)
Math.cos(Unit.new("3.14159 rad"))   #=> -1.0 (approximately π)

# Inverse functions return Unit objects in radians
Math.asin(0.5)                       #=> Unit.new("0.524 rad") (30°)
Math.atan(1)                         #=> Unit.new("0.785 rad") (45°)
Math.acos(0)                         #=> Unit.new("1.571 rad") (90°)

# Root functions preserve dimensional analysis
Math.sqrt(Unit.new("4 m^2"))        #=> Unit.new("2 m")
Math.cbrt(Unit.new("27 m^3"))       #=> Unit.new("3 m")
Math.sqrt(Unit.new("9 kg*m/s^2"))   #=> Unit.new("3 kg^(1/2)*m^(1/2)/s")

# Hypot for distance calculations (Pythagorean theorem)
Math.hypot(Unit.new("3 m"), Unit.new("4 m"))     #=> Unit.new("5 m")
Math.hypot(Unit.new("30 cm"), Unit.new("40 cm")) #=> Unit.new("50 cm")

# atan2 for converting Cartesian to polar coordinates
Math.atan2(Unit.new("1 m"), Unit.new("1 m"))     #=> Unit.new("0.785 rad") (45°)
Math.atan2(Unit.new("1 m"), Unit.new("0 m"))     #=> Unit.new("1.571 rad") (90°)

# Logarithmic functions (units must be compatible for input)
Math.log10(Unit.new("100"))         #=> 2.0
Math.log(Unit.new("2.718"))         #=> 1.0 (natural log, approximately)
Math.log(Unit.new("8"), 2)          #=> 3.0 (log base 2)

Note: Trigonometric functions expect angular units or dimensionless numbers. If you pass a Unit with dimensions (like meters), it will be converted to radians, which may produce unexpected results.

Temperatures

Ruby-units makes a distinction between a temperature (which technically is a property) and degrees of temperature (which temperatures are measured in).

Temperature units (i.e., 'tempK') can be converted back and forth, and will take into account the differences in the zero points of the various scales. Differential temperature (e.g., Unit.new('100 degC')) units behave like most other units.

Unit.new('37 tempC').convert_to('tempF')   #=> 98.6 tempF

Ruby-units will raise an exception if you attempt to create a temperature unit that would fall below absolute zero.

Unit math on temperatures is fairly limited.

Unit.new('100 tempC') + Unit.new('10 degC')   # '110 tempC'.to_unit
Unit.new('100 tempC') - Unit.new('10 degC')   # '90 tempC'.to_unit
Unit.new('100 tempC') + Unit.new('50 tempC')  # exception (can't add two temperatures)
Unit.new('100 tempC') - Unit.new('50 tempC')  # '50 degC'.to_unit (get the difference between two temperatures)
Unit.new('50 tempC')  - Unit.new('100 tempC') # '-50 degC'.to_unit
Unit.new('100 tempC') * scalar                # '100*scalar tempC'.to_unit
Unit.new('100 tempC') / scalar                # '100/scalar tempC'.to_unit
Unit.new('100 tempC') * unit                  # exception
Unit.new('100 tempC') / unit                  # exception
Unit.new('100 tempC') ** N                    # exception

Unit.new('100 tempC').convert_to('degC')  #=> Unit.new('100 degC')

This conversion references the 0 point on the scale of the temperature unit

Unit.new('100 degC').convert_to('tempC')  #=> '-173 tempC'.to_unit

These conversions are always interpreted as being relative to absolute zero. Conversions are probably better done like this...

Unit.new('0 tempC') + Unit.new('100 degC') #=> Unit.new('100 tempC')

Defining Units

It is possible to define new units or redefine existing ones.

Define New Unit

The easiest approach is to define a unit in terms of other units using the block form.

Unit.define("foobar") do |foobar|
  foobar.definition   = Unit.new("1 foo") * Unit.new("1 bar")   # anything that results in a Unit object
  foobar.aliases      = %w{foobar fb}                            # array of synonyms for the unit
  foobar.display_name = "Foobar"                                 # How unit is displayed when output
end

You can also create a unit definition directly and pass it to Unit.define:

unit_definition = Unit::Definition.new("foobar") do |foobar|
  foobar.definition = Unit.new("1 baz")
  foobar.aliases = %w{foobar fb}
  foobar.display_name = "Foobar"
end
Unit.define(unit_definition)

For more control, you can set the unit attributes explicitly:

Unit.define("electron-volt") do |ev|
  ev.aliases      = %w{eV electron-volt electron_volt}
  ev.scalar       = 1.602e-19
  ev.kind         = :energy
  ev.numerator    = %w{<kilogram> <meter> <meter>}
  ev.denominator  = %w{<second> <second>}
  ev.display_name = "electron-volt"
end

Redefine Existing Unit

Redefining a unit allows the user to change a single aspect of a definition without having to re-create the entire definition. This is useful for changing display names, adding aliases, etc.

Unit.redefine!("cup") do |cup|
  cup.display_name  = "cup"
end

Useful methods

1. scalar will return the numeric portion of the unit without the attached units
2. base_scalar will return the scalar in base units (SI)
3. units will return the name of the units (without the scalar)
4. base will return the unit converted to base units (SI)
5. best_prefix will return a new unit scaled with an appropriate prefix for human readability (e.g., '1000 m' becomes '1 km')

Storing in a database

Units can be stored in a database as either the string representation or in two separate columns defining the scalar and the units. Note that if sorting by units is desired you will want to ensure that you are storing the scalars in a consistent unit (i.e, the base units).

Namespaced Class

Sometimes the default class 'Unit' may conflict with other gems or applications. Internally ruby-units defines itself using the RubyUnits namespace. The actual class of a unit is the RubyUnits::Unit. For simplicity and backwards compatibility, the ::Unit class is defined as an alias to ::RubyUnits::Unit.

To load ruby-units without this alias...

require 'ruby_units/namespaced'

When using bundler...

gem 'ruby-units', require: 'ruby_units/namespaced'

Note: when using the namespaced version, the Unit.new('unit string') helper will not be defined.

Configuration

Configuration options can be set like:

RubyUnits.configure do |config|
  config.format = :rational
  config.separator = :none
  config.default_precision = 0.001
end

Configuration Options

Option	Description	Valid Values	Default
format	Only used for output formatting. :rational is formatted like 3 m/s^2. :exponential is formatted like 3 m*s^-2.	:rational, :exponential	:rational
separator	Use a space separator for output. :space is formatted like 3 m/s, :none is like 3m/s.	:space, :none	:space
default_precision	The precision used when rationalizing fractional values in unit output.	Any positive number	0.0001

Examples

# Change output format to exponential notation
RubyUnits.configure do |config|
  config.format = :exponential
end
# => "1 m*s^-2"

# Remove spaces between numbers and units
RubyUnits.configure do |config|
  config.separator = :none
end
# => "1m/s"

# Adjust precision for rational number conversion
RubyUnits.configure do |config|
  config.default_precision = 0.001
end

# Reset to defaults
RubyUnits.reset

Note: Boolean values (true/false) for separator are deprecated but still supported for backward compatibility. Use :space instead of true and :none instead of false.

NOTES

Performance vs. Accuracy

Ruby units was originally intended to provide a robust and accurate way to do arbitrary unit conversions. In some cases, these conversions can result in the creation and garbage collection of a lot of intermediate objects during calculations. This in turn can have a negative impact on performance. The design of ruby-units has emphasized accuracy over speed. YMMV if you are doing a lot of math involving units.

Support Policy

Only currently maintained versions of ruby and jruby are supported.

License