The Java Units Library
The units library is a tool that helps programmers avoid mistakes related to units of measurement. It does this by keeping track of the units of measurement, and by ensuring that all operations are performed with the correct units. This can help to prevent errors that can lead to incorrect results, such as adding a distance in inches to a distance in meters.
An added benefit is readability and maintainability, which also reduces bugs. By making the units of measurement explicit in your code, it becomes easier to read and understand what your code is doing. This can also help to make your code more maintainable, as it is easier to identify and fix errors related to units of measurement.
The units library has a number of features:
A set of predefined units, such as meters, degrees, and seconds.
The ability to convert between different units.
Support for performing arithmetic and comparisons on quantities with units.
Support for displaying quantities with units in a humanreadable format.
Terminology
 Dimension
Dimensions represent the nature of a physical quantity, such as length, time, or mass. They are independent of any specific unit system. For example, the dimension of meters is length, regardless of whether the length is expressed in meters, millimeters, or inches.
 Unit
Units are specific realizations of dimensions. They are the way of expressing physical quantities. Each dimension has a base unit, such as the meter for length, the second for time, the kilogram for mass. Derived units are formed by combining base units, such as meters per second for velocity.
 Measure
Measures are the specific magnitude of physical quantities, expressed in a particular unit. For example, 5 meters is a measure of distance.
These concepts are used within the Units Library. For example, the measure 10 seconds has a magnitude of 10, the dimension is time, and the unit is seconds.
Using the Units Library
The Java units library is available in the edu.wpi.first.units
package. The most relevant classes are:
The various classes for predefined dimensions, such as Distance and Time
Units, which contains a set of predefined units. Take a look a the Units javadoc to browse the available units and their types.
Measure, which is used to tag a value with a unit.
Note
It is recommended to static import edu.wpi.first.units.Units.*
to get full access to all the predefined units.
Java Generics
Units of measurement can be complex expressions involving various dimension, such as distance, time, and velocity. Nested generic type parameters allow for the definition of units that can represent such complex expressions. Generics are used to keep the library concise, reusable, and extensible, but it tends to be verbose due to the syntax for Java generics.
For instance, consider the type Measure<Velocity<Distance>>
. This type represents a measurement for velocity, where the velocity itself is expressed as a unit of distance per unit of time. This nested structure allows for the representation of units like meters per second or feet per minute. Similarly, the type Measure<Per<Voltage, Velocity<Distance>>>
represents a measurement for a ratio of voltage to velocity. This type is useful for representing quantities like volts per meter per second, the unit of measure for some feedforward gains.
It’s important to note that not all measurements require such complex nested types. For example, the type Measure<Distance>
is sufficient for representing simple units like meters or feet. However, for more complex units, the use of nested generic type parameters is essential.
For local variables, you may choose to use Java’s var keyword instead of including the full type name. For example, these are equivalent:
Measure<Per<Voltage, Velocity<Distance>>> v = VoltsPerMeterPerSecond.of(8);
var v = VoltsPerMeterPerSecond.of(8);
Creating Measures
The Measure
class is a generic type that represents a magnitude (physical quantity) with its corresponding unit. It provides a consistent and typesafe way to handle different dimensions of measurements, such as distance, angle, and velocity, but abstracts away the particular unit (e.g. meter vs. inch). To create a Measure
object, you call the Unit.of
method on the appropriate unit object. For example, to create a Measure<Distance>
object representing a distance of 6 inches, you would write:
Measure<Distance> wheelDiameter = Inches.of(6);
Other measures can also be created using their Unit.of
method:
Measure<Mass> kArmMass = Kilograms.of(1.423);
Measure<Distance> kArmLength = Inches.of(32.25);
Measure<Angle> kMinArmAngle = Degrees.of(5);
Measure<Angle> kArmMaxTravel = Rotations.of(0.45);
Measure<Velocity<Distance>> kMaxSpeed = MetersPerSecond.of(2.5);
Performing Calculations
The Measure
class also supports arithmetic operations, such as addition, subtraction, multiplication, and division. These are done by calling methods on the objects. These operations always ensure that the units are compatible before performing the calculation, and they return a new Measure
object. For example, you can add two Measure<Distance>
objects together, even if they have different units:
Measure<Distance> distance1 = Inches.of(10);
Measure<Distance> distance2 = Meters.of(0.254);
Measure<Distance> totalDistance = distance1.plus(distance2);
In this code, the units library will automatically convert the measures to the same unit before adding the two distances. The resulting totalDistance
object will be a new Measure<Distance>
object that has a value of 0.508 meters, or 20 inches.
This example combines the wheel diameter and gear ratio to calcualate the distance per rotation of the wheel:
Measure<Distance> wheelDiameter = Inches.of(3);
double gearRatio = 10.48;
Measure<Distance> distancePerRotation = wheelDiameter.times(Math.PI).divide(gearRatio);
Warning
By default, arithmetic operations create new Measure
instances for their results. See Java Garbage Collection for discussion on creating a large number of shortlived objects. See also, the Mutability and Object Creation section below for a possible workaround.
Converting Units
Unit conversions can be done by calling Measure.in(Unit)
. The Java type system will prevent units from being converted between incompatible types, such as distances to angles. The returned values will be bare double
values without unit information  it is up to you, the programmer, to interpret them correctly! It is strongly recommended to only use unit conversions when interacting with APIs that do not support the units library.
Measure<Velocity<Distance>> kMaxVelocity = FeetPerSecond.of(12.5);
Measure<Velocity<Velocity<Distance>>> kMaxAcceleration = FeetPerSecond.per(Second).of(22.9);
kMaxVelocity.in(MetersPerSecond); // => OK! Returns 3.81
kMaxVelocity.in(RadiansPerSecond); // => Compile error! Velocity<Angle> cannot be converted to Unit<Velocity<Distance>>
// The WPILib math libraries use SI metric units, so we have to convert to meters:
TrapezoidProfile.Constraints kDriveConstraints = new TrapezoidProfile.Constraints(
maxVelocity.in(MetersPerSecond),
maxAcceleration.in(MetersPerSecondPerSecond)
);
Usage Example
Pulling all of the concepts together, we can create an example that calculates the end effector position of an arm mechanism:
Measure<Distance> armLength = Feet.of(3).plus(Inches.of(4.25));
Measure<Distance> endEffectorX = armLength.times(Math.cos(getArmAngle().in(Radians)));
Measure<Distance> endEffectorY = armLength.times(Math.sin(getArmAngle().in(Radians)));
Humanreadable Formatting
The Measure
class has methods that can be used to get a humanreadable representation of the measure. This feature is useful to display a measure on a dashboard or in logs.
toString()
andtoShortString()
return a string representation of the measure in a shorthand form. The symbol of the backing unit is used, rather than the full name, and the magnitude is represented in scientific notation. For example, 1.234e+04 V/mtoLongString()
returns a string representation of the measure in a longhand form. The name of the backing unit is used, rather than its symbol, and the magnitude is represented in a full string, not scientific notation. For example, 1234 Volt per Meter
Mutability and Object Creation
To reduce the number of object instances you create, and reduce memory usage, a special MutableMeasure
class is available. You may want to consider using mutable objects if you are using the units library repeatedly, such as in the robot’s periodic loop. See Java Garbage Collection for more discussion on creating a large number of shortlived objects.
MutableMeasure
allows the internal state of the object to be updated, such as with the results of arithmetic operations, to avoid allocating new objects. Special care needs to be taken when mutating a measure because it will change the value every place that instance is referenced. If the object will be exposed as part of a public method, have that method return a regular Measure
in its signature to prevent the caller from modifying your internal state.
Extra methods are available on MutableMeasure
for updating the internal value. Note that these methods all begin with the mut_
prefix  this is to make it obvious that these methods will be mutating the object and are potentially unsafe!
For the full list of methods and API documentation, see the MutableMeasure API documentation

Increments the internal value by an amount in another unit. The internal unit will stay the same 

Increments the internal value by another measurement. The internal unit will stay the same 

Decrements the internal value by an amount in another unit. The internal unit will stay the same 

Decrements the internal value by another measurement. The internal unit will stay the same 

Multiplies the internal value by a scalar 

Divides the internal value by a scalar 

Overrides the internal state and sets it to equal the given value and unit 

Overrides the internal state to make it identical to the given measurement 

Overrides the internal value, keeping the internal unit. Be careful when using this! 
MutableMeasure<Distance> measure = MutableMeasure.zero(Feet);
measure.mut_plus(10, Inches); // 0.8333 feet
measure.mut_plus(Inches.of(10)); // 1.6667 feet
measure.mut_minus(5, Inches); // 1.25 feet
measure.mut_minus(Inches.of(5)); // 0.8333 feet
measure.mut_times(6); // 0.8333 * 6 = 5 feet
measure.mut_divide(5); // 5 / 5 = 1 foot
measure.mut_replace(6.2, Meters) // 6.2 meters  note the unit changed!
measure.mut_replace(Millimeters.of(14.2)) // 14.2mm  the unit changed again!
measure.mut_setMagnitude(72) // 72mm
Revisiting the arm example from above, we can use mut_replace
 and, optionally, mut_times
 to calculate the end effector position
import edu.wpi.first.units.Measure;
import edu.wpi.first.units.MutableMeasure;
import static edu.wpi.first.units.Units.*;
public class Arm {
// Note the two ephemeral object allocations for the Feet.of and Inches.of calls.
// Because this is a constant value computed just once, they will easily be garbage collected without
// any problems with memory use or loop timing jitter.
private static final Measure<Distance> kArmLength = Feet.of(3).plus(Inches.of(4.25));
// Angle and X/Y locations will likely be called in the main robot loop, let's store them in a MutableMeasure
// to avoid allocating lots of shortlived objects
private final MutableMeasure<Angle> m_angle = MutableMeasure.zero(Degrees);
private final MutableMeasure<Distance> m_endEffectorX = MutableMeasure.zero(Feet);
private final MutableMeasure<Distance> m_endEffectorY = MutableMeasure.zero(Feet);
private final Encoder m_encoder = new Encoder(...);
public Measure<Distance> getEndEffectorX() {
m_endEffectorX.mut_replace(
Math.cos(getAngle().in(Radians)) * kArmLength.in(Feet), // the new magnitude to store
Feet // the units of the new magnitude
);
return m_endEffectorX;
}
public Measure<Distance> getEndEffectorY() {
// An alternative approach so we don't have to unpack and repack the units
m_endEffectorY.mut_replace(kArmLength);
m_endEffectorY.mut_times(Math.sin(getAngle().in(Radians)));
return m_endEffectorY;
}
public Measure<Angle> getAngle() {
double rawAngle = m_encoder.getPosition();
m_angle.mut_replace(rawAngle, Degrees); // NOTE: the encoder must be configured with distancePerPulse in terms of degrees!
return m_angle;
}
}
Warning
MutableMeasure
objects can  by definition  change their values at any time! It is unsafe to keep a stateful reference to them  prefer to extract a value using the Measure.in
method, or create a copy with Measure.copy
that can be safely stored. For the same reason, library authors must also be careful about methods accepting Measure
.
Can you spot the bug in this code?
private Measure<Distance> m_lastDistance;
public Measure<Distance> calculateDelta(Measure<Distance> currentDistance) {
if (m_lastDistance == null) {
m_lastDistance = currentDistance;
return currentDistance;
} else {
Measure<Distance> delta = currentDistance.minus(m_lastDistance);
m_lastDistance = currentDistance;
return delta;
}
}
If we run the calculateDelta
method a few times, we can see a pattern:
MutableMeasure<Distance> distance = MutableMeasure.zero(Inches);
distance.mut_plus(10, Inches);
calculateDelta(distance); // expect 10 inches and get 10  good!
distance.mut_plus(2, Inches);
calculateDelta(distance); // expect 2 inches, but get 0 instead!
distance.mut_plus(8, Inches);
calculateDelta(distance); // expect 8 inches, but get 0 instead!
This is because the m_lastDistance
field is a reference to the same MutableMeasure
object as the input! Effectively, the delta is calculated as (currentDistance  currentDistance) on every call after the first, which naturally always returns zero. One solution would be to track m_lastDistance
as a copy of the input measure to take a snapshot; however, this approach does incur one extra object allocation for the copy. If you need to be careful about object allocations, m_lastDistance
could also be stored as a MutableMeasure
.
private Measure<Distance> m_lastDistance;
public Measure<Distance> calculateDelta(Measure<Distance> currentDistance) {
if (m_lastDistance == null) {
m_lastDistance = currentDistance.copy();
return currentDistance;
} else {
var delta = currentDistance.minus(m_lastDistance);
m_lastDistance = currentDistance.copy();
return delta;
}
}
private final MutableMeasure<Distance> m_lastDistance = MutableMeasure.zero(Meters);
private final MutableMeasure<Distance> m_delta = MutableMeasure.zero(Meters);
public Measure<Distance> calculateDelta(Measure<Distance> currentDistance) {
// m_delta = currentDistance  m_lastDistance
m_delta.mut_replace(currentDistance);
m_delta.mut_minus(m_lastDistance);
m_lastDistance.mut_replace(currentDistance);
return m_delta;
}
Defining New Units
There are four ways to define a new unit that isn’t already present in the library:
Using the
Unit.per
orUnit.mult
methods to create a composite of two other units;Using the
Milli
,Micro
, andKilo
helper methods;Using the
derive
method and customizing how the new unit relates to the base unit; andSubclassing
Unit
to define a new dimension.
New units can be defined as combinations of existing units using the Unit.mult
and Unit.per
methods.
Per<Voltage, Distance> VoltsPerInch = Volts.per(Inch);
Velocity<Mass> KgPerSecond = Kilograms.per(Second);
Mult<Mass, Velocity<Velocity<Distance>> Newtons = Kilograms.mult(MetersPerSecondSquared);
Using mult
and per
will store the resulting unit. Every call will return the same object to avoid unnecessary allocations and garbage collector pressure.
@Override
public void robotPeriodic() {
// Feet.per(Millisecond) creates a new unit on the first loop,
// which will be reused on every successive loop
SmartDashboard.putNumber("Speed", m_drivebase.getSpeed().in(Feet.per(Millisecond)));
}
Note
Calling Unit.per(Time)
will return a Velocity
unit, which is different from and incompatible with a Per
unit!
New dimensions can also be created by subclassing Unit
and implementing the two constructors. Note that Unit
is also a parameterized generic type, where the generic type argument is selfreferential; Distance
is a Unit<Distance>
. This is what allows us to have stronger guarantees in the type system to prevent conversions between unrelated dimensions.
public class ElectricCharge extends Unit<ElectricCharge> {
public ElectricCharge(double baseUnitEquivalent, String name, String symbol) {
super(ElectricCharge.class, baseUnitEquivalent, name, symbol);
}
// required for derivation with Milli, Kilo, etc.
public ElectricCharge(UnaryFunction toBaseConverter, UnaryFunction fromBaseConverter, String name, String symbol) {
super(ElectricCharge.class, toBaseConverter, fromBaseConverter, name, symbol);
}
}
public static final ElectricCharge Coulomb = new ElectricCharge(1, "Coulomb", "C");
public static final ElectricCharge ElectronCharge = new ElectricCharge(1.60217646e19, "Electron Charge", "e");
public static final ElectricCharge AmpHour = new ElectricCharge(3600, "Amp Hour", "Ah");
public static final ElectricCharge MilliampHour = Milli(AmpHour);