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Delft Java UNIT System Version 6

DJUNITS is a set of Java classes that make life easy for scientific software writers by catching many common errors with the use of quantities and units at compile time and some others at runtime.

  • DJUNITS performs automatic conversions between most commonly used units of the same type. E.g., conversion of distances from miles to kilometers.
  • DJUNITS stores all values internally in the basic SI unit for that quantity. The value can be converted to any (user-selectable) suitable unit for display.
  • DJUNITS distinguishes absolute and relative values to catch common errors at compile time,
  • DJUNITS ensures that quantities expressed in different (but compatible) units are correctly added together. E.g. a distance in miles is correctly added to a distance in kilometers.
  • DJUNITS knows or computes the SI type of the result when a value in one unit is multiplied, or divided by another value (that may have another unit),
  • DJUNITS handles Scalars, Vectors and Matrices, as well as quantity tables.
  • DJUNITS stores everything in immutable objects.
  • DJUNITS stores the data for vectors and matrices as float or double values, and using dense or sparse storage.

Origin

DJUNITS was developed at Delft University of Technology as part of the Open Traffic Simulator project (started in 2014).

In August 2015 it became obvious that the units and values classes developed for the Open Traffic Simulator were sufficiently mature to be used in other projects. In 2026, a complete re-implementation of djunits version 6 took place.

The main authors/contributors of the DJUNITS project are Alexander Verbraeck and Peter Knoppers.

Absolute and Relative values

Values in DJUNITS are either absolute or relative.

An absolute value is a value measured from a standard reference. Examples are time with a reference point 1-1-1970 (UNIX epoch) or a reference point 1-1-0000 (Gregorian calendar time). As an other example, geographical directions, a direction can use North and East as reference points. Adding two absolute values together makes no sense. Subtracting one absolute value from another does make sense (and results in a relative value). Subtracting East from North should result in an angle of ±90° or ±π/2 (depending on the unit used to express the result). An absolute quantity always needs a reference to be useful. Values subtracted from each other need to know their reference to be able to carry out the subtraction. Therefore, a reference is explicitly stored with an absolute quantity.

A relative value expresses the difference between two (absolute or relative) values. The angle in the example above is a relative value. Relative values can be added together and subtracted from each other (resulting in relative values). Adding a relative value to an absolute value results in an absolute value. Subtracting a relative value from an absolute value also results in an absolute value.

In the geographical example, directions are absolute and angles are relative. Similarly, when applied to lengths, positions are absolute and distances are relative.

Generally, if adding a value to itself makes no sense, the value is absolute; otherwise it is relative.

Operation Operands Result
+ (plus) Absolute + Absolute Not allowed
+ (plus) Absolute + Relative Absolute
+ (plus) Relative + Absolute Absolute
+ (plus) Relative + Relative Relative
- (minus) Absolute - Absolute Relative (corresponding quantity)
- (minus) Absolute - Relative Absolute
- (minus) Relative - Absolute Not allowed
- (minus) Relative - Relative Relative
* (times) Absolute * Absolute Not allowed
* (times) Absolute * Relative Not allowed
* (times) Relative * Absolute Not allowed
* (times) Relative * Relative Relative (different quantity)
/ (divide) Absolute / Absolute Not allowed
/ (divide) Absolute / Relative Not allowed
/ (divide) Relative / Absolute Not allowed
/ (divide) Relative / Relative Relative (different quantity)

Attempts to perform operations that are marked not allowed are caught at compile time.

All quantities make sense as relative values. The four quantities that also make sense as absolute values are listed in the table below.

Quantity Absolute interpretation Absolute class
and Unit		 Relative interpretation Relative class
and Unit
Length Position Position
Length.Unit		 Distance Length
Length.Unit
Angle Direction or Slope Direction
Angle.Unit		 Angle (direction or slope difference) Angle
Angle.Unit
Temperature Temperature Temperature
Temperature.Unit		 Temperature difference TemperatureDifference
Temperature.Unit
Time Time (instant) Time
Duration.Unit		 Duration Duration
Duration.Unit

Dimensionless is a special relative unit in DJUNITS that has a Unitless unit.

Units

DJUNITS has a large number of pre-defined units. Internally, all values are stored in SI-units or an equivalent standard unit. For scalar values, the field is called si and can be retrieved as it is a public (immutable) field. Alternatively, the getSI() method can be used. The internal storage in SI units allows addition and subtraction of values that have been initialized using different units. Formatting and expressing the unit can be done using any defined unit. The code below illustrates some of the features.

Speed speed1 = new Speed(30, Speed.Unit.mi_h);
System.out.println("speed1:     " + speed1);
Speed speed2 = new Speed(10, Speed.Unit.m_s);
System.out.println("speed2:     " + speed2);
Speed diff = speed1.subtract(speed2);

// Default display unit will be SI unit for speed:
System.out.println("difference: " + diff);

// Change default display unit; internal SI value is unaltered:
diff.setDisplayUnit(Speed.Unit.mi_s);
System.out.println("difference: " + diff);

// Works, but not mistake-safe:
System.out.println("difference: " + diff.getInUnit(Speed.Unit.kt) + " kt");

// Safer:
System.out.println("difference: " + diff.toString(Speed.Unit.kt));

// Programmer must be really sure that SI-unit is m/s:
System.out.println("difference: " + diff.si() + " m/s (si)");

// Safer:
System.out.println("difference: " + diff.toString(Speed.Unit.SI) + " (si)");
System.out.println("difference: " + diff.toString(Speed.Unit.km_h));

This would create the following output:

speed1:     30.0000000 mi/h
speed2:     10.0000000 m/s
difference: 7.63063708 mi/h
difference: 0.00211962 mi/s
difference: 6.630842332613389 kt
difference: 6.63084233 kt
difference: 3.411199999999999 m/s (si)
difference: 3.41120000 m/s (si)
difference: 12.2803200 km/h

It is possible to use units without the Quantity.Unit. The of() methods are helper methods to easily use a unit, e.g., Length.of(12.0, "m") instead of new Length(12.0, Length.Unit.m).

Multiplication and Division

Multiplying or dividing physical quantities produces a result in a different physical unit. There is no general way where the Java compiler can check the type of the result in the general case. Therefore DJUNITS has an extensive list of built-in multiplication and division operations with known result type. For instance

Speed speed = new Speed(50, Speed.Unit.km_h);
Duration duration = new Duration(0.5, Duration.Unit.h);
Length distance = speed.multiply(duration);
Acceleration acc = speed.divide(duration);
Area area = distance.multiply(distance);
Volume vol = area.multiply(distance);

DJUNITS knows that the result of multiplication of a speed and a time is a distance. The value of the distance in the above case is 2500 m.

There is never a need for multiplication or division with an absolute operand. It just does not make sense to multiply 23 September 2025, 3 PM (an absolute Time) by 2.

Catch mistakes at compile time where possible

DJUNITS is designed to protect the programmer from easily made mistakes:

Speed speed = new Speed(12, Speed.Unit.km_h);
Length length = new Length(4, Length.Unit.mi);

// Good:
Duration howLongOK = length.divide(speed); 

// Does not compile; result would be a frequency:
Duration howLongWrong = speed.divide(length); 

// Does not compile; subtracting a length from a speed make no sense:
Speed other = speed.subtract(length); 

// Throws a UnitRuntimeException:
Acceleration acceleration = speed.multiply(speed).as(Acceleration.Unit.m_s2); 

// OK:
Energy kineticEnergy = speed.multiply(speed).multiply(new Mass(3, Mass.Unit.kg)
    .scaleBy(0.5)).as(Energy.Unit.J);

The mistakes on the lines with comments starting with Does not compile will be caught at compile time. In a development environment that continously checks for coding errors (like Eclipse) such mistakes will be marked in by the java editor.

The before-last line multiplies a speed by another speed. The result of this operation is not something that DJUNITS supports directly. Such scalars can be cast to something DJUNITS does know of with an as(TargetUnit) method. Whether that cast is permitted can only be checked at runtime and this example would fail with:

IllegalArgumentException: org.djunits.quantity.def.Quantity.as (804): 
    Quantity.as(m/s2) called, but units do not match: m2/s2 <> m/s2

A correct example where DJUNITS does not know the unit of the result (thus requiring an as(TargetUnit) cast) is:

Energy kineticEnergy = speed.multiply(speed).multiply(new Mass(3, Mass.Unit.kg)
    .scaleBy(0.5)).as(Energy.Unit.J);
System.out.println(kineticEnergy);

This would print:

16.6666667 J

Scalars, Vectors and Matrices

Simple values are referred to as quantities or scalars. DJUNITS also handles groups of values (these must all be of the same unit) as vectors or matrices. Efficient classes have been created for the 'small' vectors and matrices of size 1 to 3. The following vector and matrix classes exist:

  • Vector1 for a vector with just one element
  • Vector2.Row and Vector2.Col for a row and column vector of size 2
  • Vector3.Row and Vector3.Col for a row and column vector of size 3
  • VectorN.Row and VectorN.Col for a row and column vector of any size
  • Matrix1x1 for a square matrix of size 1 x 1
  • Matrix2x2 for a square matrix of size 2 x 2
  • Matrix3x3 for a square matrix of size 3 x 3
  • MatrixNxN for a square matrix of any size
  • MatrixNxM for a non-square or square matrix of any size

The larger vectors and matrices (VectorN, MatrixNxN, MatrixNxM) come in four varieties:

  • Dense, Double
  • Dense, Float
  • Sparse, Double
  • Sparse, Float

Dense vectors and matrices use arrays to store the values. Sparse vectors and matrices use an indexed structure to store only the non-zero values. Numeric 0.0 values are not stored explicitly in Sparse vectors and matrices. Very large vectors and matrices with lots of 0.0 values are more efficiently stored using Sparse data storage.

The Java double precision floating point value takes 8 bytes of memory, the float value takes 4 bytes. Both are available in DJUNITS for storage in VectorN, MatrixNxN, MatrixNxM.

Creating vectors and matrices is straightforward:

System.out.println("\n\nMatrices");
var mat = Matrix2x2.of(new double[][] {{1.0, 2.0}, {5.0, 4.0}}, Duration.Unit.s);
System.out.println("matrix:\n" + mat);
System.out.println("\nmatrix + matrix:\n" + mat.add(mat));
System.out.println("\nmatrix + 1 day:\n" + mat.add(Duration.of(1.0, "day")));
System.out.println("\ndeterminant: " + mat.determinant());

This prints:

Matrices
matrix:
[1.00000000, 2.00000000
 5.00000000, 4.00000000] s

matrix + matrix:
[2.00000000, 4.00000000
 10.0000000, 8.00000000] s

matrix + 1 day:
[86401.0000, 86402.0000
 86405.0000, 86404.0000] s

determinant: -6.0000000 s2

Vector and Matrix calculations

All standard vector and matrix operations are available, such as row and column extraction, calculation of determinant, inverse, and adjugate, transposing of vectors and matrices, matrix-matrix multiplication, matrix-vector multiplication, vector-vector multiplication, matrix-quantity multiplication, and vector-quantity multiplication. Hadamard operations on the elements of a vector or matrix are also supported. In all cases, units of the reculting vector or matrix are calculated. This means that if we multiply a Length matrix with a Length matrix, we get a resulting matrix of quantity Area with an Area.Unit as its unit.

The following example first shows a Hadamard operation (element-wise), followed by an algebraic matrix multiplication:

VectorN.Col<Length, Length.Unit> lv1 = VectorN.Col.of(new double[] {10, 20.0, 60, 120.0, 400.0}, Length.Unit.km);
Duration duration = Duration.of(2.0, "h");
VectorN.Col<Speed, Speed.Unit> sv1 = lv1.divideElements(duration).as(Speed.Unit.km_h);
System.out.println("Length: " + lv1);
System.out.println("Speed : " + sv1);

MatrixNxM<Length, Length.Unit> lm4x2 = MatrixNxM.of(new double[][] {{1, 2, 3, 4}, {5, 6, 7, 8}}, Length.Unit.m);
MatrixNxM<Length, Length.Unit> lm2x4 = MatrixNxM.of(new double[][] {{1, 2}, {3, 4}, {5, 6}, {7, 8}}, Length.Unit.m);

var mult44 = lm4x2.multiply(lm2x4).as(Area.Unit.m2);
System.out.println("\nMatrix1:\n" + lm4x2);
System.out.println("Matrix2:\n" + lm2x4);
System.out.println("Multiplication:\n" + mult44);

Matrix2x2<Area, Area.Unit> mult22 = lm4x2.multiply(lm2x4).asMatrix2x2().as(Area.Unit.a);
System.out.println("\nMatrix1:\n" + lm2x4);
System.out.println("Matrix2:\n" + lm4x2);
System.out.println("Multiplication:\n" + mult22);

The last matrix is cast to a strongly typed Matrix2x2<Area, Area.Unit>, where values are expressed in are. The code results in the following output:

Length: Col[10.0, 20.0, 60.0, 120.0, 400.0] km
Speed : Col[5.0, 10.0, 30.0, 60.0, 200.0] km/h

Matrix1:
[1.00000000, 2.00000000, 3.00000000, 4.00000000
 5.00000000, 6.00000000, 7.00000000, 8.00000000] m
Matrix2:
[1.00000000, 2.00000000
 3.00000000, 4.00000000
 5.00000000, 6.00000000
 7.00000000, 8.00000000] m
Multiplication:
[50.0000000, 60.0000000
 114.000000, 140.000000] m2

Matrix1:
[1.00000000, 2.00000000
 3.00000000, 4.00000000
 5.00000000, 6.00000000
 7.00000000, 8.00000000] m
Matrix2:
[1.00000000, 2.00000000, 3.00000000, 4.00000000
 5.00000000, 6.00000000, 7.00000000, 8.00000000] m
Multiplication:
[0.50000000, 0.60000000
 1.14000000, 1.40000000] a

QuantityTable

For those cases where a tabular storage of data is needed, but it is not necessary to carry out matrix or vector operations, the QuantityTable exists. It behaves like a MatrixNxM without the overhead of a matrix. Hadamard (element-wise) operations are allowed on the QuantityTable.

Localization

DJUNITS has been designed with localization in mind. This means that quantities, units, vectors and matrices can print the unit information based on a resource bundle file for that country. On the input side, quantities can also be created using localized string representations, as the example below shows:

System.out.println("\nLOCALIZATION US");
Locale.setDefault(Locale.US);
var speed = Speed.of(50.0, "km/h");
System.out.println("Absorbed dose name: " + AbsorbedDose.ONE.getName());
System.out.println("50 km/h = " + speed);
System.out.println("Acceleration: " + Units.localizedQuantityName(Acceleration.Unit.class));

System.out.println("\nLOCALIZATION NL");
Locale.setDefault(Locale.forLanguageTag("nl"));
System.out.println("Absorbed dose name: " + AbsorbedDose.ONE.getName());
System.out.println("50 km/h = " + speed);
System.out.println("Acceleration: " + Units.localizedQuantityName(Acceleration.Unit.class));

var d3du = Duration.valueOf("3 dag");
d3du.setDisplayUnit("u");
System.out.println("3 dagen in uren: " + d3du);

This results in:

LOCALIZATION US
Absorbed dose name: Absorbed dose
50 km/h = 50.0000000 km/h
Acceleration: Acceleration

LOCALIZATION NL
Absorbed dose name: Geabsorbeerde straling
50 km/h = 50,0000000 km/u
Acceleration: Versnelling
3 dagen in uren: 72,0000000 u

The following localizations are currently bundled with DJUNITS: en_US, de, en_GB, es, fr, it, ja, ko, nl, pt, zh_TW, zh.

Difference with previous versions

DJUNITS version 6 is different from versions 1 to 5, and not upward compatible. Version 6 is a completely new implementation of the code with the following notable differences:

  • The Quantity is now the central object from which all quantities inherit.
  • Unit classes are inner classes of the quantity, such as Energy.Unit.
  • The SIQuantity and SIUnit classes have been implemented as a normal quantity.
  • The DimensionlessUnit unit class has been renamed to Unitless.
  • Localization is built-in as a design guideline and not as an afterthought.
  • Absolute quantities have been re-implemented using a Reference for the reference point.
  • Operation names are streamlined across quantities, vectors and matrices, e.g., add, subtract, multiply, divide.
  • Vector and matrix classes use generics for definitions such as Matrix3x3<Area, Area.Unit>, and only allow correct operations.
  • Vector and matrix operations sich as trace, multiplication, and inverse are now fully supported with consistent unit calculations.
  • Hadamard operations have been added to vector and matrix calculations.
  • The QuantityTable has been added for storage of tabular quantity data.

The manual of the latest version 5 can be found at https://djunits.org/docs/5.4.2/manual/.

Documentations and test reports

DJUNITS documentation and test reports for the current version can be found at https://djunits.org/docs/latest. The manual is at https://djunits.readthedocs.io, or at https://djunits.org/manual The API can be found at https://djunits.org/docs/latest/apidocs/index.html.