Quantities and units

Language overview

Write a physical dimension after : and an explicit unit after a number in square brackets. A dimension alias names a physical dimension; it does not rescale a value.

units.eqi

dimension Pressure = kg / (m * s ^ 2);

model UnitInputs() {
  parameter pressure: Pressure = 210[GPa];
  parameter duration: s = 10[ms];
  parameter resistance: Ohm = 2[kOhm];
  variable measured: Pressure;
  relation specified { measured = pressure; }
}

Open the complete example source

These inputs are 210,000,000,000 Pa, 0.01 s, and 2000 ohms in coherent SI units. parameter duration: s = 0.01; describes the same duration as 10[ms].

Dimensions and familiar units

Products, quotients, and exact rational powers of the SI base symbols describe dimensions. The base symbols are kg, m, s, A, K, mol, and cd; 1 is dimensionless. Common derived units give shorter equivalent spellings.

Quantity	Derived unit	Base dimensions
Force	N	kg * m / s^2
Pressure or stress	Pa	kg / (m * s^2)
Energy	J	kg * m^2 / s^2
Power	W	kg * m^2 / s^3
Voltage	V	kg * m^2 / (s^3 * A)
Resistance	Ohm	kg * m^2 / (s^3 * A^2)
Dynamic viscosity	Pa * s	kg / (m * s)

Symbols are case-sensitive: A is electric current, K is temperature, and s is time. For temperature values in these examples use kelvin.

Where units must be explicit

Bare numeric declaration initializers inherit the declaration’s coherent SI unit. Instance bindings and general expressions do not inherit units:

eqi

instance resistor: electrical.Resistor(resistance = 2[kOhm]);

This fragment uses the electrical import from the electrical package example. 2 alone would be dimensionless in this binding.

Addition, subtraction, and the two sides of an equation must have matching dimensions. Multiplication combines dimensions; differentiation with respect to time divides by seconds. Thus derivative(temperature) has dimension K / s when temperature is a continuous state in kelvin.

A bare exact zero may take the other side’s dimension in an equation, so current = 0 is valid. Explicit 0[A] is often clearer.

Shape is separate from dimension

vector<m / s, 2> describes two velocity components. It is distinct from both a scalar speed m / s and a three-component vector vector<m / s, 3>. Spatial operators also carry support information: a boundary trace is attached to a boundary of the original field’s body.

Continue with quantities, dimensions, and units for worked dimensional reasoning, or equations and state for periodic-clock time literals.