# 1. Introduction¶

## 1.1. What is a Quantity?¶

“The value of a quantity is generally expressed as the product of a number and a unit. The unit is simply a particular example of the quantity concerned which is used as a reference, and the number is the ratio of the value of the quantity to the unit.” (Bureau International des Poids et Mesures: The International System of Units, 8th edition, 2006)

Basic types of quantities are defined “by convention”, they do not depend on other types of quantities, for example Length, Mass or Duration.

Derived types of quantities, on the opposite, are defined as products of other types of quantities raised by some exponent.

Examples:

• Volume = Length ** 3

• Velocity = Length ** 1 * Duration ** -1

• Acceleration = Length ** 1 * Duration ** -2

• Force = Mass ** 1 * Acceleration ** 1

Each type of quantity may have one special unit which is used as a reference for the definition of all other units, for example Metre, Kilogram and Second. The other units are then defined by their relation to the reference unit.

If a type of quantity is derived from types of quantities that all have a reference unit, then the reference unit of that type is defined by a formula that follows the formula defining the type of quantity.

Examples:

• Velocity -> Metre per Second = Metre ** 1 * Second ** -1

• Acceleration -> Metre per Second squared = Metre ** 1 * Second ** -2

• Force -> Newton = Kilogram ** 1 * Metre ** 1 * Second ** -2

### 1.1.1. “Systems of Measure”¶

There may be different systems which define quantities, their units and the relations between these units in a different way.

This is not directly supported by this module. For each type of quantity there can be only no or exactly one reference unit. But, if you have units from different systems for the same type of quantity, you can define these units and provide mechanisms to convert between them (see Converters).

## 1.2. Main Package Contents¶

### 1.2.1. The Basics: Quantity and Unit¶

The essential functionality of the package `quantity` is provided by the two classes `Quantity` and `Unit`.

A basic type of quantity is declared just by sub-classing `Quantity`. A derived type of quantity is declared by giving a definition based on more basic types of quantities. For details see Defining a quantity class.

### 1.2.2. Utility Functions and Classes¶

In addition, the package `quantity` provides some utility functions (see Functions), base classes for defining unit converters (see Converter classes) and some specific exceptions (see Exceptions).

### 1.2.3. Commonly Used Quantities¶

The module `quantity.predefined` provides definitions of commonly used quantities and units.

### 1.2.4. A Special Quantity: Money¶

Money is a special type of quantity. Its unit type is known as currency.

Money differs from physical quantities mainly in two aspects:

• Money amounts are discrete. For each currency there is a smallest fraction that can not be split further.

• The relation between different currencies is not fixed, instead, it varies over time.

The sub-package `quantity.money` provides classes and functions dealing with these specifics.