1.4 SI System

Definition

The International System of Units (SI) is the internationally accepted standard system of measurement used in science, engineering, industry, and commerce. It provides a consistent set of units for measuring physical quantities, allowing scientists and engineers around the world to communicate and compare measurements accurately. The SI system is based on seven base units. All other units, known as derived units, are formed by combining these base units according to the relationships between physical quantities.

Why Do We Need a Standard System?

A standard system of units ensures that measurements are expressed and interpreted consistently. The SI provides an internationally agreed system of units, allowing measurements to be communicated and compared reliably.

The Seven SI Base Units

The SI system defines seven fundamental quantities, each with its own base unit.

Base QuantitySI UnitSymbol
Lengthmeterm
Masskilogramkg
Timeseconds
Electric currentampereA
Thermodynamic temperaturekelvinK
Amount of substancemolemol
Luminous intensitycandelacd
Table 1.4.1 — The Seven SI Base Units. The seven base quantities and their corresponding SI units and symbols.

SI Derived Units

Many physical quantities are obtained by combining base quantities. Their SI units are therefore combinations of the base units.

Some common examples are shown below.

Physical QuantitySI UnitBase Unit Expression
Area
Volume
Speedm/sm·s⁻¹
Accelerationm/s²m·s⁻²
Forcenewton (N)kg·m·s⁻²
Pressurepascal (Pa)kg·m⁻¹·s⁻²
Energyjoule (J)kg·m²·s⁻²
Powerwatt (W)kg·m²·s⁻³
Table 1.4.2 — Examples of SI Derived Units. Common derived quantities and their SI units expressed in terms of base units.

These derived units are obtained directly from the definitions of the corresponding physical quantities.

Example

Since speed is defined as

Speed=DistanceTime\mathrm{Speed}=\frac{\mathrm{Distance}}{\mathrm{Time}}

Its SI unit is

ms=ms1\frac{m}{s}=m\cdot s^{-1}

Similarly,

Force=Mass×Acceleration\mathrm{Force}=\mathrm{Mass}\times\mathrm{Acceleration}

Therefore, the SI base unit expression for force is

kgms2\mathrm{kg}\cdot\mathrm{m}\cdot\mathrm{s}^{-2}

This combination of base units is called the newton (N).

A Coherent System

The SI system is a coherent system of units. This means that equations written using SI units do not require additional numerical conversion factors.

For example,

F=maF=ma

where:

  • F is the force measured in newtons (N),
  • m is the mass measured in kilograms (kg),
  • a is the acceleration measured in meters per second squared (m/s²).

When these SI units are used, the calculated force is automatically expressed in newtons (N). No additional conversion constant is required.

This is one of the major advantages of the SI system. It makes equations simpler, calculations more consistent, and reduces the likelihood of errors.

Key Points

  • The SI system is the internationally accepted standard system of measurement.
  • It is based on seven base units.
  • All other SI units are derived from the base units.
  • Using SI units ensures consistency and reliability in scientific measurements worldwide.
  • SI units form a coherent system, allowing physical equations to work without additional conversion factors.