SI Units

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Recall the following SI base quantities and their units: mass (kg), length (m), time (s), current (A), temperature (K)
  2. Express derived units as products or quotients of the SI base units and use the derived units for quantities listed in this syllabus as appropriate
  3. Use SI base units to check the homogeneity of physical equations
  4. Recall and use the following prefixes and their symbols to indicate decimal submultiples or multiples of both base and derived units: pico (p), nano (n), micro (μ), milli (m), centi (c), deci (d), kilo (k), mega (M), giga (G), tera (T)

What Are SI Base Quantities?

In physics, we measure many different things — from the mass of a book to the speed of light. Every measurement needs a unit to make sense. For example, saying "the table is 2" doesn't tell us much, but "the table is 2 meters long" gives us useful information.

The SI system (International System of Units) is the standard system used by scientists worldwide. It is based on seven fundamental measurements called base quantities. These base quantities cannot be defined using other physical quantities — they are the building blocks from which all other units are made.

For this course, you need to know five SI base quantities:

Base QuantitySI Base UnitSymbol
Masskilogramkg
Lengthmetrem
Timeseconds
Electric CurrentampereA
TemperaturekelvinK

Think of these as the "alphabet" of physics measurements. Just like you can make any word from letters, you can make any physics unit from these five base units.

Why are these important?

  • They are universally agreed upon, so scientists everywhere use the same measurements
  • They form the foundation for all other units in physics
  • Understanding them helps you work with complex equations and check if your answers make sense

Most quantities we measure in physics are not base quantities. Instead, they are derived units — units that are made by combining two or more base units together through multiplication or division.

What Is a Derived Unit?

A derived unit is any unit that can be expressed using the SI base units. For example:

  • Speed is measured in metres per second (m s⁻¹), which combines length (m) and time (s)
  • Force is measured in newtons (N), but a newton can be broken down into kg m s⁻²

How to Express Derived Units in Base Units

To find the base units of any derived quantity, you need to:

  1. Start with the equation that defines the quantity
  2. Replace each quantity in the equation with its units
  3. Simplify by doing the multiplication or division

Let's look at some important examples:

Example 1: Force (Newton)

Force is defined by the equation: Force = mass × acceleration

Step 1: Write the equation F = m × a

Step 2: Replace with units

  • Mass has units of kg
  • Acceleration is "change in velocity per second" = (m s⁻¹) / s = m s⁻²

Step 3: Combine the units Force = kg × m s⁻² Force = kg m s⁻²

So 1 newton (N) = 1 kg m s⁻²

Example 2: Energy or Work (Joule)

Energy is defined by the equation: Energy = force × distance

Step 1: E = F × d

Step 2: Replace with units

  • Force = kg m s⁻² (from Example 1)
  • Distance = m

Step 3: Combine Energy = (kg m s⁻²) × m Energy = kg m² s⁻²

So 1 joule (J) = 1 kg m² s⁻²

Example 3: Pressure (Pascal)

Pressure is defined as: Pressure = force ÷ area

Step 1: P = F ÷ A

Step 2: Replace with units

  • Force = kg m s⁻²
  • Area = length × width =

Step 3: Combine Pressure = (kg m s⁻²) ÷ m² Pressure = kg m⁻¹ s⁻²

So 1 pascal (Pa) = 1 kg m⁻¹ s⁻²

Example 4: Power (Watt)

Power is defined as: Power = work done ÷ time

Step 1: P = W ÷ t

Step 2: Replace with units

  • Work = kg m² s⁻²
  • Time = s

Step 3: Combine Power = (kg m² s⁻²) ÷ s Power = kg m² s⁻³

So 1 watt (W) = 1 kg m² s⁻³

Example 5: Electric Charge (Coulomb)

Charge is defined by: Charge = current × time

Step 1: Q = I × t

Step 2: Replace with units

  • Current = A
  • Time = s

Step 3: Combine Charge = A s

So 1 coulomb (C) = 1 A s

Example 6: Voltage (Volt)

Voltage is defined as: Voltage = work done ÷ charge

Step 1: V = W ÷ Q

Step 2: Replace with units

  • Work = kg m² s⁻²
  • Charge = A s

Step 3: Combine Voltage = (kg m² s⁻²) ÷ (A s) Voltage = kg m² s⁻³ A⁻¹

So 1 volt (V) = 1 kg m² s⁻³ A⁻¹

Quick Reference Table

QuantitySymbolDerived Unit NameBase Units
ForceFnewton (N)kg m s⁻²
Energy/WorkE/Wjoule (J)kg m² s⁻²
PressurePpascal (Pa)kg m⁻¹ s⁻²
PowerPwatt (W)kg m² s⁻³
ChargeQcoulomb (C)A s
VoltageVvolt (V)kg m² s⁻³ A⁻¹

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