what do you mean by derived units

Derived units are units that are built by combining the basic (fundamental) units like metre, kilogram and second using multiplication, division or powers.

Quick Scoop: Simple Meaning

In physics, some quantities are basic (like length, mass, time), and their units are called base units (m, kg, s, etc.). When you form other physical quantities from these basics—like speed, force or energy—their units are called derived units because they are “derived” from base units.

You can think of derived units as “recipe units”: you mix base units together in different ways to create new ones.

Formal Definition

• A derived unit is any unit that can be written as a product, quotient or power of base units.

• These come from the mathematical formula of the physical quantity.

For example, if a quantity is defined as “distance divided by time”, its unit automatically becomes “metre divided by second”.

Classic Examples

1. Speed (or velocity)
   • Definition: speed = distance ÷ time
   • Base units: distance → metre (m), time → second (s)

 * Derived unit: metre per second → m/s (a derived unit).

2. Acceleration
   • Definition: acceleration = change in velocity ÷ time
   • Velocity unit: m/s
   • Derived unit: (m/s)/s=m/s2(\text{m/s})/\text{s}=\text{m/s}^2(m/s)/s=m/s2.

3. Force (newton)
   • Definition: force = mass × acceleration
   • Base units: mass → kg, acceleration → m/s²
   • Derived unit: kg·m/s², given a special name “newton” (N).

4. Energy (joule)
   • One way: energy = force × distance
   • Force unit: N = kg·m/s², distance: m
   • Derived unit: N·m = kg·m²/s², called the joule (J).

5. Density
   • Definition: density = mass ÷ volume
   • Base units: mass → kg, volume → m³
   • Derived unit: kg/m³ (kilogram per cubic metre).

Base vs Derived Units (Quick Table)

Type of unit	Quantity	Unit name	Symbol	In base units
Base	Length	metre	m	m
Base	Mass	kilogram	kg	kg
Base	Time	second	s	s
Derived	Speed	metre per second	m/s	m·s⁻¹
Derived	Force	newton	N	kg·m·s⁻²
Derived	Energy	joule	J	kg·m²·s⁻²
Derived	Density	kilogram per cubic metre	kg/m³	kg·m⁻³

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One-line answer for exams

• “Derived units are units obtained by multiplying or dividing one or more base units, according to the definition of the physical quantity (for example, m/s for speed, kg·m/s² for force).”

TL;DR: Derived units are not “independent” units; they come from combining base units using the formula of the quantity, like m/s, m/s², N, J, and kg/m³.

Information gathered from public forums or data available on the internet and portrayed here.