Master Table of Derived SI Units

Quantity	Formula	SI Unit	Symbol
Area A	Length × Width	Square Meter	m²
Volume V	Length × Width × Height	Cubic Meter	m³
Velocity v	Displacement / Time	Meter per Second	m/s
Acceleration a	Velocity / Time	Meter per Sq. Second	m/s²
Frequency f	1 / Period	Hertz	Hz
Density ρ	Mass / Volume	Kilogram per Cubic Meter	kg/m³
Force F	Mass × Acceleration	Newton	N
Pressure / Stress P	Force / Area	Pascal	Pa
Energy / Work / Heat E, W	Force × Distance	Joule	J
Power P	Energy / Time	Watt	W
Momentum p	Mass × Velocity	Kilogram Meter/Sec	kg·m/s
Torque τ	Force × Radius	Newton Meter	N·m
Surface Tension γ	Force / Length	Newton per Meter	N/m
Dynamic Viscosity η	Shear Stress / Rate	Pascal Second	Pa·s
Electric Charge Q	Current × Time	Coulomb	C
Voltage / Potential V	Power / Current	Volt	V
Capacitance C	Charge / Voltage	Farad	F
Resistance R	Voltage / Current	Ohm	Ω
Conductance G	1 / Resistance	Siemens	S
Magnetic Flux Φ	Voltage × Time	Weber	Wb
Magnetic Field (B) B	Flux / Area	Tesla	T
Inductance L	Flux / Current	Henry	H
Celsius Temperature t	T(K) - 273.15	Degree Celsius	°C
Specific Heat Capacity c	Heat / (Mass × Temp)	Joule per kg Kelvin	J/(kg·K)
Thermal Conductivity k	Power / (Dist × Temp)	Watt per Meter Kelvin	W/(m·K)
Entropy S	Heat / Temp	Joule per Kelvin	J/K
Radioactivity A	Decays / Time	Becquerel	Bq
Absorbed Dose D	Energy / Mass	Gray	Gy
Dose Equivalent H	Dose × Factor	Sievert	Sv
Luminous Flux Φv	Intensity × Solid Angle	Lumen	lm
Illuminance Ev	Flux / Area	Lux	lx
Catalytic Activity kat	Moles / Time	Katal	kat
Angle (Plane) θ	Arc / Radius	Radian	rad
Angle (Solid) Ω	Area / Radius²	Steradian	sr

The Architecture of Physics: Derived Units

If Fundamental Units are the bricks, Derived Units are the houses, bridges, and skyscrapers built with them. Almost every measurement you encounter in advanced physics—from the voltage of your battery to the pressure in your tires—is a "Derived Unit." They are formed by combining the 7 base units (kg, m, s, A, K, mol, cd) using multiplication and division.

The Logic of Derivation

Deriving a unit is like solving a puzzle. Take Speed. We know Speed = Distance / Time. Distance is measured in meters (m). Time is seconds (s). Therefore, the unit for speed is m/s. No special memory is needed—just logic!

Named Units

Sometimes, a combination is so common that we give it a special name to honor a scientist. Instead of saying "kilogram meter per second squared" ($kg \cdot m/s^2$) a thousand times a day, we simply say "Newton" ($N$).

Mastering Dimensional Analysis

One of the most powerful skills in physics is breaking down complex units into their base components. This allows you to check if your formulas are possibly correct.

Example: Proving Power

1. Formula: Power (P) = Work / Time

2. Break down Work: Work = Force × Distance

3. Break down Force: Force = Mass × Acceleration ($kg \cdot m/s^2$)

4. Combine for Work: $(kg \cdot m/s^2) \times m = kg \cdot m^2/s^2$ (Joule)

5. Combine for Power: Work / Time = $(kg \cdot m^2/s^2) / s$

Final: $kg \cdot m^2 \cdot s^-3$ (Watt)

Categories of Derived Units

Mechanics: Units related to motion and forces.
Examples: Hertz (Hz), Newton (N), Joule (J), Watt (W), Pascal (Pa).
Electromagnetism: Units related to charge and fields.
Examples: Coulomb (C), Volt (V), Ohm (Ω), Tesla (T), Henry (H).
Photometry: Units related to light perception.
Examples: Lumen (lm), Lux (lx).
Radiation: Units related to radioactivity.
Examples: Becquerel (Bq), Gray (Gy), Sievert (Sv).

Frequently Asked Questions

What is the difference between Fundamental and Derived units?

Fundamental units (like Meter, Second) are the 7 independent base building blocks. Derived units (like Speed, Force) are created by combining these base units mathematically (multiplying or dividing them).

How is the Newton (N) derived?

From Newton's Second Law ($F=ma$): Mass (kg) × Acceleration (m/s²). Therefore, 1 Newton = 1 kg⋅m/s².

Why do some units have special names?

To make communication easier. Imagine if every time you bought a lightbulb, the box said "60 kg⋅m²/s³" instead of "60 Watts". Special names like Watt, Joule, and Pascal honor famous scientists and simplify daily usage.

Is "Joule" used for both Work and Energy?

Yes! Work is defined as Force × Distance ($N \cdot m$). Energy is the capacity to do work. Since they are physically equivalent, they share the same unit: the Joule (J).

What is the base unit breakdown of a Volt?

Voltage is Energy per unit Charge ($V = J/C$). Since $J = kg \cdot m^2/s^2$ and $C = A \cdot s$, combining them gives $V = kg \cdot m^2 \cdot s^{-3} \cdot A^{-1}$.

Why is Torque (N·m) not measured in Joules?

This is a subtle point. Work is Force × Distance (parallel). Torque is Force × Radius (perpendicular). Although dimensionally they are both $N \cdot m$, Torque is a vector quantity and Work is scalar. To avoid confusion, we never express Torque in Joules.

What are the units for Radioactivity?

The SI unit is the Becquerel (Bq), which is 1 decay per second ($s^{-1}$). An older common unit is the Curie (Ci), but Bq is the official standard.

How do I check if a formula is correct?

Use Dimensional Analysis. Write the units for every variable. Improve the algebra. If the units on the left side equal the units on the right side, the formula is likely correct.

Is "Liter" a derived SI unit?

No. The official SI derived unit for volume is the Cubic Meter ($m^3$). 1 Liter is actually 1/1000th of a cubic meter ($0.001 m^3$ or $1 dm^3$).

What does "Hz" mean?

Hertz (Hz) is the unit of Frequency. It represents "cycles per second". In base units, it is simply $s^{-1}$ (inverse seconds).

Derived SI Units Master Table