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Derived SI Units and How They Are Built

Physics · Units And Measurements · NEET

A derived SI unit is a unit made by combining the seven base SI units (like metre, kilogram, second) using multiplication and division, following the formula of the physical quantity. Example: force F = m x a, so its unit is kg x m/s^2, which we name the newton (N). Memory hook: "Take the formula, swap each quantity for its base unit" - the formula tells you exactly how to build the unit.
Building a derived unit from the formulaForceF = mass x accel.→Swap each for base unitkg x (m / s^2)→Derived SI unitkg m s^-2 = newton (N)More examples (same recipe)Pressure = F / AreaN/m^2 = pascal (Pa)Energy = F x distanceN.m = joule (J)Power = Energy / timeJ/s = watt (W)
The recipe for every derived SI unit: take the quantity's formula, replace each quantity with its base SI unit, and simplify. Force gives kg m s^-2 (newton); the same steps give pascal, joule and watt.

Your doubts, answered

How are derived units formed from base units?

Start with the defining formula of the quantity and replace every quantity in it with its own SI unit. Example: speed = distance / time = metre / second = m/s. For force, F = mass x acceleration = kg x (m/s^2) = kg m/s^2. So a derived unit is just the base units multiplied or divided the same way the formula multiplies or divides the quantities. Nothing new is invented; you only reuse the seven base units.

What is the difference between a base unit and a derived unit?

A base (fundamental) unit is chosen as a starting standard and cannot be broken into other units. There are only seven: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd). A derived unit is built by combining these base units. Example: metre and second are base, but m/s (speed) and kg m/s^2 (force) are derived. Every derived unit can be written fully in base units.

Is the newton a base unit or a derived unit?

The newton (N) is a derived unit. It comes from F = m x a, so 1 N = 1 kg x 1 m/s^2 = kg m s^-2. It is given a special name (newton) only for convenience, but it is still built entirely from the base units kilogram, metre and second. Many derived units have special names: joule (J), watt (W), pascal (Pa), coulomb (C).

How do I find the SI unit of any quantity I am asked in NEET?

Write the formula, then substitute the SI unit of each part. Example: pressure = force / area = N / m^2 = pascal (Pa) = kg m^-1 s^-2. Energy = force x distance = N x m = joule (J) = kg m^2 s^-2. Power = energy / time = J / s = watt (W). This one trick lets you get the unit even for a quantity you have never memorised, which is exactly what NEET tests.

Why does thermal conductivity have the unit W m^-1 K^-1?

Thermal conductivity K comes from the heat-flow equation, where rate of heat flow (power, in watt W) = K x area x (temperature difference / thickness). Rearranging, K = (power x length) / (area x temp difference) = (W x m) / (m^2 x K) = W m^-1 K^-1. This is a classic NEET trap because students guess J m^-1 K^-1 (energy) instead of W m^-1 K^-1 (power, which is energy per second).

⚠️ The NEET trap
✗ Writing thermal conductivity as J m^-1 K^-1 because you think of heat energy.
✓ Thermal conductivity uses rate of heat flow (power), so the unit is W m^-1 K^-1. Watt = joule per second. Any 'rate of flow' quantity carries watt, not joule.
🧠 Watt vs joule: rate vs total.

Real NEET questions

2019

The unit of thermal conductivity is:

A · J m K^-1
B · J m^-1 K^-1
C · W m K^-1
D · W m^-1 K^-1 ✓
Solution: Step 1: Use the heat-conduction formula. Rate of heat flow (which is power) = K x A x (dT / dx), where A is area and dT/dx is temperature gradient. Step 2: Make K the subject: K = (power x thickness) / (area x temperature difference). Step 3: Put in SI units: power = watt (W), thickness = m, area = m^2, temperature = K. So K = (W x m) / (m^2 x K) = W m^-1 K^-1. Step 4: Match with options - this is option D. Note the trap: rate of heat flow is power (watt), not energy (joule), so J-based options are wrong.

Solved Units And Measurements NEET PYQs

Try the real previous-year questions from this chapter — each with the answer and a full solution.

See all 30 Units And Measurements NEET PYQs ›
Next concept: SI Prefixes and Powers of Ten (Multiples and Submultiples) →Keep learning — 2 minFeeling ready? Solve the Units And Measurements NEET PYQs ›Or practice on your phone — get the free MedicNEET app ›

Frequently asked

How many special-name derived SI units are there?

There are 22 derived SI units with special names, such as newton (N), joule (J), watt (W), pascal (Pa), coulomb (C), volt (V), ohm, hertz (Hz) and tesla (T). All of them can still be written fully in terms of the seven base units.

Can a derived unit be written using only base units?

Yes. Every derived unit reduces to base units. Example: watt (W) = J/s = (kg m^2 s^-2)/s = kg m^2 s^-3. This full base-unit form is useful for checking dimensional consistency in NEET problems.

Is m/s a derived unit even though it looks simple?

Yes. Speed = distance / time = m/s, so m/s is a derived unit built from the base units metre and second. A unit is 'derived' whenever it is a combination of base units, no matter how simple it looks.

Do derived units have dimensions?

Yes. Since derived units come from combining base units, they carry dimensions. Example: force (newton) has dimensions [M L T^-2]. Pure ratios like strain or refractive index are dimensionless and have no unit.

Why is learning to build derived units important for NEET?

NEET often asks the unit or dimension of a quantity you did not memorise. If you know the formula, you can build the correct SI unit on the spot from the base units, saving memorisation and avoiding common traps like joule vs watt.

Related concepts:
SI System: The Seven Base Units ExplainedFundamental vs Derived Physical Quantities (Difference)SI Prefixes and Powers of Ten (Multiples and Submultiples)Dimensional Formulae of Common Quantities (List)Dimensions of Force, Work, Energy and Power
Practise Physics for NEET:
Physics MCQs (free, chapter-wise)Units And Measurements PYQs