Physics

medium importance~1 Q in Tier 127 formulas⚡ 12 shortcuts6 subtopics

Overview Learn (6)Formulas (27)Examples (4)Practice (121)

SI units, conversions and measuring instruments

⏱ 6 min read🧩 5 question types🎯 18 practice Q

The idea in one minute

Every measurement has a number and a unit. The world uses one agreed system, the SI system, which has seven base units. All other units are built from these seven. Exams ask many recall questions here: named units, practical units and instruments.

The seven base units

A measurement needs a number and a unit. "The rod is 5" means nothing. "The rod is 5 metres" does.

The SI system (Système International, adopted in 1960) has exactly seven base quantities. They do not depend on any other quantity.

Quantity	SI unit	Symbol
Length	metre	m
Mass	kilogram	kg
Time	second	s
Electric current	ampere	A
Temperature	kelvin	K
Amount of substance	mole	mol
Luminous intensity	candela	cd

Watch: The unit of temperature is the kelvin, not "degree kelvin". Newton, joule and volt are not base units.

Derived units with names

Every other quantity is built from the seven base ones. Many derived units carry a scientist's name.

Quantity	Unit	Quantity	Unit
Force	newton (N)	Electric charge	coulomb (C)
Work, energy, heat	joule (J)	Potential difference	volt (V)
Power	watt (W)	Resistance	ohm (Ω)
Pressure	pascal (Pa)	Capacitance	farad (F)
Frequency	hertz (Hz)	Inductance	henry (H)
Magnetic field	tesla (T)	Magnetic flux	weber (Wb)
Power of a lens	dioptre (D)	Radioactivity	becquerel (Bq)
Luminous flux	lumen	Illuminance	lux
Sound level	decibel (dB)	Speed of ships	knot

Some units are built from base units. Force is kg·m/s², power is J/s, pressure is N/m², and frequency is 1/s. The dioptre is 1/metre. Momentum is kg·m/s, velocity is m/s, acceleration is m/s² and density is kg/m³.

Practical units and their values

Some units are not SI, but exams love them. Learn what each one measures.

Unit	Measures	Value
Light year	Distance, not time	about 9.46 × 10¹⁵ m
Parsec	Distance	about 3.26 light years
Astronomical unit (AU)	Distance	mean Earth–Sun distance, about 1.5 × 10¹¹ m
Ångström	Wavelength	10⁻¹⁰ m
Fermi	Nuclear size	10⁻¹⁵ m
Nautical mile	Distance at sea	1852 m
Knot	Speed of ships and aircraft	one nautical mile per hour
Fathom	Depth of water	6 feet
Carat	Weight of gems	200 mg
Horsepower	Power	about 746 W
Calorie	Heat	about 4.186 J
Electron volt	Energy	about 1.6 × 10⁻¹⁹ J
Kilowatt-hour	Energy	3.6 × 10⁶ J
Bar	Pressure	10⁵ Pa
Atmosphere	Pressure	about 1.013 × 10⁵ Pa

For gold, "carat" means purity. 24 carat gold is pure.

Watch: Words like "year" and "hour" inside a unit name do not make it a unit of time. A light year is distance. A kilowatt-hour is energy.

Scalars and vectors

A scalar has only size. Examples: mass, speed, distance, time, work, energy, power and temperature.

A vector has size and direction. Examples: displacement, velocity, acceleration, force, momentum and weight.

Tip: Ask if "towards the north" makes sense with the quantity. If it does, the quantity is a vector.

Quick conversions

km/h to m/s: multiply by $\dfrac{5}{18}$ . So 36 km/h is 10 m/s. Reverse it (m/s to km/h) by multiplying by $\dfrac{18}{5}$ .
Electricity units: units (kWh) = watts × hours ÷ 1000. A 100 W bulb used for 10 hours uses 1 unit.

The reason is simple. 1 km is 1000 m and 1 hour is 3600 s. So 1 km/h is $\dfrac{1000}{3600} = \dfrac{5}{18}$ m/s.

Rule: One "unit" on your electricity bill is 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J. It is energy, not power.

Instruments and what they measure

Most names carry a Greek root that gives the job away.

Instrument	Measures
Barometer	Atmospheric pressure
Manometer	Pressure of gases
Hygrometer	Relative humidity
Hydrometer	Relative density of liquids
Lactometer	Purity (density) of milk
Anemometer	Wind speed
Altimeter	Altitude (aircraft)
Ammeter	Current (connect in series)
Voltmeter	Potential difference (connect in parallel)
Galvanometer	Detects small currents
Seismograph	Earthquake waves
Sphygmomanometer	Blood pressure
Pyrometer	Very high temperature (furnaces)
Fathometer or SONAR	Depth of the sea (echo sounding)
Odometer / Speedometer	Distance run / speed of a vehicle
Tachometer	Rotation speed (rpm)
Audiometer	Hearing
Crescograph	Growth of plants

Question types you will see

Each type: how to recognise it, the method step by step, and one question to try.

Type 1very common3 practice Q

SI unit of a physical quantity

How to spot it:

The question says 'The SI unit of pressure / charge / magnetic flux / power is ...' or 'which pair is wrongly matched'.

Method

Decide if the quantity is one of the 7 base quantities.
If it is derived, recall its named unit: N, J, W, Pa, Hz, C, V, Ω, F, Wb, T, H.
If it has no named unit, build it from base units (momentum is kg·m/s).

Why it works:

Every unit is fixed by international agreement, so recall plus elimination is the method.

Try this

The SI unit of magnetic field (magnetic flux density) is:

Show solution

Weber is the unit of magnetic flux.
Magnetic field is flux per square metre.
That unit is the tesla.

Answer

Tesla (T)

Type 2very common4 practice Q

Instrument and what it measures

How to spot it:

An instrument name ending in '-meter' or '-graph' is given and its use is asked, or the reverse.

Method

Break the name into its root: hygro, hydro, anemo, baro, seismo, sphygmo.
Pick the option that fits the root.
Watch the pairs: hygrometer and hydrometer, manometer and sphygmomanometer.

Why it works:

Most names are Greek roots that describe the job.

Try this

An altimeter is used to measure:

Show solution

Alti means height.
It works like a barometer.
Pressure falls as height rises.

Answer

Altitude, mainly in aircraft

Type 3common3 practice Q

Practical and astronomical units

How to spot it:

Units like light year, parsec, AU, knot, nautical mile, fathom, horsepower, carat or kWh appear in 'is a unit of ...' or 'equals ...'.

Method

Sort the unit by quantity: light year, parsec, AU, fathom and nautical mile are distance.
Knot is speed. kWh, calorie and eV are energy. Horsepower is power.
Recall the value: 1852 m, 746 W, 3.6 × 10⁶ J.

Why it works:

The words 'year' and 'hour' in a unit name mislead students. The quantity decides.

Try this

A parsec is a unit of:

Show solution

It is used for star distances.
1 parsec is about 3.26 light years.
So it measures distance.

Answer

Distance

Type 4common2 practice Q

Base or derived unit; scalar or vector

How to spot it:

The question says 'Which is NOT a fundamental unit', 'which is a vector' or 'which pair are both scalars'.

Method

Base units: metre, kilogram, second, ampere, kelvin, mole, candela. All else is derived.
Vector test: does direction change the meaning?
Speed, distance, mass, work, energy, power and time are scalars.

Why it works:

A scalar has only size. A vector needs a direction too.

Try this

Which of the following is a scalar quantity? (a) Force (b) Momentum (c) Work (d) Displacement

Show solution

Force needs a direction.
Momentum and displacement need a direction.
Work has only size.

Answer

Type 5common2 practice Q

Unit conversion and energy-bill numericals

How to spot it:

A speed in km/h must be converted, or appliance watts and hours must become kWh.

1\ \text{km/h}=\tfrac{5}{18}\ \text{m/s},\quad \text{units (kWh)}=\frac{\text{W}\times\text{h}}{1000}

Method

For speed, multiply km/h by 5/18 to get m/s.
For bills, use watts × hours ÷ 1000 to get units.
Multiply units by the rate to get rupees.
Check the size: a 1 kW appliance for 1 hour is exactly 1 unit.

Why it works:

1 km = 1000 m and 1 h = 3600 s, so 1000/3600 = 5/18.

Try this

Convert 54 km/h to m/s.

Show solution

Multiply by $\dfrac{5}{18}$ .
$54 \times \dfrac{5}{18} = 15$ .

Answer

15 m/s

Formula sheet

Kilowatt-hour

1\ \text{kWh} = 3.6 \times 10^{6}\ \text{J}

1 'unit' of electricity

Horsepower

1\ \text{hp} \approx 746\ \text{W}

power unit

Light year

1\ \text{ly} \approx 9.46 \times 10^{15}\ \text{m}

a unit of distance

Shortcuts that save time

⚡ Base units in one line

Say it as Metre, Kilogram, Second, Ampere, Kelvin, Mole, Candela. Anything not on this list is derived.

Example

Which of these is NOT an SI base unit: kelvin, candela, newton, mole?

Show solution

List the seven base units: m, kg, s, A, K, mol, cd.
Kelvin, candela and mole are on the list.
Newton is not on the list.

Answer

Newton. It is derived: kg·m/s².

⚡ Read the root of the instrument name

Hygro is humidity. Hydro is liquid density. Lacto is milk. Anemo is wind. Sphygmo is pulse and blood pressure. Pyro is fire, so high temperature. Seismo is earthquake.

Mistakes to avoid

Where most students lose marks on this subtopic.

Mistake 01

Treating the light year as a unit of time.

A light year is a distance: about 9.46 × 10¹⁵ m.

Mistake 02

Calling kWh a unit of power.

kWh is energy. Power is measured in watt.

Mistake 03

Mixing up the hygrometer and the hydrometer.

Hygro means humidity. Hydro means liquid density.

Mistake 04

Writing the unit of temperature as "degree kelvin".

Say kelvin, symbol K.

Mistake 05

Calling momentum, velocity or density base quantities.

Only seven are base. These are derived from them.

Quick revision

Read this the night before the exam.

The 7 base units are m, kg, s, A, K, mol and cd.
Light year, parsec and AU are distances. Nautical mile is 1852 m. A knot is one nautical mile per hour.
1 kWh = 3.6 × 10⁶ J and it is energy. 1 horsepower is about 746 W.
km/h × 5/18 = m/s.
Scalars: speed, work, energy, power. Vectors: velocity, force, momentum, displacement.
Hygro is humidity, hydro is liquid density, lacto is milk, anemo is wind, sphygmo is blood pressure.

Practice: 18 questions

Sets of 10, mixed across the question types above. Every answer has a step-by-step explanation.

Topic test · 10 questions

Suggested time 3 min · wrong answers go to your mistake notebook automatically.

Continue learning