Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 11 World Records and 7 Distinctions, Educate A Change.

O Level Physics Complete Formulae Sheet

1. Measurement, Scalars, Vectors and Basic Skills

Quantity	Formula / Meaning	Unit	Notes
Average speed	speed = total distance / total time	m/s, km/h	Distance is scalar
Average velocity	velocity = displacement / time	m/s	Displacement has direction
Gradient	gradient = change in y / change in x	depends on graph	Used in graphs
Area under graph	area under graph = quantity represented	depends on graph	Speed-time graph area = distance

Common Unit Conversions

Conversion	Value
1 km	1000 m
1 h	3600 s
1 cm	0.01 m
1 cm²	0.0001 m²
1 cm³	0.000001 m³
1 g	0.001 kg
1 tonne	1000 kg
1 kW	1000 W
1 MJ	1 000 000 J
1 kWh	3.6 × 10⁶ J

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2. Motion

Quantity	Formula	Unit	Exam Notes
Speed	v = d / t	m/s	Use total distance for average speed
Distance	d = vt	m	Only if speed is constant
Time	t = d / v	s	Convert minutes/hours first
Acceleration	a = change in velocity / time	m/s²	a = (v – u) / t
Final velocity	v = u + at	m/s	For uniform acceleration
Distance under uniform acceleration	s = ((u + v) / 2) × t	m	Average velocity × time
Speed from rest under acceleration	v² = u² + 2as	m²/s²	Useful for falling objects
Distance fallen from rest	s = 1/2 gt²	m	If air resistance is negligible

Graphs of Motion

Graph	Gradient	Area
Distance-time graph	speed	not usually used
Speed-time graph	acceleration	distance travelled
Velocity-time graph	acceleration	displacement

Key Motion Traps

Situation	Meaning
Constant speed	resultant force = 0
Constant velocity	speed and direction constant
Acceleration	velocity changes, speed or direction or both
Deceleration	speed decreases
Terminal velocity	weight = air resistance

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3. Mass, Weight and Density

Quantity	Formula	Unit	Notes
Weight	W = mg	N	g = 9.8 N/kg on Earth
Mass	m = W / g	kg	Mass does not change with location
Gravitational field strength	g = W / m	N/kg	Also acceleration of free fall
Density	ρ = m / V	kg/m³ or g/cm³	Mass per unit volume
Mass from density	m = ρV	kg	Use matching units
Volume from density	V = m / ρ	m³	Irregular objects use displacement

Density Conversion

Conversion	Example
1 g/cm³ = 1000 kg/m³	2.4 g/cm³ = 2400 kg/m³

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Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 11 World Records and 7 Distinctions, Educate A Change.

4. Forces

Quantity	Formula	Unit	Notes
Resultant force	F = ma	N	Force causes acceleration
Force from momentum change	F = change in momentum / time	N	Also impulse questions
Momentum	p = mv	kg m/s	Momentum is vector
Change in momentum	Δp = mv – mu	kg m/s	Take direction carefully
Impulse	impulse = Ft	N s	Also equals change in momentum
Impulse	impulse = change in momentum	N s or kg m/s	Same units

Newton’s Laws

Law	Exam Meaning
First law	If resultant force is zero, object remains at rest or constant velocity
Second law	F = ma
Third law	Forces are equal and opposite, same type, on different objects

Friction and Air Resistance

Situation	Result
Driving force > resistive force	acceleration
Driving force = resistive force	constant speed
Driving force < resistive force	deceleration
Falling at terminal velocity	weight = air resistance

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5. Springs and Hooke’s Law

Quantity	Formula	Unit	Notes
Extension	extension = stretched length – original length	m or cm	Do not confuse with total length
Hooke’s law	F = kx	N	Valid before limit of proportionality
Spring constant	k = F / x	N/m	Stiffer spring = larger k
Force	F = kx	N	Extension must be in metres if k is N/m

Spring Graphs

Graph	Meaning
Straight line through origin	load proportional to extension
Limit of proportionality	point where graph stops being straight
Greater gradient on force-extension graph	stiffer spring
Smaller extension for same load	harder to stretch

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6. Moments and Stability

Quantity	Formula	Unit	Notes
Moment	moment = force × perpendicular distance from pivot	N m	Distance must be perpendicular
Principle of moments	clockwise moments = anticlockwise moments	N m	For equilibrium
Pressure from force	pressure = force / area	Pa	Often linked with stability/contact

Stability Rules

More Stable When	Less Stable When
lower centre of gravity	higher centre of gravity
wider base	narrower base
line of action of weight stays inside base	line of action of weight falls outside base

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7. Energy, Work, Power and Efficiency

Quantity	Formula	Unit	Notes
Work done	W = Fd	J	Force and distance must be same direction
Gravitational potential energy	GPE = mgh	J	h is vertical height only
Kinetic energy	KE = 1/2 mv²	J	Doubling speed makes KE 4 times
Power	P = E / t	W	Rate of energy transfer
Power	P = W / t	W	Work done per second
Energy	E = Pt	J	Power × time
Efficiency	efficiency = useful output energy / total input energy	no unit	Can ×100 for percentage
Efficiency	efficiency = useful output power / total input power	no unit	Use when power is given

Energy Store Formulae

Store	Formula
Kinetic store	KE = 1/2 mv²
Gravitational potential store	GPE = mgh
Thermal/internal store	E = mcΔθ
Latent heat store	E = mL
Electrical transfer	E = VIt or E = Pt

Efficiency Percentage

efficiency percentage = (useful output / total input) × 100

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8. Pressure

Quantity	Formula	Unit	Notes
Pressure	p = F / A	Pa or N/m²	Smaller area = larger pressure
Force from pressure	F = pA	N
Area from pressure	A = F / p	m²
Liquid pressure	p = ρgh	Pa	Due to liquid only
Total pressure in liquid	total pressure = atmospheric pressure + ρgh	Pa	Use when asked total pressure

Pressure Notes

Situation	Result
Greater depth	greater liquid pressure
Greater density	greater liquid pressure
Same liquid, same depth	same pressure
Smaller contact area	greater solid pressure

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Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 11 World Records and 7 Distinctions, Educate A Change.

9. Thermal Physics

Temperature and Heat

Quantity	Formula	Unit	Notes
Celsius to Kelvin	K = °C + 273	K	0 °C = 273 K
Kelvin to Celsius	°C = K – 273	°C
Specific heat capacity	E = mcΔθ	J	Energy to heat substance
Specific heat capacity	c = E / mΔθ	J/kg °C	Or J/kg K
Specific latent heat	E = mL	J	During change of state
Specific latent heat	L = E / m	J/kg	Temperature remains constant

Heating with Electrical Heater

Quantity	Formula
Energy supplied	E = Pt
If voltage and current given	E = VIt
Specific heat capacity	c = E / mΔθ
Power of heater	P = VI

Changes of State

Change	Direction
Melting	solid → liquid
Freezing	liquid → solid
Boiling	liquid → gas
Evaporation	liquid → gas at surface
Condensation	gas → liquid
Sublimation	solid → gas

Gas Laws

Law	Formula	Condition
Boyle’s law	P₁V₁ = P₂V₂	constant temperature
Pressure law	P₁ / T₁ = P₂ / T₂	constant volume, T in K
Charles’s law	V₁ / T₁ = V₂ / T₂	constant pressure, T in K

Gas Pressure Ideas

Change	Effect
Temperature increases at constant volume	pressure increases
Volume decreases at constant temperature	pressure increases
Volume increases at constant temperature	pressure decreases
Temperature constant	average kinetic energy unchanged

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10. Waves

Quantity	Formula	Unit	Notes
Wave speed	v = fλ	m/s	Core wave formula
Frequency	f = v / λ	Hz	Waves per second
Wavelength	λ = v / f	m	Distance between matching points
Period	T = 1 / f	s	Time for one wave
Frequency	f = 1 / T	Hz
Echo distance	distance = speed × time / 2	m	Divide by 2 for return journey

Wave Definitions

Term	Meaning
Amplitude	maximum displacement from rest position
Wavelength	distance between two consecutive crests/compressions
Frequency	number of waves passing a point per second
Period	time for one complete wave
Transverse wave	vibrations perpendicular to direction of travel
Longitudinal wave	vibrations parallel to direction of travel

Sound

Quantity	Formula / Fact
Speed of sound in air	about 330 m/s
Ultrasound	frequency greater than 20 000 Hz
Audible range	about 20 Hz to 20 000 Hz
Echo formula	distance to wall = vt / 2
Louder sound	larger amplitude
Higher pitch	higher frequency

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11. Light, Reflection, Refraction and Lenses

Reflection

Rule	Formula / Meaning
Law of reflection	angle of incidence = angle of reflection
Angles measured from	normal, not the surface
Plane mirror image	virtual, upright, same size, same distance behind mirror

Refraction

Quantity	Formula	Unit
Refractive index	n = sin i / sin r	no unit
Critical angle	sin c = 1 / n	degrees
Magnification	m = image height / object height	no unit
Magnification	m = image distance / object distance	no unit

Refraction Rules

Situation	Direction of Bending
Air to glass/water	bends towards normal
Glass/water to air	bends away from normal
At critical angle	ray travels along boundary
Greater than critical angle	total internal reflection

Lenses

Lens	Behaviour
Converging lens	brings rays together
Diverging lens	spreads rays apart
Magnifying glass	converging lens, virtual upright magnified image
Short-sighted correction	diverging lens
Long-sighted correction	converging lens

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12. Electromagnetic Spectrum

Order of EM Spectrum

Radio waves → Microwaves → Infrared → Visible light → Ultraviolet → X-rays → Gamma rays

Increasing Frequency / Decreasing Wavelength

Radio → Microwave → Infrared → Red → Orange → Yellow → Green → Blue → Violet → Ultraviolet → X-rays → Gamma

Visible Light

Colour	Frequency	Wavelength
Red	lowest	longest
Violet	highest	shortest

EM Wave Facts

Fact	Detail
All EM waves are transverse	yes
Speed in vacuum	3.0 × 10⁸ m/s
Can travel through vacuum	yes
Infrared use	remote controls, thermal imaging, heaters
Microwaves use	satellite communication, cooking
X-rays use	medical imaging
Gamma rays use	sterilising equipment, cancer treatment

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Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 11 World Records and 7 Distinctions, Educate A Change.

13. Electricity

Charge and Current

Quantity	Formula	Unit	Notes
Charge	Q = It	C	Current × time
Current	I = Q / t	A	Rate of flow of charge
Time	t = Q / I	s
Electron flow	negative to positive		Actual electron direction
Conventional current	positive to negative		Used in circuit diagrams

Potential Difference and Energy

Quantity	Formula	Unit
Potential difference	V = W / Q	V
Work done / energy	W = VQ	J
Charge	Q = W / V	C
Electromotive force	emf = energy supplied by source per unit charge	V

Resistance

Quantity	Formula	Unit
Resistance	R = V / I	Ω
Voltage	V = IR	V
Current	I = V / R	A

Resistance of a Wire

Factor	Effect on Resistance
Longer wire	larger resistance
Greater cross-sectional area	smaller resistance
Higher temperature in metal	larger resistance
Same material	resistance proportional to length / area

Formula:

R = ρL / A

Where:

• R = resistance

• ρ = resistivity

• L = length

• A = cross-sectional area

Series Circuits

Rule	Formula / Meaning
Current	same everywhere
Voltage	shared between components
Total resistance	Rtotal = R₁ + R₂ + R₃
Potential divider	V₁ / V₂ = R₁ / R₂

Parallel Circuits

Rule	Formula / Meaning
Voltage	same across each branch
Current	splits between branches
Total resistance	1/Rtotal = 1/R₁ + 1/R₂
Two equal resistors R in parallel	Rtotal = R/2
Total current	Itotal = I₁ + I₂ + I₃

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14. Electrical Power and Energy

Quantity	Formula	Unit
Electrical power	P = VI	W
Power using current and resistance	P = I²R	W
Power using voltage and resistance	P = V² / R	W
Electrical energy	E = VIt	J
Electrical energy	E = Pt	J
Energy in kWh	energy = power in kW × time in h	kWh

Fuse Selection

Rule
Choose a fuse slightly above the normal operating current
Current = power / voltage
A fuse too small blows during normal use
A fuse too large gives poor protection

Example:

I = P / V

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15. Magnetism and Electromagnetism

Magnetic Fields

Situation	Rule
Field lines outside magnet	N to S
Compass needle	points along magnetic field
Like poles	repel
Unlike poles	attract
Magnetic metals	iron, steel, nickel, cobalt
Soft iron	temporary magnet
Steel	permanent magnet

Current and Magnetic Fields

Situation	Rule
Straight wire	circular magnetic field around wire
Direction	right-hand grip rule
Solenoid	acts like a bar magnet
Stronger electromagnet	more turns, larger current, iron core

Motor Effect

Idea	Rule
Current-carrying wire in magnetic field	experiences force
Direction of force	Fleming’s left-hand rule
Larger force	larger current, stronger magnetic field, longer wire in field

D.C. Motor

Part	Function
Coil	rotates in magnetic field
Brushes	maintain electrical contact
Split-ring commutator	reverses current every half-turn
Magnet	provides magnetic field

Generator / Electromagnetic Induction

Situation	Result
Wire cuts magnetic field lines	induced e.m.f.
Magnet moves into coil	induced current
Magnet stops moving	no induced current
Faster movement	larger induced e.m.f.
More turns on coil	larger induced e.m.f.
Stronger magnet	larger induced e.m.f.

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16. Transformers

Quantity	Formula
Transformer equation	Vs / Vp = Ns / Np
Secondary voltage	Vs = Vp × Ns / Np
Primary voltage	Vp = Vs × Np / Ns
Ideal transformer power	VpIp = VsIs

Transformer Rules

Type	Turns	Voltage	Current
Step-up	Ns > Np	Vs > Vp	Is < Ip
Step-down	Ns < Np	Vs < Vp	Is > Ip

Transmission Cables

Formula / Rule
Power loss = I²R
Step-up transformer increases voltage
Higher voltage means lower current for same power
Lower current means less heating loss

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Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 11 World Records and 7 Distinctions, Educate A Change.

17. Atomic Physics and Radioactivity

Atomic Structure

Particle	Charge	Relative Mass	Location
Proton	+1	1	nucleus
Neutron	0	1	nucleus
Electron	-1	very small	shells/orbiting nucleus

Nuclide Notation

For notation: ᴬZ X

Symbol	Meaning
A	nucleon number / mass number
Z	proton number / atomic number
Number of protons	Z
Number of electrons in neutral atom	Z
Number of neutrons	A – Z

Isotopes

Term	Meaning
Isotopes	atoms of same element with same protons but different neutrons
Same element	same proton number
Different isotope	different nucleon number

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18. Alpha, Beta and Gamma Radiation

Radiation	Nature	Charge	Mass	Ionising	Penetrating	Stopped By
Alpha, α	helium nucleus	+2	4	strongest	weakest	paper / few cm air
Beta, β	fast electron	-1	very small	medium	medium	thin aluminium
Gamma, γ	EM wave	0	0	weakest	strongest	thick lead / concrete

Nuclear Decay Changes

Emission	Mass Number A	Proton Number Z
Alpha	decreases by 4	decreases by 2
Beta-minus	unchanged	increases by 1
Gamma	unchanged	unchanged

Half-Life

Quantity	Formula / Method
Half-life	time taken for count rate/activity/mass to halve
After 1 half-life	1/2 remains
After 2 half-lives	1/4 remains
After 3 half-lives	1/8 remains
After 4 half-lives	1/16 remains
Corrected count rate	measured count rate – background count rate

Radioactivity Safety

Method	Purpose
Keep distance	reduces exposure
Use shielding	absorbs radiation
Use tongs	increases distance
Short exposure time	reduces dose
Store in lead box	shields radiation

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19. Nuclear Energy

Process	Meaning
Nuclear fission	large nucleus splits into smaller nuclei and neutrons
Nuclear fusion	small nuclei join to form larger nucleus
Chain reaction	neutrons from fission cause more fission
Sun’s energy	fusion of hydrogen into helium

Fission Calculation

Total nucleons before = total nucleons after

Example pattern:

U-235 + neutron → daughter nucleus + daughter nucleus + neutrons

Use conservation of mass/nucleon number.

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20. Space Physics

Quantity	Formula / Fact
Orbital speed	v = 2πr / T
Distance travelled in orbit	circumference = 2πr
Earth’s orbit	ellipse, almost circular
Earth rotation	about 24 hours
Moon orbit around Earth	about 1 month
Earth orbit around Sun	about 1 year
Light from Sun to Earth	about 500 s / 8 min 20 s
Speed of light	3.0 × 10⁸ m/s

Light-Year

Quantity	Formula
Distance	distance = speed × time
1 light-year	distance light travels in 1 year
Approx value	9.5 × 10¹⁵ m

Redshift

Term	Meaning
Redshift	increase in observed wavelength of light from receding galaxies
Receding galaxy	moving away
Larger redshift	faster recession / further galaxy
Evidence for	expanding universe

Stars

Stage / Term	Key Idea
Nebula	cloud of gas and dust
Protostar	collapsing gas cloud heating up
Main sequence star	stable, fusion of hydrogen
Red giant / red supergiant	expansion after main sequence
White dwarf	final stage of smaller star
Supernova	explosion of massive star
Neutron star / black hole	possible final stages of massive star

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21. High-Frequency Exam Formula Traps

Trap	Correct Method
Echo questions	divide by 2
GPE on slope	use vertical height only
Pressure underwater	add atmospheric pressure only if total pressure asked
Spring length	total length = original length + extension
Density of object in water	volume = final reading – initial reading
Half-life count rate	subtract background first if given
Mirror angles	measure from normal, not mirror surface
Refraction angles	measure from normal, not surface
kWh	use power in kW and time in hours
Momentum	include direction if objects move opposite ways
Vector/scalar	speed scalar, velocity vector
Weight vs mass	mass in kg, weight in N
Transformer	works with a.c., not d.c.
Fuse	choose just above normal current
Plane mirror	virtual, upright, same size
D.C. motor	split-ring commutator
A.C. generator	slip rings

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22. Must-Know Formula List Only

Topic	Formula
Speed	v = d / t
Acceleration	a = (v – u) / t
Weight	W = mg
Density	ρ = m / V
Force	F = ma
Momentum	p = mv
Impulse	Ft = change in momentum
Moment	moment = force × perpendicular distance
Work done	W = Fd
GPE	GPE = mgh
KE	KE = 1/2 mv²
Power	P = E / t
Efficiency	useful output / total input
Pressure	p = F / A
Liquid pressure	p = ρgh
Specific heat capacity	E = mcΔθ
Specific latent heat	E = mL
Boyle’s law	P₁V₁ = P₂V₂
Wave speed	v = fλ
Echo distance	distance = vt / 2
Refractive index	n = sin i / sin r
Critical angle	sin c = 1 / n
Magnification	image height / object height
Charge	Q = It
Potential difference	V = W / Q
Resistance	R = V / I
Electrical power	P = VI
Electrical energy	E = VIt
Electrical energy	E = Pt
Series resistance	Rtotal = R₁ + R₂
Parallel resistance	1/Rtotal = 1/R₁ + 1/R₂
Transformer	Vs / Vp = Ns / Np
Ideal transformer	VpIp = VsIs
Orbital speed	v = 2πr / T
Light distance	distance = speed × time

Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 11 World Records and 7 Distinctions, Educate A Change.