IGCSE Physics Equations and Formulas

This page covers a list of all the formulas you need to know for the IGCSE Physics examinations. Yes, you need to know these by heart. As listed in the syllabus, candidates are not provided with a formula sheet.

General Physics

1. Constant Motion

v = s/t

'v' is the velocity in m/s, 's' is the distance or displacement in meters, and 't' is the time in seconds

2. Acceleration

a = (v - u)/t

u is the initial velocity, v is the final velocity,, and t is the time.

3. Graph Areas

Area of a rectangular-shaped graph = base × height

Area of a triangular-shaped graph = ½ × base × height

In velocity-time graph the area under the graph is the total distance covered by an object.

4. Weight and Mass

w = m × g

w is the weight in Newton (N), m is the mass in kg, and g is the acceleration due to gravity = 10 m/s²

5. Density

ρ = m/V

ρ is the, density in kg/m³, m is the mass and V is the volume

6. Force

F = m × a

F is force in Newton (N), m is the mass, and a is the acceleration

7. Terminal Velocity

Weight of an object (downward) = Air resistance (upward)

Terminal velocity is the constant maximum speed an object reaches when the force of air resistance equals the force of gravity during free fall.

8. Hooke's Law

F = k × x

F is the force, x is the extension in meters, and k is the spring constant.

9. Moment of a Force

Moment of force = F × d

Moment is measured in N.m, F is the force,, and d is the distance from the pivot

10. Law of Moments (Equilibrium)

Total clockwise moment = Total anticlockwise moment F₁ × d₁ = F₂ × d₂

The Law of Moments states that for a body in equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments about the same point.

11. Work Done

W = F × d

W is work done in joules (J), F is the force, and d is the distance covered by an object

12. Kinetic Energy

Eₖ = ½ × m × v²

Eₖ is kinetic energy in joules (J), m is the mass(kg), and v is the velocity (m/s)

13. Potential Energy

Eₚ = m × g × h

Eₚ is potential energy in joules (J), m is the mass (kg), g is the acceleration due to gravity, and h is the height from the ground.

14. Law of Conservation of Energy

Loss of Eₚ = Gain of Eₖ m × g × h = ½ × m × v²

The Law of Conservation of Energy states that energy cannot be created or destroyed, only transformed from one form to another.

15. Power

P = Work done/Time taken

P = Energy transferred / Time taken

Power is the rate of doing work, measured in watts (W)

16. Pressure

p = F / A

p is pressure in pascal (Pa), F is the force in newton(N) and A is the area in m²

17. Pressure Due to Liquid

p = ρ × g × h

ρ is the density in kg/m³, g is the acceleration due to gravity and h is the height or depth of liquid in meters.

18. Atmospheric Pressure

P = 760 mmHg = 76 cmHg = 1.01×10⁵ Pa

Thermal Physics

1. Pressure and Volume Relationship (Boyle's Law)

pV = constant p₁ × V₁ = p₂ × V₂

p₁ and p₂ are the two pressures in Pa and V₁ and V₂ are the two volumes in m³

2. Thermal Expansion (Linear)

ΔL = α × L₀ × Δθ

L₀ is the original length in meters, Δθ is the change in temperature in °C, ΔL is the change in length in meters (L₁ - L₀), and α is the linear expansivity of the material

3. Thermal Expansion (Cubical)

ΔV = β × V₀ × Δθ

V₀ is the original volume in m³, Δθ is the change in temperature in °C, ΔV is the change in volume in m³ (V₁ - V₀), and β is the cubical expansivity of the material.

4. Relationship Between Linear and Cubic Expansivities

β = 3α

The cubical expansivity is approximately three times the linear expansivity for the same material.

5. Charles's Law

Volume is directly proportional to absolute temperature

V ∝ T V/T = constant V₁/T₁ = V₂/T₂

V is the volume in m³ and T is the temperature in Kelvin (K).

6. Pressure Law

Pressure of a gas is directly proportional to the absolute temperature

p ∝ T p/T = constant p₁/T₁ = p₂/T₂

p is the pressure in Pa and T is the temperature in Kelvin (K).

7. Gas Law

pV/T = constant p₁V₁/T₁ = p₂V₂/T₂

In thermal physics the symbol θ is used for celsius scale and T is used for Kelvin scale.

8. Specific Heat Capacity

c = Q/(m × Δθ)

The amount of heat required to raise the temperature of 1 kg of mass by 1°C. c is the specific heat capacity in J/kg°C, Q is the total heat in joules (J), m is the mass in kg, and Δθ is the change in temperature

9. Thermal Capacity

Thermal capacity = m × c Thermal capacity = Q/Δθ

Amount of heat required to raise the temperature of a substance of any mass by 1°C. The unit of thermal capacity is J/°C.

10. Specific Latent Heat of Fusion

Lf = Q/m

From Ice to liquid. Lf is the specific latent heat of fusion in J/kg or J/g, Q is the total heat in joules (J), m is the mass of liquid change from ice in kg or g.

11. Specific Latent Heat of Vaporization

Lv = Q/m

From liquid to vapour. Lv is the specific latent heat of vaporization in J/kg or J/g, Q is the total heat in joules (J), m is the mass of vapour change from liquid in kg or g.

12. Thermal or Heat Transfer

• In solid = conduction
• In liquid and gas = convection and also convection current
• In a vacuum = radiation

13. Emitters and Radiators

• Dull black surface = good emitter, good radiator, bad reflector
• Bright shiny surface = poor emitter, poor radiator, good reflector

Waves, Light, and Sound

1. Wave Equation 1

v = f × λ

v is the speed of the wave in m/s, f is the frequency in Hz, λ is the wavelength in meters

2. Wave Equation 2

f = 1/T

T is the time period of the wave in seconds

3. Movement of the Particles of the Medium

• Longitudinal waves → back and forth in the direction of the waves
• Transverse waves → perpendicular to the direction of the waves

4. Law of Reflection

Angle of incidence i = angle of reflection r ∠i = ∠r

5. Refraction

• From lighter to denser medium → light bends towards the normal
• From denser to lighter medium → light bends away from the normal

6. Refractive Index n

The refractive index n is the ratio of the sine of the angle of incidence to the sine of the angle of refraction

n = sin∠i ÷ sin∠r

7. Refractive Index n

n = speed of light in air or vacuum ÷ speed of light in any other medium

8. Image from a Plane Mirror

Virtual, upright, same size, and laterally inverted, same distance from the mirror inside

9. Image from a Convex Lens

• When close: virtual, enlarge, upright
• When far: real, small, upside down

10. Image from a Concave Lens

Virtual, upright, small

11. Critical Angle

When light goes from denser to lighter medium, the incident angle at which the reflected angle is 90°, is called critical angle.

12. Total Internal Reflection (TIR)

When light goes from a denser to a lighter medium, the refracted ray bends inside the same medium, then this is called TIR

13. Electromagnetic Spectrum

Gamma rays ↔ X-rays ↔ Ultraviolet ↔ Visible light ↔ IR ↔ Micro waves ↔ Radio waves

This way, the frequency decreases and the wavelength increases

14. Colours of Visible Spectrum (Light)

VIBGYOR (from bottom-up)

• V – Violet
• I – Indigo
• B – Blue
• G – Green
• Y – Yellow
• O – Orange
• R – Red

15. Speed of Light

• In air: 3×10⁸ m/s
• In glass: 2×10⁸ m/s

16. Light Wave

Light waves are electromagnetic waves, unlike sound waves (see the next definition below)

17. Sound Wave

Sound waves are longitudinal waves

• Particles of the medium come close → compression
• Particles of the medium are far apart → rarefaction

18. Echo

v = 2 × d/t

v is the speed of sound waves, d is the distance in meters between the source and the reflection surface, and t is the time for echo

19. Properties of Sound Waves

• Pitch means the frequency of the wave
• Loudness means the amplitude of the wave

20. Speed of Sound Waves

• Air: 330-340 m/s
• Water: 1400 m/s
• Concrete: 5000 m/s
• Steel: 6000 – 7000 m/s

Electricity and Magnetism

1. Ferrous Materials

Items made out of ferrous materials are attracted by the magnet and can be magnetized.

Examples: iron, steel, nickel, and cobalt

2. Non-ferrous Materials

Non-ferrous materials are not attracted by a magnet and cannot be magnetized.

Examples: copper, silver, aluminum, wood, glass

3. Electric Field Intensity

E = F/q

Force exerted by the field on a unit charge placed at a point around another charge. E is the electric field intensity in N/C

4. Current

I = Q/t

Rate of flow of charges in a conductor. I is the current in amperes (A), Q is the charge in coulombs (C), t is the time in seconds (s)

5. Current in Circuits

In circuits, the current always chooses the easiest path

6. Ohm's Law

V/I = R

Voltage across the resistor is directly proportional to current, V ∝ I. V is the voltage in volts (V), I is the current in amperes (A), and R is resistance in ohms (Ω)

7. Voltage

V = Energy / Q

Energy per unit charge. Q is the charge in coulombs (C), V is the voltage in volts (V), Energy is in joules (J)

8. E.M.F. (Electromotive Force)

electromotive force. = lost volts + terminal potential difference EMF = Ir + IR

9. Resistance and Resistivity

R = ρL / A

ρ is the resistivity of the resistor in Ω, R is the resistance of a resistor, L is the length of a resistor in meters, and A is the area of cross-section of a resistor in m²

10. Circuit Rules

• In a series circuit → the current stays the same and the voltage divides
• In a parallel circuit → the voltage stays the same, and the current divides

11. Calculating Resistance in a Series Circuit

R = R₁ + R₂ + R₃

R, R₁, R₂ and R₃ are resistances of resistor in ohms (Ω)

12. Calculating Resistance in a Parallel Circuit

1/R = 1/R₁ + 1/R₂ + 1/R₃

The same as the above equation, R is measured in ohms (Ω).

13. Potential Divider 1

V₁/V₂ = R₁/R₂

The voltage across two resistors in series is proportional to their resistances.

14. Potential Divider 2

V₂ = (R₂/(R₁ + R₂)) × V V₁ = (R₁/(R₁ + R₂)) × V

The voltage across each resistor in a series circuit is based on its resistance and the total voltage.

15. Power, Voltage, Current, and Resistance

P = I × V

P = I² × R

P = V²/R

In the above formulas, P is the power in watts (W), I is the Current in amps, V is Volts, and R is the resistance in Ohms (Ω)

16. Power, Energy, and Time

P = Energy/time

W = J/s

Another formula for Power is that power is equal to energy divided by time (s). The unit of energy is joules (J)

17. Transformer (Voltage Relationship)

Vₚ/Vₛ = nₚ/nₛ

Vₚ is the voltage in the primary coil, Vₛ is the voltage in the secondary coil, nₚ is the number of turns in the primary coil, and nₛ is the number of turns in the secondary coil

18. Transformer (Power and Current)

Power of primary coil = Power of secondary coil Pₚ = Pₛ Iₚ × Vₚ = Iₛ × Vₛ Vₚ/Vₛ = Iₛ/Iₚ

Iₚ is the current in the primary coil, and Iₛ is the current in the secondary coil

19. Cathode Rays

A stream of electrons is emitted from a heated metal (cathode). This process is called thermionic emission.

Atomic Physics

1. Alpha Particles (α-particles)

• Helium nucleus
• Stopped by materials like paper
• Highest ionization potential

2. Beta Particles (β-particles)

• Fast-moving electrons
• Stopped by materials like aluminum
• Less ionization potential

3. Gamma Particles (γ-rays)

• Electromagnetic radiation
• Only stopped by a thick sheet of lead
• Least ionization potential

4. Half-life

Time in which the activity or mass becomes half

5. Atomic Symbol

X^A_Z

A is the total number of protons and neutrons, Z is the total number of protons

6. Isotopes

Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons.