0.1 What is physics?
Preface · Nature of physics
- E = mc²
- E = hf
IB DP Physics · SL and HL · Free
IB Physics formula sheet
115 equations from our DP Physics lessons, grouped by topic, each linked to the lesson that explains where it comes from and works an example. Use it next to the official IB physics data booklet.
About the official booklet. The IB Physics data booklet is published by the International Baccalaureate and is provided in the exam. It is the IB’s copyright, so we do not host it; ask your teacher for the edition that matches your syllabus. This page is our own, written from our lessons.
Welcome to Physics
0 Preface to the syllabus: formulas
0.3 The seven base units
Preface · Tools: SI units
- 1 J = 1 kg m² s⁻²
0.4 Prefixes: kilo to femto
Preface · Tools: SI prefixes
- 1 km = 10³ m
- 1 µm = 10⁻⁶ m
0.5 Derived units
Preface · Tools: derived units
- F = ma
- p = F / A
0.6 Converting units
Preface · Tools: unit conversion
- 1 cm² = 10⁻⁴ m²
- 1 cm³ = 10⁻⁶ m³
- v(m s⁻¹) = v(km/h) ÷ 3.6
Theme A · Space, time and motion
A.1 Kinematics: describing motion: formulas
A.1 · 2 Repeating motion and the birth of clocks
Opening of A.1 Kinematics · link to periodic motion (Theme C)
- f = 1/T
- T = 2π√(L/g)
A.1 · 3 Zeno: is all motion an illusion?
Enrichment · mathematics and Theory of Knowledge
- Sₙ = 1 − (½)ⁿ
A.1 · 4 Model 1D motion: Y = vt
Opening of A.1 Kinematics · uniform motion (before A.1.1)
- Y = vt
A.1 · 5 Vectors: components and the river
A.1 Kinematics · vectors and scalars
- Vx = V cos θ, Vy = V sin θ
- V = √(Vx² + Vy²)
- across = V cos θ, along = current + V sin θ
A.1 · 6 Terms to describe motion
A.1 Kinematics · distance, displacement, speed, velocity, acceleration
- Δx = vt
- a = (v − u) / t
- v = u + at
A.1 · 7 Motion graphs: x–t, v–t, a–t
A.1 Kinematics · motion graphs, uniform and non-uniform motion
- v = Δx / t
- x_f = x_i + ut + ½at²
- area under v–t = displacement
A.1 · 8 Exam questions I: a train, a bouncing ball, a skidding car
A.1 Kinematics · applying v = u + at, x = ut + ½at², v² = u² + 2as
- v = u + at
- x = ut + ½at²
- v² = u² + 2as
- area under v–t = displacement
A.1 · 9 Exam questions II: a signal, a take-off, a chase, and leaking oil
A.1 Kinematics · applying v = u + at, x = ut + ½at², v² = u² + 2as
- v² = u² + 2as
- v = u + at
- x = ut + ½at²
A.1 · 9b Independence of motion: x and y
A.1 Kinematics · projectile motion, independence of horizontal and vertical components
- s = ut + ½at²
- R = uxt
- d = √(R² + h²)
A.1 · 9c Exam question III: a parcel dropped from an aircraft
A.1 Kinematics · projectile motion: components, s = ut + ½at², v = u + at
- s = uyt + ½at²
- v = u + at
- x = uxt
- v = √(vx² + vy²)
- v² = ux² + 2gh
A.1 · 9d Exam question IV: a ball thrown over a wall
A.1 Kinematics · projectile motion at an angle, components, s = ut + ½at²
- ux = u cosθ
- uy = u sinθ
- t = d / ux
- y = y0 + uyt − ½gt²
A.1 · 9e Adding velocities: crosswind landing and the umbrella
A.1 Kinematics · relative velocity, vector addition, components
- vground = vair + vwind
- sinθ = W / V
- tanθ = W / v
- vrel = vA − vB
A.1 · 9f Stellar aberration and the speed of light
A.1 Kinematics · relative velocity applied to starlight, speed of light
- tanα = v / c
- v = 2πr / T
- c = v / tanα
A.1 · 10 Models: “This is not a pipe”
A.1 Kinematics · mathematical models · Theory of Knowledge link
- x_f = x_i + vt
- x_f = x_i + ut + ½at²
Theme A · Space, time and motion
A.2 Force and motion: formulas
A.2 · 1 Newton's first law
A.2 Forces and momentum · Newton’s laws
- If Fnet,ext = 0 then Δv = 0 and a = 0
A.2 · 2 Newton's second law
A.2 Forces and momentum · Newton’s laws, momentum
- p = mv
- Fnet,ext = Δp / t
- F = ma (constant mass)
A.2 · 3 What can a force do?
A.2 Forces and momentum · effects of a force
- F = ma
- F = mv² / r
- F = kx
A.2 · 4 Newton's third law
A.2 Forces and momentum · Newton’s laws
- FP→T = − FT→P
A.2 · 5 Momentum conservation
A.2 Forces and momentum · conservation of momentum
- Δpsys = 0 if Fnet,ext,sys = 0
- m1u1 + m2u2 = m1v1 + m2v2
A.2 · 6 Momentum vs kinetic energy
A.2 Forces and momentum · momentum and kinetic energy
- p = mv
- Ek = ½mv²
A.2 · 7 Momentum change: four cases
A.2 Forces and momentum · change in momentum
- Δp = pf − pi = mΔv
A.2 · 8 Force: the link between space and time
A.2 Forces and momentum · big picture (enrichment)
- WD / x = F = Δp / t
A.2 · 10 Friction, buoyancy, tension and the rest
A.2 Forces and momentum · contact and resistive forces
- f = μN
- μ = tan θ (at the point of sliding)
- F_B = ρ_fluid V g
- F_B = W + T sin θ (tethered underwater, cable at θ to the horizontal)
- F_drag = kv² (fast motion through air)
A.2 · 11 Exam questions: collisions and Newton’s third law
A.2 Forces and momentum · conservation of momentum, Newton’s third law, elastic and inelastic collisions
- p_i = p_f (momentum conservation)
- F = Δp / t
- KE = ½mv²
A.2 · 12 Free-body diagrams, resultant force and equilibrium
A.2 Forces and momentum · free-body diagrams, resultant force, translational equilibrium
- Fx = F cos θ, Fy = F sin θ
- Fnet = √(ΣFx² + ΣFy²)
A.2 · 13 Springs, viscous drag and field forces
A.2 Forces and momentum · elastic restoring force, viscous drag, buoyancy, gravitational, electric and magnetic forces
- FH = −kx
- Fd = 6πηrv
- Fg = mg
- Fe = qE
A.2 · 14 Impulse: a force acting for a time
A.2 Forces and momentum · impulse, F = Δp/Δt, force–time graphs
- J = FΔt = Δp
- F = Δp / Δt
A.2 · 15 Explosions and recoil
A.2 Forces and momentum · explosions, conservation of momentum, energy considerations
- m1v1 + m2v2 = 0
- KE = p² / 2m
A.2 · 16 Collisions in two dimensions (HL)
A.2 Forces and momentum · two-dimensional collisions and explosions (HL)
- Σpx (before) = Σpx (after)
- Σpy (before) = Σpy (after)
A.2 · 17 Describing circular motion: period, angular velocity and v = ωr
A.2 Forces and momentum · circular motion, angular velocity ω, v = 2πr/T = ωr
- ω = 2π / T = 2πf
- v = ωr = 2πr / T
A.2 · 18 Centripetal acceleration and centripetal force
A.2 Forces and momentum · centripetal acceleration and force, work done in circular motion
- a = v²/r = ω²r = 4π²r/T²
- F = mv²/r = mω²r
A.2 · 19 Circular motion in practice: horizontal and vertical circles
A.2 Forces and momentum · uniform and non-uniform circular motion in horizontal and vertical planes
- T − mg = mv²/r (bottom)
- T + mg = mv²/r (top)
A.2 · 20 Exam-style questions: impulse, explosions and circular motion
A.2 Forces and momentum · impulse, explosions, circular motion (practice)
- J = FΔt = Δp
- F = mv² / r = mω²r
A.2 · Quiz Quiz: momentum and force
A.2 Forces and momentum · practice
- F = Δp / t
- Ft = Δp
- Δp = m(vf − vi)
Theme D · Fields
D Fields: formulas
D · 1 What is a field?
D.1 / D.2 · Gravitational, electric and magnetic fields
- g = FG / m
- E = FE / q
D · 2 Newton’s law of gravitation and Coulomb’s law
D.1 / D.2 · Gravitational and electric force laws
- FG = G M m / r²
- FE = k Q q / r²
- g = G M / r²
- E = k Q / r²
D · 3 Magnetic field strength and currents
D.2 · Magnetic fields, force between parallel currents
- B = F / (q v)
- B = F / (I L)
- F / L = μ0 I1 I2 / (2π r)
D · 4 Potential energy and potential
D.1 / D.2 · Gravitational and electric potential
- EPE = ½kx²
- Vg = −GM / r
- V = kQ / r
- WD = q ΔV
D · 5 Orbits and escape speed
D.1 · Orbital motion, escape speed
- v = √(GM / r)
- T² = 4π² r³ / (GM)
- TE = −GMm / 2r
- vesc = √(2GM / R)
Theme E · Nuclear and quantum physics
E5 Fusion and stars: formulas
E5 · 1 How a star ends: the Chandrasekhar and TOV limits
E.5 · Stellar evolution, white dwarfs, neutron stars and black holes
- p + e⁻ → n + νₑ
- L = 4πR²σT⁴
Constants used in the lessons
| Quantity | Symbol | Value |
|---|---|---|
| Speed of light in a vacuum | c | 3.00 × 10⁸ m s⁻¹ |
| Gravitational constant | G | 6.67 × 10⁻¹¹ N m² kg⁻² |
| Coulomb constant | k = 1 / 4πε0 | 8.99 × 10⁹ N m² C⁻² |
| Permeability of free space | μ0 | 4π × 10⁻⁷ T m A⁻¹ |
| Elementary charge | e | 1.60 × 10⁻¹⁹ C |
| Gravitational field strength at the Earth’s surface | g | 9.81 N kg⁻¹ (m s⁻²) |
| Mass of the Earth | MEarth | 5.97 × 10²⁴ kg |
| Radius of the Earth | REarth | 6.37 × 10⁶ m |
Values as used in the worked examples. In an exam, use the values printed in your official data booklet.
IB physics data booklet: common questions
Is this the official IB physics data booklet?
No. The official IB Physics data booklet is published by the International Baccalaureate and is given to you in the exam. It is the IB’s copyright, so we do not host it. This page is our own formula sheet, built from the lessons on this site, and it is meant to sit beside the official booklet while you revise.
Where can I get the IB physics data booklet?
Your school or teacher has the current edition that matches your syllabus, and you receive a copy in the exam. Always revise from the edition for your own exam session, because the booklet changed with the 2025 first-assessment syllabus.
Do I need to memorise the formulas in the IB physics data booklet?
You do not need to memorise the equations that are printed in the booklet, but you must know what each symbol means, which units it uses and when it applies. The lessons here focus on exactly that: where a formula comes from, what each term means and a worked example with context.
Which topics does this formula sheet cover?
Every lesson published so far: the syllabus preface (units and conversions), kinematics and motion graphs, Newton’s laws and momentum, and Theme D fields (field strength, Newton’s law of gravitation, Coulomb’s law, magnetic fields, potential, orbits and escape speed). New lessons add their formulas here automatically.
Ready to practise? Open the interactive DP Physics lessons.