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IB Physics Formula Explorer
Levels & boards: IB Diploma Physics (SL / HL; Years 12-13) International Baccalaureate Diploma Programme. Independent equation explorer; consult the current IB data booklet.
Search this IB Physics formula resource by topic, save useful equations and reveal original worked examples. Original equation explanations and practice examples alongside the official IB course are organised into individual cards with notation, conditions and common mistakes.
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43 formulas
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Average speed
v = s/t
Notation / units: v m/s; s m; t s.
Use when: Distance over elapsed time; t>0.
Worked example and common mistake
90 m in 6 s gives 15 m/s.
Watch out: Speed uses total distance; average velocity uses displacement.
Acceleration
a = (v-u)/t
Notation / units: a m/s^2; velocities m/s; t s.
Use when: Average acceleration over the interval.
Worked example and common mistake
From 4 to 16 m/s in 3 s: a=4 m/s^2.
Watch out: Use change in velocity, not final velocity alone.
Constant-acceleration velocity
v = u+a*t
Notation / units: u and v m/s; a m/s^2.
Use when: Acceleration is constant.
Worked example and common mistake
u=3, a=2, t=4 gives v=11 m/s.
Watch out: This equation is not a general variable-acceleration model.
Constant-acceleration displacement
s = u*t + a*t^2/2
Notation / units: s m; t s.
Use when: Acceleration constant along the chosen axis.
Worked example and common mistake
u=0, a=3, t=4 gives s=24 m.
Watch out: Only the second term includes t squared.
Velocity-displacement relation
v^2 = u^2 + 2*a*s
Notation / units: SI units; sign convention consistent.
Use when: Constant acceleration; time is eliminated.
Worked example and common mistake
u=2, a=3, s=10 gives v^2=64; forward speed=8 m/s.
Watch out: The square-root sign alone does not determine direction.
Resultant force
F = m*a
Notation / units: F N; m kg; a m/s^2.
Use when: Constant mass; F is the net force.
Worked example and common mistake
A 4 kg object at 2.5 m/s^2 has resultant force 10 N.
Watch out: One applied force is not necessarily the resultant force.
Weight
W = m*g
Notation / units: W N; m kg; g N/kg.
Use when: Use the gravitational field strength supplied.
Worked example and common mistake
m=3 kg, g=9.8 gives W=29.4 N.
Watch out: Weight is a force; mass is not measured in newtons.
Momentum
p = m*v
Notation / units: p kg m/s.
Use when: Non-relativistic motion.
Worked example and common mistake
m=0.6 kg, v=5 m/s gives p=3 kg m/s.
Watch out: Include signs when opposite directions are compared.
Impulse
impulse = F*delta(t) = delta(p)
Notation / units: N s, equivalent to kg m/s.
Use when: F constant or interpreted as mean resultant force.
Worked example and common mistake
12 N for 0.5 s changes momentum by 6 kg m/s.
Watch out: Do not use a peak force as the average force without justification.
Moment of a force
moment = F*d_perpendicular
Notation / units: N m.
Use when: Distance perpendicular from pivot to force line.
Worked example and common mistake
20 N at 0.15 m gives 3 N m.
Watch out: Lever length is not always the perpendicular distance.
Pressure
p = F/A
Notation / units: p Pa; F N; A m^2.
Use when: Force normal to the area.
Worked example and common mistake
80 N over 0.02 m^2 gives 4000 Pa.
Watch out: Convert cm^2 by dividing by 10000, not 100.
Liquid pressure difference
delta(p) = rho*g*h
Notation / units: rho kg/m^3; h m.
Use when: Static liquid of uniform density.
Worked example and common mistake
1000 * 9.8 * 0.5 = 4900 Pa.
Watch out: Add atmospheric pressure only when absolute pressure is required.
Density
rho = m/V
Notation / units: rho kg/m^3; m kg; V m^3.
Use when: Uniform sample or average density.
Worked example and common mistake
2 kg in 0.001 m^3 gives 2000 kg/m^3.
Watch out: Volume must be in cubic units.
Hooke law
F = k*x
Notation / units: F N; k N/m; extension x m.
Use when: Within the limit of proportionality.
Worked example and common mistake
k=200 N/m and x=0.03 m gives F=6 N.
Watch out: x means extension, not the spring's total length.
Elastic energy
E = k*x^2/2
Notation / units: E J.
Use when: Spring obeys Hooke law.
Worked example and common mistake
k=200, x=0.1 gives E=1 J.
Watch out: A non-linear force-extension curve requires its actual area.
Work by a parallel force
W = F*s
Notation / units: W J; F N; s m.
Use when: Force constant and parallel to displacement.
Worked example and common mistake
15 N through 4 m gives 60 J.
Watch out: A perpendicular force does no work on that displacement.
Kinetic energy
E_k = m*v^2/2
Notation / units: J; kg; m/s.
Use when: Non-relativistic translation.
Worked example and common mistake
m=2, v=6 gives E_k=36 J.
Watch out: Doubling speed multiplies kinetic energy by four.
Gravitational energy change
delta(E_p) = m*g*delta(h)
Notation / units: J.
Use when: Approximately uniform gravitational field.
Worked example and common mistake
m=2, g=9.8, rise=3 gives 58.8 J.
Watch out: Use height change, not total path length.
Power
P = E/t
Notation / units: P W; E J; t s.
Use when: Average transfer rate.
Worked example and common mistake
600 J in 5 s gives 120 W.
Watch out: Kilowatts must be converted when the rest is SI.
Efficiency
efficiency = useful output / total input * 100%
Notation / units: Both inputs in energy units or both in power units.
Use when: Include all input energy in the denominator.
Worked example and common mistake
Useful 45 J from 60 J gives 75%.
Watch out: A machine cannot produce more useful energy than its total input.
Specific heat capacity
Q = m*c*delta(T)
Notation / units: c J/(kg K); delta(T) K or degrees C.
Use when: No change of state; c approximately constant.
Worked example and common mistake
m=2, c=4200, rise=5 gives 42000 J.
Watch out: The equation does not describe energy during a phase change.
Specific latent heat
Q = m*L
Notation / units: L J/kg.
Use when: Change of state at constant temperature under stated conditions.
Worked example and common mistake
0.2 kg at L=334000 J/kg needs 66800 J.
Watch out: No temperature-rise factor belongs in this equation.
Wave speed
v = f*lambda
Notation / units: v m/s; f Hz; wavelength m.
Use when: A repeating wave in a specified medium.
Worked example and common mistake
f=50 Hz, lambda=0.8 m gives v=40 m/s.
Watch out: Frequency is not the same as period.
Frequency and period
f = 1/T
Notation / units: Hz and s.
Use when: One complete cycle takes T seconds.
Worked example and common mistake
T=0.02 s gives f=50 Hz.
Watch out: Milliseconds must be converted to seconds.
Electric charge
Q = I*t
Notation / units: Q C; I A; t s.
Use when: Current constant or mean over time.
Worked example and common mistake
0.5 A for 120 s transfers 60 C.
Watch out: Two minutes equals 120 s, not 2 s.
Potential difference
V = E/Q
Notation / units: V volts; E J; Q C.
Use when: Energy transferred per charge.
Worked example and common mistake
24 J transferred by 3 C gives 8 V.
Watch out: Voltage is energy per charge, not energy itself.
Resistance
R = V/I
Notation / units: R ohms; V volts; I amperes.
Use when: Ratio at an operating point; constant R needs ohmic behaviour.
Worked example and common mistake
12 V and 0.4 A gives 30 ohms.
Watch out: Do not assume a filament lamp has constant resistance.
Electrical power
P = V*I
Notation / units: P W.
Use when: Use the voltage across and current through the same device.
Worked example and common mistake
12 V and 2 A gives 24 W.
Watch out: Current in another branch is not the device current.
Half-life count
N = N0 * (1/2)^n
Notation / units: n number of half-lives.
Use when: A single decaying isotope; background handled separately for count rate.
Worked example and common mistake
Starting at 800, after 3 half-lives the expectation is 100.
Watch out: Half-life is not the time for every nucleus to decay.
Angular speed
omega = 2*pi/T
Notation / units: rad/s; period T s.
Use when: Uniform circular motion.
Worked example and common mistake
T=4 s gives omega=pi/2 rad/s.
Watch out: Frequency and angular speed differ by 2pi.
Centripetal acceleration
a = v^2/r = omega^2*r
Notation / units: m/s^2.
Use when: Acceleration towards centre.
Worked example and common mistake
v=6 m/s,r=3 m gives a=12 m/s^2.
Watch out: Centripetal force is a resultant direction, not an extra force.
Newtonian gravitation
F = G*M*m/r^2
Notation / units: F N; r centre-to-centre m.
Use when: Spherical masses or point-mass approximation.
Worked example and common mistake
If separation doubles, force becomes one quarter.
Watch out: Distance is from centres, not surfaces.
Gravitational field
g = G*M/r^2
Notation / units: N/kg.
Use when: Outside a spherical mass.
Worked example and common mistake
Doubling r gives one quarter of g.
Watch out: The surface value 9.8 is not universal.
Electric force
F = k*q1*q2/r^2
Notation / units: N; q coulombs; r m.
Use when: Point charges in vacuum; sign determines attraction/repulsion.
Worked example and common mistake
Doubling either charge doubles force magnitude.
Watch out: Millimetres and microcoulombs must be converted.
Uniform electric field
E = V/d
Notation / units: V/m, equivalent N/C.
Use when: Approximately uniform field between large parallel plates.
Worked example and common mistake
100 V across 0.02 m gives E=5000 V/m.
Watch out: Edge regions are not approximately uniform.
Electric field force
F = q*E
Notation / units: N.
Use when: Vector direction reverses for negative charge.
Worked example and common mistake
q=2e-6 C, E=3000 N/C gives 0.006 N.
Watch out: An electron accelerates opposite to the field direction.
Magnetic force on a wire
F = B*I*L*sin(theta)
Notation / units: B tesla; L m.
Use when: Straight wire in uniform field.
Worked example and common mistake
B=0.4 T,I=3 A,L=0.5 m perpendicular gives 0.6 N.
Watch out: Theta is the angle between current direction and magnetic field.
Magnetic force on a charge
F = B*q*v*sin(theta)
Notation / units: N.
Use when: Moving charge; angle between velocity and field.
Worked example and common mistake
Parallel motion gives zero magnetic force.
Watch out: A magnetic force perpendicular to velocity does no work.
Magnetic flux
Phi = B*A*cos(theta)
Notation / units: Wb.
Use when: Uniform field; theta is angle to area normal.
Worked example and common mistake
B=0.2 T,A=0.1 m^2,theta=0 gives 0.02 Wb.
Watch out: Use cosine of the angle to the normal, not to the plane.
Faraday induction magnitude
abs(emf) = abs(delta(N*Phi)/delta(t))
Notation / units: V.
Use when: Average rate of flux-linkage change.
Worked example and common mistake
Flux linkage changes by 0.12 Wb turns in 0.03 s: magnitude 4 V.
Watch out: Lenz law supplies direction; the magnitude alone does not.
SHM acceleration
a = -omega^2*x
Notation / units: a m/s^2; x displacement m.
Use when: Simple harmonic motion.
Worked example and common mistake
omega=3,x=0.02 gives a=-0.18 m/s^2.
Watch out: The minus sign shows acceleration towards equilibrium.
Spring oscillator period
T = 2*pi*sqrt(m/k)
Notation / units: s.
Use when: Ideal mass-spring oscillator; effective mass model applies.
Worked example and common mistake
m=1 kg,k=4pi^2 N/m gives T=1 s.
Watch out: A larger spring constant reduces the period.
Photon energy
E = h*f = h*c/lambda
Notation / units: J.
Use when: Photon energy; wavelength and c for the same propagation context.
Worked example and common mistake
Doubling frequency doubles photon energy.
Watch out: Intensity changes photon number, not each photon's energy at fixed f.
How to use the IB Physics Formula Explorer
- Choose a topic or enter a formula name, symbol or unit in the search field.
- Open the worked example and check the conditions before substituting values.
- Save difficult formulas for a focused list, test recall, then print or export that list.
A worked example
A photon with frequency 5.0 x 10^14 Hz has energy E=hf. Using h=6.62607015 x 10^-34 J s gives approximately 3.31 x 10^-19 J. Keep frequency and wavelength separate when choosing the equation.
What to check before using your result
- This independent collection is not the official IB data booklet, does not reproduce that booklet, and does not certify SL/HL coverage. Use your school-authorised current booklet for examination preparation.
- Use consistent units before substitution; a correct formula with incompatible units still gives a wrong result.
- A saved formula is a revision prompt, not evidence that you can apply it to an unfamiliar problem.
Make your next practice session count
Use this result as a starting point, not a label for your ability. Record one error, explain its cause and complete a similar question without the worked answer. Then try a different example to check that you understood the method rather than remembered a number.
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Reference sources and scope
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