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The Grand Physics Compendium... all your formulas in one place.


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I do not recommend this for learning physics, only for finding formulas when necessary or understanding what they mean. Either scroll down to your unit or CTRL+F any formula you need!


I want more formulas!

I will only be adding formulas from units we cover in my IB Physics HL course. If you have any other, please go to 'About Us' to find the github page and contribute your own formulas to this project!




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Unit 1: Kinematics

Formula Note
$$v = \frac{d}{\Delta t}$$ Calculate constant velocity.
$$v_f = v_i +at$$ Change in velocity is equal to acceleration x time.
$$\Delta d = v_it + \frac{1}{2}at^2$$ Quadratic equation for object undergoing acceleration.
$$t=\frac{-V_i \pm \sqrt{V_i^2+2a \Delta d}}{a}$$ Quadratic formula, time when projectile hits the ground.
$$\Delta d = \frac{v_i+v_f}{2}$$ Find distance travelled based on acerage velocity.
$$t=\sqrt{\frac{2 \Delta d}{a}}$$ If initial velocity is zero, easy way to solve for time.
$$v_f^2 = v_i^2+2a \Delta d$$ Square proportionality between both velocities, acceleration and distance travelled.

Unit 2: Dynamics

Formula Note
$$a = \frac{F_{net}}{m}$$ Newton's second law.
$$F_g = mg$$ This is weight. 'g' is the gravitational constant, which is why you weigh differently on the moon!
$$F_N = -mg$$ Normal force, acts perpendicular to weight. Example, exerted by table on book to keep it on the table.
$$F_f = \mu F_N$$ Friction force, acts opposite to motion of an object.
$$F_s = -k \Delta x$$ Spring force which is proportional to negative displacement of an object since it tries to reach equilibrium.
$$\mu_s = \tan \theta$$ Find static coefficient of friction of an object on an inclined plane, theta being the angle when the object begins to slide.
$$F_x = mg \sin \theta$$ Force parralel to incline plane, moving the object.
$$F_y = mg \cos \theta$$ Force perpendicular to incline plane.
$$F_{on1by2} = -F_{on2by1}$$ Newton's third law of motion.
$$W = F \Delta d$$ Work done by an object.
$$W = F \Delta d \cos \theta$$ Work done by an object force is acting at an angle.
$$F_T = ma = Ma$$ Frictionless pulley with two objects attached on a string.
$$a = \frac{M_g - m_g}{m+M}$$ Find acceleration of objects on a pulley.
$$PE_g = mgh$$ Potential gravitational energy.
$$KE = \frac{1}{2}mv^2$$ Kinetic energy.
$$PE_{el} = \frac{1}{2}k \Delta x^2$$ Potential elastic energy.
$$W = \Delta KE + \Delta PE_g + \Delta PE_e$$ Change in mechanical energy is work.
$$h = L(1-\cos \theta)$$ Vertical height of pendulum string.
$$P = \frac{W}{t} = Fv$$ Power of an object.
$$e = \frac{P_{out}}{P_{in}}$$ Efficiency of a mechanical system.
$$p = mv$$ Momentum of an object.
$$F = \frac{\Delta p}{\Delta t} = m(\frac{v_f-v_i}{t})$$ Newton's second law.
$$\Delta p = F \Delta t$$ Impulse-momentum formula.
$$m_1v_{i1} + m_2v_{i2} = m_1v_{f1} + m_2v_{f2}$$ Perfectly elastic collisions.
$$m_1v_1 + m_2v_2 = v_f(m_1+m_2)$$ Perfectly inelastic collisions. Objects move at same speed before or after collision.

Unit 3: Thermodynamics

Formula Note
$$Q = mc \Delta T$$ Energy, or heat, in a medium of set mass.
$$Q_{latent} = mL$$ Latent heat of an object as it goes through phase changes.
$$Q_1 = -Q_2$$ Heat gained by one object is lost by the other object.
$$PV=nRT$$ Relationship between pressure, volume, and temperature in an ideal gas.
$$PV = NK_BT$$ Same as previous formula but using Boltzman's constant.
$$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$$ Derivation of what happens to a a set object when it changes pressure, temperature, or volume.
$$P=\frac{F}{A}$$ Formula for pressure acting on a given surface.
$$PV = \frac{N}{3}mv^2$$ Theoretical equation of an ideal gas.
$$KE = \frac{3}{2}K_BT$$ Average kinetic energy of molecules in an ideal gas.
$$v = \sqrt{\frac{3K_BT}{m}}$$ Mean value of speed of molecules in an ideal gas.

Unit 4: Waves

Formula Note
$$\Delta x = x_0 \cos (\omega t)$$ Displacement of an oscillating object.
$$\omega = 2 \pi f$$ Speed of wave.
$$\omega^2 = \frac{k}{m}$$ Speed of wave in an elastic string.
$$T = \frac{1}{f} \rightarrow f = \frac{1}{T}$$ Relationship between frequency and time.
$$a = -{\omega}^2x$$ Current acceleration.
$$a_{max} = -{\omega}x_0$$ Maximum acceleration.
$$v_{max} = \omega x_0$$ Maximum velocity.
$$v(t) = -x_0 \omega \sin (\omega t)$$ Velocity as a function of time.
$$a(t) = x_0 \cos (\omega t)$$ Acceleration as a function of time.
$$KE(t) = \frac{1}{2}mx_0^2 {\omega}^2 \sin (\omega t)$$ Kinetic energy as a function of time.
$$PE_{elastic}(t) = \frac{1}{2}kx_0^2 {\cos}^2 (\omega t)$$ Potential elastic energy as a function of time.
$$\lvert \Delta d \rvert = n \lambda$$ Path difference for constructive interference of double slit.
$$\lvert \Delta d \rvert = (n+\frac{1}{2}) \lambda$$ Path difference for destructive interference of double slit.
$$d \sin \theta = n \lambda$$ Local maximum of intensity acting on a wall after a double slit.
$$\frac{S}{D} = \frac{n \lambda}{d}$$ Small angle approximation derived from previous formula.
$$\theta_i = \theta_r$$ Angle of incident is equal to angle of reflection.
$$n_1 \sin \theta_i = n_2 \sin \theta_r$$ Snell's law for angle of refraction.
$$\sin \theta_c = \frac{n_2}{n_1}$$ Snell's law when $\theta_r = 90°$ for critical angle of refraction.
$$n = \frac{c}{v}$$ Refractive index of a wave. Higher index means wave travels slower in a given medium.
$$b \sin \theta = \frac{n \lambda}{b}$$ Destructive interference in a single slit.
$$I \propto A^2$$ Intensity is related to the square of the amplitude of the wave.
$$I \propto x^{-2}$$ If distance from source increases, intensity decreases by the square of that.
$$I = I_0 \cos^2 \theta$$ Intensity of a polarized light source, maximum at $n\pi, n \in \mathbb{N}$.

Unit 5: Electricity and Magnetism

Formula Note
$$F = k \frac{q_1q_2}{r^2}$$ Coulomb's Law. The electric force between two charges, seperated by distance r. What's $k$, you may ask?
$$k = \frac{1}{4\pi\varepsilon_0} \approx 8.99 Nm^2C^{-2}$$ Coulomb constant, defined in terms of the permittivity of free space.
$$W=Vq$$ Work done (energy) by a particle is equal to the voltage times the charge.
$$E = \frac{F}{q_2} = \frac{q_1}{r^2}$$ Electric field strength acting on a charge. Divide by the charge of which you are finding the field strength.
$$I = nAvq \rightarrow v = \frac{I}{nAq}$$ More details on current in terms of the velocity of the electrons, the right formula will come in handy to calculate their speed!
$$I = \frac{\Delta q}{\Delta t}$$ Current is the rate of change of charge (how fast/many electrons are flowing).
$$V = IR$$ Ohm's Law. Beautiful. In an ohmic system, voltage is the product of current times resistance.
$$\Sigma V = 0$$ Kirchhoff's voltage law, sum of all voltages across any loop in a circuit will be 0.
$$\Sigma I = 0$$ Kirchhoff's current law, sum of all current intering a node equals the sum of all current leaving the node.
$$P = VI = I^2R = \frac{V^2}{R}$$ Power dissipated in a source of resistance (joule heating)
$$R_{total} = \Sigma R = R_1 + R_2 + ...$$ Sum resistance when resistors are IN SERIES (same wire).
$$R_{total} = \frac{1}{\Sigma \frac{1}{R}} = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2} + ...}$$ Sum reciprocal resistance when resistors are IN PARALLEL (seperated by node).
$$\delta = \frac{RA}{L} = \frac{R\pi r^2}{L}$$ Resistivity equals resistance times cross sectional area of wire divided by length of wire.
$$\varepsilon = I(R + r) \rightarrow V = \varepsilon - Ir$$ Internal resistance of a battery cell, notably the output voltage DECREASES when current INCREASES.
$$F = qvB \sin \theta$$ Lorentz force for a particle in a magnetic field of charge $q$ and velocity $v$, where $\theta$ is the angle to the normal (they will try and trick you with this, force is highest when at a right angle!)
$$F = BIL \sin \theta$$ Lorentz force for wire of length $L$ and current $I$, where $\theta$ is the angle to the normal (they will try and trick you with this, force is highest when at a right angle!)