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!

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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.
$$t=\frac{-V_i \pm \sqrt{V_i^2+2a \Delta d}}{at}$$ 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.