Physics Equations

Based SI Units

Meters, mKilograms, kgSeconds, sAmperes, AKelvin, KMoles, molCandela, cd

Derived SI Units

Area𝑚 ²ForceNewton, N = (kgm)/s ²
Volume𝑚^3PressurePascal, Pa = N/m ²
Velocitym/sEnergyJoules, J = 𝑁 ∗ 𝑚
Accelerationm/s ²PowerWatts, W = J/s


sin 30 1/2cos 30 0.9tan 30 1/2
sin 45cos 45tan 45
sin 600.9cos 601/2tan 602
1 km 0.62 miles1 mile1.6 km
1 meter3.28 feet1 atm101325 Pa
1 kg2.2 lbs

Prefixes for Units

Giga – GMega – MKilo – KCenti – cMili – mMicro – μNano – n

Electricity Equations

Electric field E = R/q₀
Electric field due to point charge E = Kq/ r²
Electrostatic force F = Kq₁q₂/ r²
Electric potential energy kQq/r
Electric potential U/q = kQ/r
∆V = ∆U/q₀
(ratio of charge’s electric potential energy to magnitude of charge itself)
Potential energy in capacitor U = 1/2CV ²
Magnitude of electric field Fe/q = kQ/r ²
Magnitude of uniform electric field V/d (V=Ed)

Energy Equations

1st law of thermodynamics change in total internal energy(U) = Q-W
Elastic potential energy U=1/2kx ²
Area under Force*distance graph=work
EnergyE=F*dcapacity to do work (force*distance)=Joules
Kinetic energy formula KE = 1/2 mv²
Kinetic Energy of Ejected Electron E = hf-W w= work function, w=hf (threshold)
PE mgh
Spring PE PE = 1/2 Kx²

Flow Equations

Laminar flow/Poiseuille’s law πr^4ΔP/8nL n=viscosity
Turbulent flow Nn/pDN=constant, n=viscosity, p=density, D=diameter

Force Equations

Buoyant Force 1)density x volume of fluid displaced x gravity
2)density of the fluid x Volume submerged x gravity
Centripetal Force Ac = V²/ r
Fc = mv²/ r
Conservation of momentum m₁v₁ + m₂v₂ = m₁v₁ + m₂v₂
Frictional Coefficient U=Ff/FnU=coefficient of friction (kinetic or static)
static > kinetic
Hooke’s law F = -Kx (K= spring const)
Kinetic Friction Fk = µkFn
Static friction Fs≤ µsFn
Gravitation Force F=Gmm/r ²U=coefficient of friction (kinetic or static)
Fn=normal force
Causes Kinetic energy to be converted into heat energy
Law of gravitation F=GM₁M₂/ r²
Magnitude of electrostatic force between 2 charges kqq/r^2
Momentum p=mv
Newtons second law Fnet = ma
Impulse change in momentum=mass*change in velocity
Torquet = F x r
t = Flsinθ (l=length)
a force that causes rotation distance from center

Gas Equations

Internal energy of ideal gas U = 3/2 nRT
Kinetic Gas Theory KE= 3/2 PV

Heat Equations

Equilibrium gibbs energy ∆G˚ = -RTlnKeq
Gibbs free enegy ∆G = ∆H – T∆S
Heat Equation Heat (q) = mcΔT c is specific heat; or Q=mL if there is a phase change, L is heat of transformation
Latent heat ∆Q = mL
Thermal expansion ΔL = ɑLΔT alpha is coefficient of linear expansion, L is original length, and t is change in temp

Kinematics Equations

Distance formula d=vt
Vƒ = V¡ + at
Vƒ² = V¡² + 2aΔx
Find distance when given time and rate Δx = V¡t + 1/2at²
Δx = Vƒ- 1/2at²
Δx = 1/2(V¡ + Vƒ)t

Lens Equations

Critical angle (Θ)= sin-1(n2/n1)
Lensmakers equation 1/f = 1/o + 1/i
Lens slit systems with one slit asinΘ=n wavelength  A is width, theta is angle, n is integer indicating number of the fringe
Lens slit system with multiple slits dsinΘ=(n+½)wavelength D is distance
Lenses where thickness can’t be neglected 1/f=(n-1)(1/r1-1/r2) N is index of refraction, r is radius of curvature of each lens
Magnification m = -i/o i = image o=object
Power of lenses 1/f Power is positive for converging and negative for diverging

Light Equations

Energy of a photon E = hf = hc/wavelength
Index of Refraction n = c/vc = 3×10^8
v = velocity wave
Snell’s law n₁sinθ₁ = n₂sinθ₂

Magnetic Equations

Magnetic force qvBsinΘ Thumb towards velocity, fingers towards magnetic field, palm in direction of force
Magnetic force by external magnetic field (straight wire) ILBsinΘ
Magnitude of magnetic field ᘈI/2πr, Circular its just ᘈI/2r

Sound Equations

Doppler effect f’=f[(v+-vd)/(v+-vs)] numerator: listener moving towards +, denominator: source moving away +
Sound level 10log I/Io I- intensity of sound wave, Io is threshold of hearing
Speed of sound radical(B/p) B = bulk modulus, measure of the medium’s resistance to compression. p = density of medium

Sound Waves Equations

Open pipes/standing waves Wavelength = 2L/n (Frequency = nv/2L) L = length, n = number of half wavelengths
Closed pipes wavelength = 4L/n (Frequency = nv/4L)
Doppler effect f = f (v±Vd)/ (v±Vs)
Spring angular frequency w= 2πf = √K/m
Pendulum angular freqency w = 2πf = √g/L
Wave speed v=fλ
Wave frequency and period f = 1/T

Temperature Equations

Celsius to Kelvin K=C+273
Farenheit to Celsius C= 5/9 (F-32)
Boiling point Celcius and Fahrenheit 100, 180

Voltage Equations

Capacitance q = VC
Capacitors in parallel Cp = C₁ + C₂ + etc
Capacitors in series 1/Cs = 1/C₁ + 1/C₂ + etc
Energy stored by capacitor U = 1/2CV²
Current I = ∆q/ ∆t (q = charge)
Ohms law P=IV
(v = volts, I= current, R = resistance, P= power)
Magnetic force F =qvBsinθ
F = ILBsinθ
Magnetic force around wire B = µ₀I/ 2πr (I= current)
Magnetic field at center of wire loop B = µ₀I/ 2r
Resistors in parallel 1/Rp = 1/R₁ + 1/R₂ + etc
Resistors in series Rs = R₁ + R₂ + etc

Water Equations

Buoyant force Fb = pVg
Density p = m/V
Osmotic pressure π = MRT
Pressure P = F/A
Specific gravity s.g = psub/ pwater (p = density)
Total pressure of fluid Ptot = Patm + Pgauge

Work Equations

1st law of thermo ∆U = Q-W (work = W)
Work W=Fdcosθ
W =energy transferred (=change in energy)
W =area under P-V graph
PowerP =work/time=Watts (joules/sec)
P =Force*velocity