Physics Formulas: The Complete List You Actually Need

• F = net force (in Newtons, N)
• m = mass (in kilograms, kg)
• a = acceleration (in m/s²)
• When you'd use it: Any problem that gives you mass and asks about force or acceleration. "A 5 kg box is pushed with a net force of 20 N. Find its acceleration" that's F = ma.
• Common mistake: Using total weight instead of net force. If there's friction, you need to subtract it first.

• W = weight (force of gravity, in Newtons)
• m = mass (kg)
• g = gravitational acceleration (9.8 m/s² on Earth)
• When you'd use it: Converting between mass and gravitational force. Weight and mass are not the same thing mass is how much stuff is in an object, weight is the force gravity pulls on it.
• Common mistake: Plugging weight in where mass is required. Always check what the problem is actually asking for.

• p = momentum (kg·m/s)
• m = mass (kg)
• v = velocity (m/s)
• When you'd use it: Collision problems, or any time a problem mentions "momentum" or "conservation of momentum."

• J = impulse (N·s)
• F = force (N)
• Deltat = time interval (s)
• When you'd use it: Impulse and momentum are linked impulse equals the change in momentum. Useful when you're given a force acting over a short time.

• W = work done (Joules)
• F = force applied (N)
• d = displacement (m)
• Theta = angle between force and displacement
• When you'd use it: When a force is applied at an angle (like pushing a box across the floor with a rope at 30°). If the force is perfectly horizontal, cosTheta = cos(0°) = 1 and you can simplify to W = Fd.
• Common mistake: Forgetting the cosine when the force isn't parallel to the direction of motion. Always check the angle.

• P = power (Watts)
• W = work done (Joules)
• t = time (seconds)
• When you'd use it: Any question asking "at what rate" something is done, or anytime "power" shows up in the question.

• KE = kinetic energy (Joules)
• m = mass (kg)
• v = velocity (m/s)
• When you'd use it: Any moving object. Rollercoasters, thrown balls, sliding boxes if it's moving, it has kinetic energy.
• Common mistake: Forgetting to square the velocity. The "²" does a lot of work in this formula. Double the velocity and the kinetic energy quadruples.

• PE = potential energy (Joules)
• m = mass (kg)
• g = 9.8 m/s²
• h = height above reference point (m)
• When you'd use it: Any time an object has height a ball about to roll down a ramp, a diver at the top of a platform.

• k = spring constant (N/m)
• x = compression or stretch distance (m)
• When you'd use it: Any spring problem. The stiffer the spring (higher k), the more energy stored for the same stretch.

• When you'd use it: Any time energy is being converted from one type to another without friction. A ball dropped from a height converts all PE into KE by the time it hits the ground.
• Common mistake: Forgetting that this equation assumes no energy loss. If there's friction, you need to account for it.

Work-Energy Theorem: W = DeltaKE

• When you'd use it: When work is done on an object, it changes that object's kinetic energy. This ties mechanics (force/work) to energy.

• Q = heat transferred (Joules)
• m = mass (kg)
• c = specific heat capacity (J/kg·K). This is a property of the material, given in problems
• DeltaT = change in temperature (K or °C, since it's a change)
• When you'd use it: Problems with heating or cooling substances. "How much heat does it take to raise 2 kg of water by 10°C?"
• Common mistake: Using the wrong specific heat capacity. Water is c = 4,186 J/kg·K. Other materials have different values; always check.

• P = pressure (Pascals)
• V = volume (m³)
• n = number of moles
• R = gas constant (8.314 J/mol·K)
• T = temperature (must be in Kelvin)
• When you'd use it: Any problem involving a gas at different pressure, volume, or temperature conditions.
• Common mistake: Using Celsius instead of Kelvin. You must convert: K = °C + 273.

• DeltaU = change in internal energy
• Q = heat added to the system
• W = work done by the system
• When you'd use it: Problems about gas cycles, heat engines, or any system where you're tracking energy in and out.

• DeltaL = change in length (m)
• a = coefficient of linear expansion (depends on material)
• Lo = original length (m)
• DeltaT = temperature change
• When you'd use it: Problems about solids expanding when heated, like bridges or rails.

• V = voltage (Volts)
• I = current (Amperes)
• R = resistance (Ohms, Omega)
• When you'd use it: Almost every basic electricity problem. Solve for any of the three variables when you know the other two.

• P = IV (when you know current and voltage)
• P = I²R (when you know current and resistance)
• P = V²/R (when you know voltage and resistance)
• When you'd use it: Any problem asking for power consumption in a circuit.

• F = electrostatic force (N)
• k = Coulomb's constant (8.99 × 109 N·m²/C²)
• q1, q2 = magnitudes of the two charges (Coulombs)
• r = distance between charges (m)
• When you'd use it: Force between two point charges.

• E = electric field strength (N/C)
• F = force on a test charge (N)
• q = test charge (C)

• Series: R_total = R1 + R2 + R3 ...
• Parallel: 1/R_total = 1/R1 + 1/R2 + 1/R3 ...
• Common mistake: This is the most frequently confused formula in electricity. The series adds directly. Parallel uses the reciprocal formula. Get these backwards, and every circuit problem falls apart.

• F = magnetic force (N)
• q = charge (C)
• v = velocity of the charge (m/s)
• B = magnetic field strength (Tesla)
• Theta = angle between velocity and magnetic field
• When you'd use it: Problems involving charged particles moving through magnetic fields.

• v = wave speed (m/s)
• f = frequency (Hz, cycles per second)
• Lambda = wavelength (m)
• When you'd use it: Any wave sound, light, or otherwise. You'll often be given two of these and asked to find the third.

• T = period (seconds per cycle)
• f = frequency (cycles per second)
• When you'd use it: Converting between how often a wave oscillates and how long each oscillation takes. Period and frequency are reciprocals.
• Common mistake: Confusing which is which. Frequency is how many cycles per second. Period is how many seconds per cycle.

• n = index of refraction (different for each medium)
• Theta = angle of incidence or refraction (measured from the normal)
• When you'd use it: Any problem about light bending as it passes from one medium to another (air to water, glass, etc.).

• f = focal length of the mirror or lens
• do = distance from object to mirror/lens
• di = distance from image to mirror/lens
• When you'd use it: Problems involving mirrors, lenses, or images formed by optical systems.

• E = energy (Joules)
• m = mass (kg)
• c = speed of light (3 × 108 m/s)
• When you'd use it: Nuclear reactions and problems involving mass-energy conversion. In standard high school physics, this is more conceptual than computational you'll know it for tests but won't do much with the math.

• E = energy of a photon (Joules)
• h = Planck's constant (6.626 × 10-34 J·s)
• f = frequency of light (Hz)
• When you'd use it: Any problem involving photons, the photoelectric effect, or quantum energy calculations. This is the formula you'll actually compute with in quantum-related problems.

• Lambda = wavelength of a particle (m)
• h = Planck's constant
• m = mass of the particle (kg)
• v = velocity (m/s)
• When you'd use it: Problems dealing with wave-particle duality, showing that particles like electrons also have wavelength properties.

• N = remaining amount of substance
• N0 = initial amount
• Lambda = decay constant (specific to each isotope)
• t = time elapsed
• When you'd use it: Half-life problems and radioactive decay calculations.

Step 1: List what you know. Read the problem and write down every value you're given. Assign each one to a variable. Identify what you're solving for.

Step 2: Match your knowns to the right formula. Look at your list of known variables. Which formula uses exactly those variables plus the one you're missing? That's your formula. If you cover the topics you'll encounter in physics homework, the variable-matching method will carry you through most of them.

Step 3: Check units before calculating. Physics problems love unit traps. Make sure your values are in compatible units before you plug them in. Celsius versus Kelvin, grams versus kilograms, centimeters versus meters, unit errors kill otherwise correct answers.

Step 4: Double-check significant figures. Your answer should match the precision of the values you were given. Three sig figs in, three sig figs out.