A graph-paper notebook open on a desk under a lamp at night, with a mechanical pencil and a mug beside it

Published September 19, 2026 · The Electra Editorial Team · fact-checked against the sources below

A physics formula sheet is only useful if each entry carries the condition that makes it legal to use. This sheet groups the formulas a first-year course actually reaches for by topic, states what each one requires, and links every entry to a page that works it through with real numbers.

Most sheets are a wall of symbols, and that is the format’s weakness. The symbols are the part you can look up in ten seconds. The conditions are the part that decides whether the answer comes out right, and they are almost never printed next to the equation. The Physics Classroom is unusually blunt about this for the four kinematics equations: they apply to motion at constant velocity or constant acceleration, and they can never be used across any interval in which the acceleration is changing. Nothing in the written equation says so.

So every entry below is a link. The name and the equation are here; the conditions, the variable list, the common errors and a worked example live on the page behind it.

What belongs on a physics formula sheet?

Three things, in this order. The relationship itself. The meaning and SI unit of every symbol in it, because a formula with an unlabeled symbol is not a formula. And the conditions under which it holds, which is the entry most sheets omit and the entry that does the work.

A fourth thing belongs on the sheet only if you can state it: what the formula is a special case of. The kinematics equations are a special case of calculus for constant acceleration. OpenStax makes the assumption explicit, and says the reason for it is precisely to avoid needing calculus for instantaneous acceleration. Knowing that, you stop trying to use them on a problem where the force changes partway through.

Mechanics: which formula for which situation?

Mechanics is most of a first course, and almost all of it is one of four ideas: forces, energy, momentum, or rotation. Pick the idea first, then the formula.

Motion with constant acceleration. The kinematics equations are v = v₀ + at, x = x₀ + v₀t + ½at², v² = v₀² + 2a(x - x₀) and x = x₀ + ½(v₀ + v)t. Each one omits a different quantity, so you pick the one that skips the variable you neither know nor need. The Physics Classroom frames the selection the same way: each equation holds four variables, and knowing three of them gives you the fourth.

Forces. Newton’s second law is ΣF = ma, applied one axis at a time as ΣF_x = ma_x and ΣF_y = ma_y, with weight w = mg. Tension is not a separate law at all: T = mg for a hanging mass at rest, T = m(g + a) when it accelerates, and in every other case you apply ΣF = ma to each object on its own.

Energy. The work-energy theorem says W_net = ΔKE = ½mv² - ½mv₀², with work from a constant force given by W = Fd·cos θ. This is the formula to reach for when a problem gives you distances and speeds but no time.

Momentum. Momentum is p = mv, and for two objects m₁v₁ + m₂v₂ = m₁v₁’ + m₂v₂’. Impulse is the same idea over a time interval: J = F_avg·Δt = Δp. Collisions and anything involving a short, hard contact belong here rather than in energy, because kinetic energy is usually not conserved and momentum usually is.

Two dimensions and circles. Projectile motion splits into v₀ₓ = v₀·cos θ₀ horizontally and v₀ᵧ = v₀·sin θ₀ vertically, with the two halves sharing only the time. Centripetal force is F_c = mv²/r, which names the size of the force needed rather than adding a new force to the diagram.

Rotation. Torque is τ = rF·sin θ, and Στ = Iα is Newton’s second law with rotational parts swapped in. The I in it comes from the moment of inertia, which is ½mR² for a solid disk, (1/12)mL² for a thin rod about its center, and I_cm + md² whenever the axis moves off the center of mass.

Electricity and magnetism: which of these is not a law?

Ohm’s law, as it happens. OpenStax says directly that despite the name it is not considered a law of nature the way Newton’s laws or the laws of thermodynamics are. V = IR is an empirical statement that holds for ohmic materials, where current stays proportional to voltage, and fails for nonohmic ones such as a diode. Power follows from it as P = VI = I²R = V²/R.

The rest of the standard set: Coulomb’s law gives the electrostatic force between point charges as F = k·|q₁q₂|/r². Kirchhoff’s laws are ΣI_in = ΣI_out at a junction and ΣV = 0 around a loop, which are conservation of charge and conservation of energy written for circuits. Faraday’s law of induction is ε = -N·ΔΦ/Δt, with flux Φ = BA·cos θ, and the minus sign is the physics rather than a typographical decoration.

Waves and optics: why is the sheet so short?

Because two relationships carry most of an introductory treatment. The wave speed equation is v = fλ, with f = 1/T. Snell’s law is n₁·sin θ₁ = n₂·sin θ₂, where n = c/v, and the critical angle sin θ_c = n₂/n₁ exists only when light is going from the denser medium to the less dense one.

The short sheet is honest here. Optics problems are hard because of geometry and sign conventions, not because there are many formulas to hold.

Fluids and thermodynamics: where do the units go wrong?

In the temperature, almost every time. The ideal gas law is pV = nRT, and OpenStax states flatly that T must be in kelvin. Celsius in that equation is not an approximation, it is a wrong answer. The same page gives R as 8.31 J/(mol·K) in SI units, or 0.0821 L·atm/(mol·K) when pressure is in atmospheres, and the two are not interchangeable mid-problem.

Pressure is p = F/A, with p = p₀ + ρgh at depth in a fluid of constant density. Bernoulli’s equation is p + ½ρv² + ρgy = constant along a streamline, and in practice it almost always arrives with the continuity equation A₁v₁ = A₂v₂ attached, because one equation with two unknown speeds does not solve.

One entry from modern physics earns its place on a first-year sheet: the half-life formula, N = N₀·(1/2)^(t/T½). It is worth doing the arithmetic once to see how fast it moves. After three half-lives the fraction left is (1/2)³ = 1/8 = 0.125, so 12.5 percent of the original sample remains.

Which constants belong on the sheet?

The ones you will use, at the precision you will use them, taken from NIST rather than from memory. The CODATA 2022 values give the speed of light as exactly 299,792,458 m/s, the elementary charge as exactly 1.602176634 × 10⁻¹⁹ C, the Boltzmann constant as exactly 1.380649 × 10⁻²³ J/K, the Avogadro constant as exactly 6.02214076 × 10²³ mol⁻¹, the molar gas constant as 8.314462618 J/(mol·K), the Newtonian constant of gravitation as 6.67430 × 10⁻¹¹ m³/(kg·s²), and standard gravity as exactly 9.80665 m/s².

The Coulomb constant is the one students most often half-remember, and it is worth deriving rather than trusting. NIST gives the vacuum electric permittivity as ε₀ = 8.8541878188 × 10⁻¹² F/m. Then k = 1/(4πε₀) = 1 / (4 × 3.14159265 × 8.8541878188 × 10⁻¹²) = 8.9876 × 10⁹, which is the 8.99 × 10⁹ N·m²/C² that appears in textbooks, rounded to three significant figures.

How do you use a sheet while working a problem?

Late. The sheet is for the fourth step, not the first. The method on how to solve physics problems puts the formula after the knowns, the diagram and the principle, for the simple reason that scanning a sheet for a formula whose symbols match your variables is how people end up applying constant-acceleration equations to a problem where the acceleration changes.

Use it this way instead. Name the principle, open the page for the formula that expresses it, and read the conditions before the equation. If one condition does not hold, the formula is the wrong one and you have saved yourself a page of algebra.

This is the part where a sheet stops being able to help and a tutor can. Electra’s formula sheet states when each formula applies, and if you photograph the problem you are actually stuck on, it names the principle, checks the condition, and shows the algebra line by line so you can see which step you would have gotten wrong. Every step is visible on purpose, because the point is to be able to do the next one yourself.

The full set, with the variables, the conditions and a worked example on every page, lives at physics formulas.

Sources