Physics Formulas
A copy-able sheet — kinematics, forces, energy, rotation, waves, electricity, heat, and gravitation.
Showing 52 of 52. Click any formula to copy it.
Every formula assumes SI units: metres, kilograms, seconds, newtons, joules, kelvin. Near Earth’s surface g = 9.807 m/s². Convert before substituting or the answer will be out by a power of ten.
Introductory physics runs on about fifty equations. The four constant-acceleration formulas cover motion, F = ma covers forces, and energy questions reduce to KE = ½mv² and PE = mgh. The sheet above groups them by topic so you can filter to the family a problem needs and copy any line.
How the families fit together
The kinematic equations describe motion without asking what causes it — each one leaves out a different variable, so you pick the one missing the quantity you neither know nor want. Newton’s second law then supplies the cause: once you know the net force you know the acceleration, and the kinematics take over from there.
Energy offers a shortcut around both. Where a kinematics-plus-forces route needs several steps, conservation of energy often answers the same question in one line, because the total of kinetic and potential energy stays fixed when no friction acts. Momentum plays the same role for collisions: it is conserved even when energy is not, which is what makes inelastic collisions solvable at all.
Rotation mirrors translation
Every linear quantity has an angular twin, and the formulas have the same shape. Force becomes torque, mass becomes moment of inertia, velocity becomes angular velocity: F = ma turns into τ = Iα, and ½mv² turns into ½Iω². Learning the mapping is faster than memorising the rotational set separately.
The four kinematic equations
For constant acceleration only. Each omits one variable — pick the one missing what you neither know nor need.
| Equation | Leaves out | Use when you have |
|---|---|---|
| v = v₀ + at | displacement | Initial velocity, acceleration, and time |
| x = x₀ + v₀t + ½at² | final velocity | Initial velocity, acceleration, and time |
| v² = v₀² + 2a(x − x₀) | time | Velocities, acceleration, and displacement |
| x = x₀ + ½(v₀ + v)t | acceleration | Both velocities and the time |
Constants these formulas assume
Standard values in SI units. The site’s physical constants page carries the full list.
| Symbol | Name | Value |
|---|---|---|
| g | Standard gravity at Earth’s surface | 9.807 m/s² |
| G | Gravitational constant | 6.674×10⁻¹¹ N·m²/kg² |
| c | Speed of light in vacuum | 2.998×10⁸ m/s |
| k | Coulomb constant | 8.988×10⁹ N·m²/C² |
| R | Gas constant | 8.314 J/(mol·K) |
The mistakes that cost marks
Three recur. The first is using a kinematic equation when the acceleration is not constant — all four are derived on that assumption and none survives without it. The second is mixing units: a velocity in km/h substituted into a formula expecting m/s is out by a factor of 3.6, and the arithmetic will look perfectly reasonable.
The third is dropping vector direction. Force, velocity, acceleration, and momentum all carry a sign that encodes direction, and a collision problem where one object moves left needs that velocity entered as negative. Choose a positive direction before you start and keep it for the whole problem.