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Reference · Formulas

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.

EquationLeaves outUse when you have
v = v₀ + atdisplacementInitial velocity, acceleration, and time
x = x₀ + v₀t + ½at²final velocityInitial velocity, acceleration, and time
v² = v₀² + 2a(x − x₀)timeVelocities, acceleration, and displacement
x = x₀ + ½(v₀ + v)taccelerationBoth velocities and the time

Constants these formulas assume

Standard values in SI units. The site’s physical constants page carries the full list.

SymbolNameValue
gStandard gravity at Earth’s surface9.807 m/s²
GGravitational constant6.674×10⁻¹¹ N·m²/kg²
cSpeed of light in vacuum2.998×10⁸ m/s
kCoulomb constant8.988×10⁹ N·m²/C²
RGas constant8.314 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.

Which kinematic equation should I use?
Pick the one that omits the variable you neither know nor need. If a problem gives both velocities, the acceleration, and asks for displacement, use v² = v₀² + 2a(x − x₀), because it is the equation with no time in it.
When can I use conservation of energy instead of forces?
Whenever no friction or other dissipative force acts, or when you can account for the energy it removes. Energy methods skip the intermediate acceleration entirely, so a ball rolling down a slope is one line rather than several.
What is the difference between mass and weight in these formulas?
Mass m is the amount of matter, measured in kilograms, and appears in F = ma and KE = ½mv². Weight is the gravitational force on that mass, W = mg in newtons, and changes with location while mass does not.
Why do the rotational formulas look like the linear ones?
Because they are the same physics in angular coordinates. Mass maps to moment of inertia, force to torque, and velocity to angular velocity, so F = ma becomes τ = Iα and ½mv² becomes ½Iω².
Do these formulas work in any units?
Only if the units are consistent, and every constant listed here is in SI. Convert to metres, kilograms, seconds, and kelvin before substituting; a temperature left in degrees Celsius inside a gas or Carnot formula gives a badly wrong answer.
Why is Hooke’s law written with a minus sign?
F = −kx says the spring force points opposite to the displacement — stretch it right and it pulls left. The sign matters for direction and for deriving oscillation; when you only need the magnitude of the force, F = kx is enough.