A Comprehensive List of All the Physics Formulas

Learning physics is all about applying concepts to solve problems. This article provides a comprehensive physics formulas list, that will act as a ready reference, when you are solving physics problems. You can even use this list, for a quick revision before an exam.

Physics is the most fundamental of all sciences. It is also one of the toughest sciences to master. Learning physics is basically studying the fundamental laws that govern our universe. I would say that there is a lot more to ascertain than just remember and mug up the physics formulas. Try to understand what a formula says and means, and what physical relation it expounds. If you understand the physical concepts underlying those formulas, deriving them or remembering them is easy. This ScienceStruck article lists some physics formulas that you would need in solving basic physics problems.

Physics Formulas

• Mechanics
• Friction
• Moment of Inertia
• Newtonian Gravity
• Projectile Motion
• Simple Pendulum
• Electricity
• Thermodynamics
• Electromagnetism
• Optics
• Quantum Physics

Derive all these formulas once, before you start using them. Study physics and look at it as an opportunity to appreciate the underlying beauty of nature, expressed through natural laws. Physics help is provided here in the form of ready to use formulas. Physics has a reputation for being difficult and to some extent that’s true, due to the mathematics involved.

 If you don’t wish to think on your own and apply basic physics principles, solving physics problems is always going to be tough. Our physics formulas list is aimed at helping you out in solving problems. The joy of having solved a physics problem on your own, is worth all the effort! Understanding physics concepts challenges your imagination and thinking potential, wherein, if you visualize a problem, then you can come up with a solution. So here is the promised list which will help you out.

Mechanics

Motion in One Dimension

The formulas for motion in one dimension (Also called Kinematical equations of motion) are as follows. (Here ‘u’ is initial velocity, ‘v’ is final velocity, ‘a’ is acceleration and t is time):

• s = ut + ½ at²
• v = u + at
• v² = u² + 2as
• v_av (Average Velocity) = (v+u)/2

Momentum, Force and Impulse

Formulas for momentum, impulse and force concerning a particle moving in 3 dimensions are as follows (Here force, momentum and velocity are vectors ):

• Momentum is the product of mass and velocity of a body. Momentum is calculate using the formula: P = m (mass) x v (velocity)
• Force can defined as something which causes a change in momentum of a body. Force is given by the celebrated newton’s law of motion: F = m (mass) x a (acceleration)
• Impulse is a large force applied in a very short time period. The strike of a hammer is an impulse. Impulse is given by I = m(v-u)

Pressure

Density

Density is the mass contained in a body per unit volume. 

The formula for density is: 

Angular Momentum

Angular momentum is an analogous quantity to linear momentum in which the body is undergoing rotational motion. The formula for angular momentum (J) is given by:

J = r x p
where J denotes angular momentum, r is radius vector and p is linear momentum.

Torque

Circular Motion

The formulas for circular motion of an object of mass ‘m’ moving in a circle of radius ‘r’ at a tangential velocity ‘v’ are as follows: 

Center of Mass

Reduced Mass for two Interacting Bodies

The physics formula for reduced mass (μ) is :

where m₁ is mass of the first body, m₂ is the mass of the second body.

Work and Energy

Formulas for work and energy in case of one dimensional motion are as follows:

W (Work Done) = F (Force) x D (Displacement)

Energy can be broadly classified into two types, Potential Energy and Kinetic Energy. In case of gravitational force, the potential energy is given by 

P.E.(Gravitational) = m (Mass) x g (Acceleration due to Gravity) x h (Height) 

The transitional kinetic energy is given by ½ m (mass) x v²(velocity squared)

Power

Friction

Moment of Inertia

Newtonian Gravity

Projectile Motion

Electricity

Ohm’s Law

Ohm’s law gives a relation between the voltage applied a current flowing across a solid conductor:

V (Voltage) = I (Current) x R (Resistance)

Power

In case of a closed electrical circuit with applied voltage V and resistance R, through which current I is flowing, 

= I²R. . . (because V = IR, Ohm’s Law)

Kirchoff’s Voltage Law

For every loop in an electrical circuit:

Σ_iV_i = 0
where V_i are all the voltages applied across the circuit.

Kirchoff’s Current Law

At every node of an electrical circuit: 

Σ_iI_i = 0
where I_i are all the currents flowing towards or away from the node in the circuit.

Resistance

The physics formulas for equivalent resistance in case of parallel and series combination are as follows:
Resistances R₁, R₂, R₃ in series: 

R_eq = R₁ + R₂ + R₃

Resistances R₁ and R₂ in parallel:

For n number of resistors, R₁, R₂…R_n, the formula will be:

1/R_eq = 1/R₁ + 1/R₂ + 1/R₃…+ 1/R_n

Capacitors

A capacitor stores electrical energy, when placed in an electric field. A typical capacitor consists of two conductors separated by a dielectric or insulating material. Here are the most important formulas related to capacitors. Unit of capacitance is Farad (F) and its values are generally specified in mF (micro Farad = 10 ^-6 F).

Capacitance (C) = Q / V

Energy Stored in a Capacitor (E_cap) = 1/2 CV²= 1/2 (Q² / C) = 1/2 (QV)

Current Flowing Through a Capacitor I = C (dV / dt)

Equivalent capacitance for ‘n’ capacitors connected in parallel:

C_eq (Parallel) = C₁ + C₂ + C₃…+ C_n = Σ_{i=1 to n} C_i

Equivalent capacitance for ‘n’ capacitors in series: 

1 / C_eq (Series) = 1 / C₁ + 1 / C₂…+ 1 / C_n = Σ_{i=1 to n} (1 / C_i)

Here

• C is the capacitance
• Q is the charge stored on each conductor in the capacitor
• V is the potential difference across the capacitor

Parallel Plate Capacitor Formula: 

C = kε₀ (A/d) 

Where

• k = dielectric constant (k = 1 in vacuum)
• ε₀ = Permittivity of Free Space (= 8.85 × 10^-12 C² / Nm²)
• A = Plate Area (in square meters)
• d = Plate Separation (in meters)

Cylinrical Capacitor Formula:

C = 2π kε₀ [L / ln(b / a)] 

Where

• k = dielectric constant (k = 1 in vacuum)
• ε₀ = Permittivity of Free Space (= 8.85 × 10^-12 C² / Nm²)
• L = Capacitor Length
• a = Inner conductor radius
• b = Outer conductor radius

Spherical Capacitor Formula:

C = 4π kε₀ [(ab)/(b-a)] 

Where

• k = dielectric constant (k = 1 in vacuum)
• ε₀ = Permittivity of Free Space (= 8.85 × 10^-12 C² / Nm²)
• a = Inner conductor radius
• b = Outer conductor radius

Inductors

An inductor is an electrical component which resists the flow of electrons or electric current through it. This property of inductance, in these devices, is caused by the electromotive force, created by magnetic field induced in them. The unit of inductance is Henry. Here are some important formulas associated with inductors. 

Energy Stored in Inductor (E_stored) = 1/2 (LI²)

Where, L is inductance and I is the current flowing through the inductor. 

Inductance of a cylindrical air core Coil (L) = (m₀KN²A / l)

Where

• L is inductance measured in Henries
• N is the number of turns on the coil
• A is cross-sectional area of the coil
• m₀ is the permeability of free space (= 4π × 10^-7 H/m)
• K is the Nagaoka coefficient
• l is the length of coil

Inductors in a Series Network

For inductors, L₁, L₂…L_n connected in series,

L_eq = L₁ + L₂…+ L_n (L is inductance)

Inductors in a Parallel Network

For inductors, L₁, L₂…L_n connected in parallel,

1 / L_eq = 1 / L₁ + 1 / L₂…+ 1 / L_n

Thermodynamics Formulas

Thermodynamics is a vast field providing an analysis of the behavior of matter in bulk. It’s a field focused on studying matter and energy in all their manifestations. Here are some of the most important formulas associated with classical thermodynamics and statistical physics.

First Law of Thermodynamics

dU = dQ + dW

where, dU is the change in internal energy, dQ is the heat absorbed by the system and dW is the work done on the system.

Thermodynamic Potentials

All of thermodynamical phenomena can be understood in terms of the changes in five thermodynamic potentials under various physical constraints. They are Internal Energy (U), Enthalpy (H), Helmholtz Free Energy (F), Gibbs Free Energy (G), Landau or Grand Potential (Φ). Each of these scalar quantities represents the potentiality of a thermodynamic system to do work of various kinds under different types of constraints on its physical parameters. 

Ideal Gas Equations

An ideal gas is a physicist’s conception of a perfect gas composed of non-interacting particles which are easier to analyze, compared to real gases, which are much more complex, consisting of interacting particles. The resulting equations and laws of an ideal gas conform with the nature of real gases under certain conditions, though they fail to make exact predictions due the interactivity of molecules, which is not taken into consideration. Here are some of the most important physics formulas and equations, associated with ideal gases. Let’s begin with the prime ideal gas laws and the equation of state of an ideal gas. 

Kinetic Theory of Gases

Based on the primary assumptions that the volume of atoms or molecules is negligible, compared to the container volume and the attractive forces between molecules are negligible, the kinetic theory describes the properties of ideal gases. Here are the most important physics formulas related to the kinetic theory of monatomic gases. 

Pressure (P) = 1/3 (Nm v²) 

Here, P is pressure, N is the number of molecules and v² is the mean squared particle velocity. 

Internal Energy (U) = 3/2 (NkT)

Heat Capacities

Heat Capacity at Constant Pressure (C_p) = 5/2 Nk = C_v + Nk

Heat Capacity at Constant Volume (C_v) = 3/2 Nk

Ratio of Heat Capacities (γ) = C_p / C_v = 5/3

Velocity Formulas

Electromagnetism

Relativistic Mechanics

Here are some of the most important relativistic mechanics formulas. The transition from classical to relativistic mechanics is not at all smooth, as it merges space and time into one by taking away the Newtonian idea of absolute time. If you know what is Einstein’s special theory of relativity, then the following formulas will make sense to you.

Lorentz Transformations

Lorentz transformations can be perceived as rotations in four dimensional space. Just as rotations in 3D space mixes the space coordinates, a Lorentz transformation mixes time and space coordinates. Consider two, three dimensional frames of reference S(x,y,z) and S'(x’,y’,z’) coinciding with each other. 

Now consider that frame S’ starts moving with a constant velocity v with respect to S frame. In relativistic mechanics, time is relative! So the time coordinate for the S’ frame will be t’ while that for S frame will be t. 

Consider

The coordinate transformations between the two frames are known as Lorentz transformations and are given as follows:
Lorentz Transformations of Space and Time

x = γ (x’ + vt’) and x’ = γ (x – vt)

y = y’

z= z’

t = γ(t’ + vx’/c²) and t’ = γ(t – vx/c²)

Relativistic Velocity Transformations

In the same two frames S and S’, the transformations for velocity components will be as follows (Here (U_x, U_y, U_z) and (U_x‘, U_y‘, U_z‘) are the velocity components in S and S’ frames respectively):

U_x = (U_x‘ + v) / (1 + U_x‘v / c²)

U_y = (U_y‘) / γ(1 + U_x‘v / c²)

U_z = (U_z‘) / γ(1 + U_x‘v / c²) and

U_x‘ = (U_x – v) / (1 – U_xv / c²)

U_y‘ = (U_y) / γ(1 – U_xv / c²)

U_z‘ = (U_z) / γ(1 – U_xv / c²)

Momentum and Energy Transformations in Relativistic Mechanics

Consider the same two frames (S, S’) as in case of Lorentz coordinate transformations above. S’ is moving at a velocity ‘v’ along the x-axis. Here again γis the Lorentz factor. In S frame (P_x, P_y, P_z) and in S’ frame (P_x‘, P_y‘, P_z‘) are momentum components. Now we consider formulas for momentum and energy transformations for a particle, between these two reference frames in relativistic regime.

Component wise Momentum Transformations and Energy Transformations

P_x = γ(P_x‘ + vE’ / c²)

P_y = P_y‘ 

P_z = P_z‘

E = γ(E’ + vP_x) 

and

P_x‘ = γ(P_x – vE’ / c²)

P_y‘ = P_y 

P_z‘ = P_z

E’ = γ(E – vP_x)

Physical Formulas for Quantities in Relativistic Dynamics

All the known quantities in classical mechanics get modified, when we switch over to relativistic mechanics which is based on the special theory of relativity. Here are formulas of quantities in relativistic dynamics.

Relativistic momentum p = γm₀v 
where m₀ is the rest mass of the particle.

Rest mass energy E = m₀c²

Total Energy (Relativistic) E = √(p²c² + m₀²c⁴))

Optics

Snell’s Law

• where i is angle of incidence
• r is the angle of refraction
• n₁ is refractive index of medium 1
• n₂ is refractive index of medium 2
• v₁, v₂ are the velocities of light in medium 1 and medium 2 respectively

Gauss Lens Formula: 1/u + 1/v = 1/f 
where

• u – object distance
• v – image distance
• f – Focal length of the lens

Lens Maker’s Equation

The most fundamental property of any optical lens is its ability to converge or diverge rays of light, which is measued by its focal length. Here is the lens maker’s formula, which can help you calculate the focal length of a lens, from its physical parameters. 

1 / f = [n-1][(1 / R₁) – (1 / R₂) + (n-1) d / nR₁R₂)]

Here,

• n is refractive index of the lens material
• R₁ is the radius of curvature of the lens surface, facing the light source
• R₂ is the radius of curvature of the lens surface, facing away from the light source
• d is the lens thickness

If the lens is very thin, compared to the distances – R₁ and R₂, the above formula can be approximated to:

(Thin Lens Approximation) 1 / f ≈ (n-1) [1 / R₁– 1 / R₂] 

Compound Lenses

The combined focal length (f) of two thin lenses, with focal length f₁ and f₂, in contact with each other:

1 / f = 1 / f₁ + 1 / f₂

If the two thin lenses are separated by distance d, their combined focal length is provided by the formula: 

1 / f = 1 / f₁ + 1 / f₂ – (d / f₁ – f₂)) 

Newton’s Rings Formulas

Here are the important formulas for Newton’s rings experiment which illustrates diffraction.

n^th Dark ring formula: r²_n = nRλ

n^th Bright ring formula: r²_n = (n + ½) Rλ

where

• n^th ring radius
• Radius of curvature of the lens
• Wavelength of incident light wave

Quantum Physics

De Broglie Wave

Planck Relation

Uncertainty Principle

This concludes my review of some of the important physics formulas. This list, is only representative and is by no means anywhere near complete. Physics is the basis of all sciences and therefore its domain extends over all sciences. Every branch of physics theory abounds with countless formulas. If you resort to just mugging up all these formulas, you may pass exams, but you will not be doing real physics. If you grasp the underlying theory behind these formulas, physics will be simplified. To view physics through the formulas and laws, you must be good at maths. There is no way you can run away from it. Mathematics is the language of nature! 

The more things we find out about nature, more words we need to describe them. This has led to increasing jargonization of science with fields and sub-fields getting generated. You could refer to a glossary of science terms and scientific definitions for any jargon that is beyond your comprehension.

If you really want to get a hang of what it means to be a physicist and get an insight into physicist’s view of things, read ‘Feynman Lectures on Physics’, which is highly recommended reading, for anyone who loves physics. It is written by one of the greatest physicists ever, Prof. Richard Feynman. Read and learn from the master. Solve as many problems as you can, on your own, to get a firm grasp of the subject.