Physics Equations Sheet by Topic: Kinematics, Forces, Energy, Waves, and Electricity

Overview

This hub is designed as a practical physics equations sheet by topic. Instead of giving a long formula dump, it pairs each equation with a short note about when to use it. That matters because many physics mistakes happen before any algebra begins: students choose the wrong model, mix variables from different situations, or ignore units.

Use this article as a living reference for introductory physics. The topics here are the ones most students revisit repeatedly in high school physics, AP Physics, GCSE physics help, A-Level revision, and college introductory courses:

• Kinematics: motion, velocity, acceleration, and projectile ideas
• Forces: Newton’s laws, weight, friction, and momentum basics
• Energy: work, kinetic energy, gravitational potential energy, and power
• Waves: speed, frequency, wavelength, and period
• Electricity: charge, current, voltage, resistance, and electrical power

A useful equation sheet should answer four questions fast:

1. What does the formula say?
2. What do the symbols mean?
3. What units should I expect?
4. When is this formula valid?

If you build that habit, step by step physics solutions become clearer because you stop treating formulas as isolated facts. You start seeing them as tools attached to conditions.

Topic map

Below is a topic-based map of common physics formulas with symbol guides and when-to-use notes.

Kinematics formulas

These equations describe motion. They work best when acceleration is constant unless stated otherwise.

• Average speed: speed = distance / time
  Symbols: v or speed, distance d, time t
  Common units: m/s, km/h
  Use when: you only need total distance over total time.
• Average velocity: velocity = displacement / time
  Use when: direction matters and you are tracking change in position.
• Acceleration: a = (v - u) / t
  Symbols: initial velocity u, final velocity v
  Units: m/s²
  Use when: velocity changes over time.
• Constant-acceleration equation 1: v = u + at
  Use when: you know any three of u, v, a, t.
• Constant-acceleration equation 2: s = ut + 1/2 at²
  Symbols: displacement s
  Use when: you need displacement from initial velocity, acceleration, and time.
• Constant-acceleration equation 3: v² = u² + 2as
  Use when: time is not given or not needed.
• Constant-acceleration equation 4: s = (u + v)t / 2
  Use when: acceleration is constant and average velocity is easy to use.

Projectile motion note: Horizontal and vertical motion are usually treated separately. Horizontal acceleration is often zero, while vertical acceleration near Earth is approximately g downward. A common exam error is mixing the x-direction and y-direction equations in one line.

Forces formulas

Force equations connect motion to interactions.

• Newton’s second law: F = ma
  Symbols: force F, mass m, acceleration a
  Units: N = kg·m/s²
  Use when: a net force produces acceleration.
• Weight: W = mg
  Use when: finding gravitational force near Earth’s surface.
• Friction: F_f = μN
  Symbols: coefficient of friction μ, normal force N
  Use when: a problem states or implies kinetic or limiting friction.
• Momentum: p = mv
  Units: kg·m/s
  Use when: analyzing collisions or impulse.
• Impulse: J = FΔt = Δp
  Use when: force acts over a time interval and changes momentum.

When-to-use reminder: In force problems, start with a free-body diagram. That often matters more than memorizing extra formulas. Label weight, normal force, tension, friction, drag if relevant, and then write the net force in the direction of motion.

Energy formulas

Energy methods often simplify problems that become messy with force components.

• Work done by a constant force: W = Fd cos θ
  Symbols: displacement d, angle θ between force and displacement
  Units: joules (J)
  Use when: a constant force acts through a displacement.
• Kinetic energy: KE = 1/2 mv²
  Use when: motion depends on speed.
• Gravitational potential energy: GPE = mgh
  Use when: height changes near Earth’s surface.
• Elastic potential energy: E_e = 1/2 kx²
  Symbols: spring constant k, extension or compression x
  Use when: springs store energy.
• Work-energy theorem: W_net = ΔKE
  Use when: net work changes kinetic energy.
• Power: P = W / t
  Also: P = E / t
  Units: watts (W)
  Use when: comparing rate of energy transfer.

Common pitfall: Work is not just force times distance. The force must act in the direction of motion or have a component in that direction. That is why the cos θ term matters.

Waves formulas

Wave equations are compact, but students often confuse frequency and period or forget that wave speed depends on the medium.

• Wave speed: v = fλ
  Symbols: frequency f, wavelength λ
  Units: m/s
  Use when: relating how fast a wave travels to its spacing and oscillation rate.
• Period-frequency relation: T = 1 / f
  Also: f = 1 / T
  Units: seconds, hertz
  Use when: converting between cycle time and cycles per second.

Important idea: When a wave enters a new medium, frequency usually stays the same while speed and wavelength may change. That is a concept-level rule worth attaching to the formula sheet.

Electricity formulas

Electricity formulas are among the most revisited in introductory physics and are essential for circuit analysis help.

• Charge: Q = It
  Symbols: charge Q, current I, time t
  Units: coulombs (C)
  Use when: current flows for a known time.
• Ohm’s law: V = IR
  Symbols: voltage V, current I, resistance R
  Units: volts, amps, ohms
  Use when: relating current, resistance, and potential difference in ohmic components.
• Electrical power: P = IV
  Also: P = I²R and P = V² / R
  Use when: analyzing energy transfer rate in circuits.
• Electrical energy: E = Pt
  Use when: power is delivered over time.
• Equivalent resistance in series: R_total = R_1 + R_2 + ...
  Use when: components are connected in a single path.
• Equivalent resistance in parallel: 1 / R_total = 1 / R_1 + 1 / R_2 + ...
  Use when: current has multiple branches.

Series-parallel reminder: In series, current is the same through each component. In parallel, voltage is the same across each branch. Those ideas often matter as much as the formulas themselves.

Core symbols and units at a glance

Students often lose marks through unit confusion rather than physics misunderstanding. A short unit memory list helps:

• Displacement, distance, height, wavelength: meters (m)
• Time, period: seconds (s)
• Speed, velocity: m/s
• Acceleration: m/s²
• Mass: kilograms (kg)
• Force, weight: newtons (N)
• Energy, work: joules (J)
• Power: watts (W)
• Frequency: hertz (Hz)
• Charge: coulombs (C)
• Current: amperes (A)
• Voltage: volts (V)
• Resistance: ohms (Ω)

Before substituting values, convert mixed units into a consistent system. If a problem gives time in minutes and speed in m/s, convert before solving. That simple step prevents many avoidable errors.

Related subtopics

The formulas above cover the core of many introductory courses, but each topic connects to wider subtopics. If you revisit this hub regularly, these are the branches most worth adding to your own notes.

Kinematics extensions

• Graph interpretation: slope of position-time and velocity-time graphs
• Projectile motion by components
• Relative velocity

Forces extensions

• Inclined planes
• Tension in connected systems
• Circular motion and centripetal force
• Conservation of momentum in collisions

Energy extensions

• Efficiency
• Energy dissipation and non-conservative forces
• Spring systems

Waves extensions

• Wave reflection and refraction
• Interference and standing waves
• Sound intensity and musical relationships
• Basic optics formulas if your course includes light

Electricity extensions

• Kirchhoff-style circuit rules in more advanced classes
• Internal resistance
• Electric fields and potential
• Capacitance in later courses

If you teach or study with data collection tools, pairing formulas with measured data can deepen understanding. For uncertainty work, see How to Build a Classroom Uncertainty Activity Using Sensor Data. For wave teaching ideas that connect equations to patterns and rhythm, see Lesson Plan: Teaching Waves with Rhythm, Pattern, and Group Collaboration. If you want a sharper framework for choosing what matters in multi-step problems, Physics Problem Solving with KPI Thinking: What to Measure, What to Ignore offers a useful companion approach.

How to use this hub

The best way to use a physics equations sheet is not to read it passively. Use it while solving actual problems. Here is a reliable method that works for homework, revision, and exam prep.

1. Identify the topic first. Ask whether the problem is mainly about motion, force, energy, waves, or electricity. Many problems contain more than one topic, but one will usually lead.
2. Write knowns and unknowns with units. List every given quantity and what you need to find. Convert units immediately.
3. Choose the model before the formula. Is acceleration constant? Is energy conserved? Is the circuit series or parallel? The model tells you which equation belongs.
4. Select the simplest valid equation. If time is missing, v² = u² + 2as may be better than an equation that introduces an extra variable.
5. Substitute symbols before numbers if possible. This makes unit checking easier and helps you spot algebra mistakes.
6. Check direction and sign conventions. Decide what counts as positive before calculating.
7. Test the answer. Does the magnitude make sense? Are the units correct? Is the direction physically reasonable?

For exam use, many students find it helpful to annotate their own reference sheet. Add brief notes such as:

• “Use only for constant acceleration”
• “Split into horizontal and vertical parts”
• “Need free-body diagram first”
• “Frequency unchanged across media”
• “Series: same current; parallel: same voltage”

That style turns a formula list into a decision guide. It is especially useful for physics questions and answers where the challenge is choosing a path, not just calculating.

If you are building a personal physics study guide, consider organizing one page per topic with four columns:

1. Formula
2. Symbol meanings
3. Units
4. When to use / common mistake

This structure works well because it trains recognition. Over time, you will not just remember that P = IV exists; you will know it belongs to electrical power, uses watts, and can connect to E = Pt when energy is asked for.

Teachers and tutors can also use this hub as a scaffold for review sheets, starter activities, and topic checklists. Students who struggle with formula overload often benefit when equations are grouped by idea rather than alphabetically or by chapter number.

When to revisit

This hub is meant to be revisited, not finished once. Return to it whenever your course adds a new layer, or when your problem-solving starts feeling mechanical and error-prone.

Revisit this equations sheet when:

• You begin a new mechanics unit and need to separate kinematics from forces
• You move from force methods to energy methods
• You start projectile motion and need component thinking
• You begin wave problems involving frequency, period, and wavelength
• You start circuit work and need series-parallel rules alongside Ohm’s law
• You are preparing for a test and want a compact physics formula review
• You notice repeated mistakes with units, signs, or choosing equations

Update your own copy when:

• Your class introduces a new subtopic such as circular motion, optics, or thermodynamics
• Your teacher uses a different symbol convention than your textbook
• You find a mistake pattern that deserves a note beside a formula
• You want to add worked examples or links to a physics calculator

A practical next step is to create a one-page version of this hub for your current course. Keep only the formulas you actively need, leave space for notes, and add one worked example under each topic. Then, after each quiz or homework set, mark which equations you used correctly and which ones you misapplied. That turns the sheet into a revision tool rather than a static handout.

If you are studying long term, save this page and revisit it as your course expands. A strong physics equations sheet grows with you: it starts as a reference, becomes a problem-solving checklist, and ends up as a compact map of the subject.