SI Units and Physical Constants Cheat Sheet for Physics Students

Overview

This guide gives you a compact, reusable reference for SI units physics, derived units in physics, unit prefixes, and a practical physical constants cheat sheet. The goal is not to replace understanding. The goal is to reduce friction, so you can spend less time hunting for definitions and more time solving problems.

In physics, many errors are not conceptual at first. They begin with a missing prefix, a hidden conversion, or an inconsistent unit system. A student may know Newton's second law but still lose marks by mixing centimeters with meters, electronvolts with joules, or degrees Celsius with kelvin. A good reference page helps you catch these mistakes early.

Start with the seven SI base units:

• Length: meter (m)
• Mass: kilogram (kg)
• Time: second (s)
• Electric current: ampere (A)
• Thermodynamic temperature: kelvin (K)
• Amount of substance: mole (mol)
• Luminous intensity: candela (cd)

Most quantities in introductory and intermediate physics are built from these. The important habit is to see every derived unit as a combination of base units. That makes dimensional checks possible, and dimensional checks are one of the fastest forms of physics homework help you can give yourself.

Here are some of the most common derived SI units you should know on sight:

• Velocity: m s^-1
• Acceleration: m s^-2
• Force: newton (N) = kg m s^-2
• Energy / work: joule (J) = kg m² s^-2
• Power: watt (W) = kg m² s^-3
• Pressure: pascal (Pa) = kg m^-1 s^-2
• Charge: coulomb (C) = A s
• Potential difference: volt (V) = kg m² s^-3 A^-1
• Resistance: ohm (Ω) = kg m² s^-3 A^-2
• Capacitance: farad (F) = kg^-1 m^-2 s⁴ A²
• Magnetic flux density: tesla (T) = kg s^-2 A^-1
• Frequency: hertz (Hz) = s^-1

For fast study, keep the unit name, symbol, and base-unit form together. If you only memorize names, you will struggle with derivations. If you only memorize base-unit forms, you may miss common notation in textbooks and labs. You need both.

Prefixes are equally important because many physics quantities span huge ranges. These are the prefixes most students use repeatedly:

• tera (T) = 10¹²
• giga (G) = 10⁹
• mega (M) = 10⁶
• kilo (k) = 10³
• centi (c) = 10^-2
• milli (m) = 10^-3
• micro (μ) = 10^-6
• nano (n) = 10^-9
• pico (p) = 10^-12
• femto (f) = 10^-15

Two practical warnings: first, uppercase and lowercase matter. M is mega, while m is milli. Second, the kilogram already contains a prefix in its name, but it remains the base SI unit for mass.

Now for the constants. A working cheat sheet should prioritize constants you actually use. Here is a compact list of widely used physics constants with standard symbols and common units:

• Speed of light, c ≈ 3.00 × 10⁸ m s^-1
• Gravitational constant, G ≈ 6.67 × 10^-11 N m² kg^-2
• Standard gravitational acceleration near Earth, g ≈ 9.81 m s^-2
• Planck constant, h ≈ 6.63 × 10^-34 J s
• Reduced Planck constant, ħ = h/2π ≈ 1.05 × 10^-34 J s
• Elementary charge, e ≈ 1.60 × 10^-19 C
• Electron mass, m_e ≈ 9.11 × 10^-31 kg
• Proton mass, m_p ≈ 1.67 × 10^-27 kg
• Vacuum permittivity, ε₀ ≈ 8.85 × 10^-12 F m^-1
• Vacuum permeability, μ₀ ≈ 4π × 10^-7 N A^-2
• Coulomb constant, k = 1/(4π ε₀) ≈ 8.99 × 10⁹ N m² C^-2
• Boltzmann constant, k_B ≈ 1.38 × 10^-23 J K^-1
• Avogadro constant, N_A ≈ 6.02 × 10²³ mol^-1
• Gas constant, R ≈ 8.31 J mol^-1 K^-1
• Stefan-Boltzmann constant, σ ≈ 5.67 × 10^-8 W m^-2 K^-4

For many courses, that list is enough to cover most introductory and intermediate work. If you study modern physics, you may also want common energy conversions such as 1 eV = 1.60 × 10^-19 J. If you want a broader formula companion, see Physics Formula Sheet by Topic: Mechanics, E&M, Waves, Thermodynamics, and Modern Physics.

Maintenance cycle

A cheat sheet is most useful when it is treated as a living study tool rather than a one-time handout. This section shows how to maintain it through the semester so it stays accurate and relevant.

Weekly review: spend five minutes checking whether the units and constants in your current chapter are already on your sheet. If not, add them in a consistent format: quantity, symbol, value if needed, SI unit, and common warning. For example, under temperature you might add: “Use kelvin in gas-law calculations; convert from °C when required.”

Before each new topic: create a small “active set” of units and constants for the chapter you are studying. In mechanics, this may mean N, J, W, Pa, and g. In electromagnetism, it may mean C, V, Ω, T, ε₀, μ₀, and k. In quantum physics explained style courses, it may mean h, ħ, e, c, and eV conversions.

Before lab sessions: add instrument-specific reminders. For instance, note whether a sensor reports in mV, cm, or arbitrary units; whether uncertainty should be written with the same decimal place as the measurement; and whether graph axes must use SI base or derived units.

Before exams: compress your long reference into a two-layer sheet. Layer one is the non-negotiable core: SI base units, prefixes, the most common derived units, and constants required across multiple topics. Layer two is module-specific: optics constants, thermodynamics relationships, or quantum conversions, depending on the exam.

A useful format is a four-column table:

• Quantity
• Symbol / value
• SI unit
• Common mistake or note

That last column matters more than many students expect. For example:

• Energy in eV must often be converted to J before using SI-based formulas.
• Mass is in kg, not g, when applying F = ma.
• Temperature differences in °C and K have the same numerical size, but absolute temperature in formulas should usually be in K.
• Area scales as length squared, so converting cm to m changes area by a factor of 10⁴, not 10².

Because this is an update-friendly reference page, the best maintenance habit is to revise the sheet after contact with real problems. Every time you make a unit error once, add a note so you do not make it twice.

Signals that require updates

You do not need to rebuild your reference every week, but some signals mean it is time to refresh it.

1. Your current course has shifted topics. If you have moved from kinematics to circuits, or from thermal physics to wave optics, your old sheet may still be correct but no longer efficient. The right constants should be easier to find than the irrelevant ones.

2. You keep making the same conversion mistake. This is the clearest sign that the sheet is missing a practical cue. Add a conversion line or a worked reminder. For example: “1 cm = 10^-2 m, so 1 cm² = 10^-4 m².”

3. Your lab reports are losing marks for notation. That often means your sheet needs a section on unit formatting, significant figures, uncertainty notation, or graph labels. A cheat sheet is not only about constants. It is also about clean scientific communication.

4. Search intent has shifted from memorization to application. Early in a course, you may need a list. Later, you may need examples of how to use the list. At that point, expand the sheet with quick checks such as dimensional analysis steps or standard conversions used in your problem sets.

5. You are using multiple resources with inconsistent notation. One textbook may write the gas constant as R, another may emphasize k_B. One instructor may use μ for coefficient of friction, while another uses it mainly in electromagnetism. Add a notation note to keep symbols from colliding in your memory.

6. You are beginning advanced topics. In relativity, particle physics, or condensed matter, additional constants and natural units may appear. Even if your course still expects SI answers, your reference should note when a paper, lecture, or problem set uses conventions like c = 1 or ħ = 1 so you are not surprised.

As a rule, update the sheet when friction appears. If you hesitate while checking a unit, converting a value, or deciding which constant belongs in a formula, the sheet can be improved.

Common issues

The most common unit and constant errors are predictable. If you know them in advance, you can prevent many lost marks.

Confusing mass and weight. Mass is measured in kilograms. Weight is a force measured in newtons. If a problem asks for weight, you will usually need W = mg, not just the mass value.

Forgetting that prefixes scale powers too. Students often convert lengths correctly but forget that area and volume require squared or cubed conversions. This matters in pressure, density, electric field calculations over surfaces, and lab work.

Mixing SI and non-SI units inside one calculation. A classic example is using speed in km/h with distance in meters and time in seconds. Another is combining liters, atmospheres, and kelvin in one place and SI constants in another. If you are solving in SI, convert everything first.

Using Celsius where kelvin is required. Many thermodynamics formulas depend on absolute temperature. If the formula comes from kinetic arguments or proportionality with thermal energy, kelvin is usually the safe default.

Dropping units while doing algebra. Keep units attached through the calculation until the final line. This makes dimensional checking possible and catches mistakes before they spread.

Misreading symbols. Physics notation is compact, and small differences matter: m for meter, m for mass in some contexts, and m as a prefix in milli if attached to a unit symbol. Likewise, W can mean weight informally in some classes, but watt as a unit symbol has a specific meaning.

Rounding constants too early. It is usually better to keep a few guard digits during intermediate steps and round at the end to a sensible number of significant figures. Your cheat sheet can include standard rounded classroom values and, when useful, a note to carry extra digits in multi-step calculations.

Memorizing without context. A list of constants becomes much easier to retain when each one is tied to a formula family. For example, pair ε₀ and k with electrostatics, k_B and R with thermal physics, and h, ħ, and e with quantum and atomic problems.

Assuming every constant must be memorized. In many courses, what matters more is recognizing which constants are fundamental to the topic and which are provided on the exam sheet. Your personal reference should help you study efficiently, not overload you.

One effective way to avoid these issues is to work backward from solved examples. After finishing a problem, ask three questions: Which units entered? Which conversion was required? Which constant did I need? Then add only the information that would have made the setup faster next time. That is how a generic sheet becomes a real physics study guide.

When to revisit

Revisit this cheat sheet on a schedule, not only when something goes wrong. A simple rhythm works well:

• At the start of a term: build the core version with base units, prefixes, top derived units, and essential constants.
• At the start of each chapter: add topic-specific units and conversions.
• After each quiz, lab, or homework set: record any unit or constant mistake you made.
• Before midterms and finals: condense the sheet into a high-priority exam version.
• When using new textbooks or research-style materials: check for notation differences and add them.

If you want this page to stay useful all year, treat it as both reference and revision log. Date each update. Mark what changed. Remove clutter from topics you are no longer studying, but keep a master version in case cumulative exams return to earlier material.

A practical action plan for today:

1. Copy the seven SI base units onto one page.
2. Add the 10 most common prefixes you use.
3. Add the 10-15 derived units most common in your course.
4. Add only the constants that appear in your current module.
5. Create a final column called “watch out” for mistakes and conversions.
6. Review the sheet once a week for five minutes.

That small routine pays off because it supports every part of problem solving: setting up equations, checking dimensions, interpreting lab data, and reading formulas with less hesitation. If you also want a topic-organized companion for equations, keep a formula reference alongside this units page, such as Physics Formula Sheet by Topic: Mechanics, E&M, Waves, Thermodynamics, and Modern Physics. For broader study habits and tool choices, you may also find Study Guides, Mind Maps, and AI Podcasts: Do Student Learning Tools Actually Help? useful.

The best cheat sheets are not the longest ones. They are the ones you actually return to, update, and trust under pressure. Build yours so it reflects the physics you are studying now, then revisit it whenever your course, your mistakes, or your goals change.