This physics constants and units reference gives you a reusable table of standard values, practical SI conversion templates, worked examples, and a checklist for checking whether your reference is still current. Use it for homework, laboratory reports, exam preparation, and quick dimensional checks.
Overview
A reliable calculation begins with two decisions: which physical model applies and which units make the calculation consistent. Constants are useful only when their numerical value is paired with the correct unit and, where relevant, an uncertainty. For example, using the speed of light in metres per second requires a distance in metres and a time in seconds if you want the result in SI units.
The table below uses SI units and lists selected values from the CODATA 2022 recommended values, together with exact SI-defined constants and common conventional values. Check the edition required by your course, laboratory, textbook, or examination board before submitting work. A number in parentheses indicates the uncertainty in the final digits: 6.67430(15) means 6.67430 ± 0.00015.
| Quantity | Symbol | Value | SI unit | Uncertainty or status | Typical use |
|---|---|---|---|---|---|
| Speed of light in vacuum | c | 299,792,458 | m s−1 | Exact | Relativity, waves, electromagnetic radiation |
| Planck constant | h | 6.62607015 × 10−34 | J s | Exact | Quantum energy, E = hf |
| Elementary charge | e | 1.602176634 × 10−19 | C | Exact | Electric charge and particle physics |
| Boltzmann constant | kB | 1.380649 × 10−23 | J K−1 | Exact | Thermal energy and statistical mechanics |
| Avogadro constant | NA | 6.02214076 × 1023 | mol−1 | Exact | Particles, moles, and chemistry-related physics |
| Newtonian constant of gravitation | G | 6.67430 × 10−11 | m3 kg−1 s−2 | ±0.00015 × 10−11 | Gravity and orbital mechanics |
| Electron mass | me | 9.1093837139 × 10−31 | kg | ±0.0000000028 × 10−31 | Atomic and quantum physics |
| Proton mass | mp | 1.67262192595 × 10−27 | kg | ±0.00000000052 × 10−27 | Nuclear and particle physics |
| Fine-structure constant | α | 7.2973525643 × 10−3 | dimensionless | ±0.0000000011 × 10−3 | Electromagnetism and atomic physics |
| Vacuum permittivity | ε0 | 8.8541878188 × 10−12 | F m−1 | ±0.0000000014 × 10−12 | Electric fields and capacitance |
| Vacuum permeability | μ0 | 1.25663706127 × 10−6 | N A−2 | ±0.00000000020 × 10−6 | Magnetic fields and circuits |
| Molar gas constant | R | 8.31446261815324 | J mol−1 K−1 | Exact from defined constants | Ideal gases and thermodynamics |
| Standard acceleration of gravity | gn | 9.80665 | m s−2 | Defined conventional value | Weight and introductory mechanics |
Do not confuse gn, a defined standard value, with the local acceleration due to gravity. A laboratory measurement may use a nearby value that differs slightly. Similarly, constants such as G have measured uncertainties, while several SI constants are exact because the SI system defines units through fixed numerical values.
Checklist by scenario
For a standard physics problem
- Write the given quantities with units before substituting numbers.
- Choose one unit system, usually SI: metres, kilograms, seconds, amperes, kelvin, and moles.
- Copy the constant with its complete unit, not just its numerical value.
- Convert prefixes such as kilo, milli, micro, and nano before calculating.
- Estimate the expected order of magnitude and check the final unit.
For an SI unit conversion
Use the fillable template:
quantity × (conversion unit / original unit) = converted quantity
The conversion fraction must equal one, so the units cancel correctly. For example:
72 km h−1 × (1,000 m / 1 km) × (1 h / 3,600 s) = 20 m s−1
For area and volume, apply the conversion factor to the relevant power. Thus, 1 cm = 10−2 m, but 1 cm2 = 10−4 m2 and 1 cm3 = 10−6 m3.
For electricity and magnetism
Check whether the equation expects charge in coulombs, current in amperes, distance in metres, and potential difference in volts. For example, in Coulomb's law, F = keq1q2/r2, you may use ke ≈ 8.99 × 109 N m2 C−2 or express it through 1/(4πε0). Do not combine a rounded value of ke with a high-precision value of ε0 and then report excessive significant figures.
For a laboratory report
Record the instrument units, conversion factors, and uncertainty propagation separately. Keep measured precision distinct from the precision of a physical constant. A constant with many digits does not make a ruler, timer, or voltmeter more precise. For a fuller workflow, see Physics Lab Uncertainty and Error Analysis.
What to double-check
- Dimensions: Use dimensional analysis to test the equation before evaluating it. The left and right sides must have equivalent dimensions.
- Prefixes: Write powers of ten explicitly. A millimetre is 10−3 m; a millimetre squared is 10−6 m2.
- Temperature: Temperature differences can be expressed in kelvins or degrees Celsius with the same numerical size, but thermodynamic equations require absolute temperature in kelvins.
- Energy: The SI unit is the joule. If using electronvolts, remember 1 eV = 1.602176634 × 10−19 J exactly, based on the defined elementary charge.
- Angles: Radians are dimensionless in SI, but write rad when explaining rotational equations or angular measurements.
- Significant figures: Round at the end, generally to match the least precise measured input unless your course specifies another rule.
- Source edition: Note the CODATA edition or textbook table used when a value or uncertainty matters, especially in a lab or research summary.
Dimensional analysis is a particularly efficient error check. The guide Dimensional Analysis in Physics provides a focused method for checking equations, units, and conversions.
Common mistakes
Using a familiar number without its unit. The value 9.8 could represent m s−2, not a universal answer to every gravity problem. State what the number means.
Mixing centimetres and metres. Substituting centimetres into an SI equation without conversion can introduce factors of 100, 10,000, or more. Convert first, then calculate.
Squaring only the numerical part of a conversion. When a length conversion is squared or cubed, the conversion factor must also be squared or cubed.
Confusing mass and weight. Mass is measured in kilograms; weight is a force measured in newtons and is approximately W = mg near Earth's surface.
Reporting false precision. Carry guard digits through intermediate steps, but do not present a final result with more meaningful digits than the measured data support.
Assuming every table is current. Recommended values and uncertainties can be revised. Exact defined constants remain exact, but related derived values or measured constants may be updated.
When to revisit
Use this reference whenever you begin a new unit, problem set, lab, or exam revision cycle. Before an AP Physics, IB Physics, or college physics assessment, compare the values here with the formula sheet supplied by your instructor or examination board; that sheet controls if it uses rounded constants or a specified convention.
Editors and instructors should review the table when CODATA publishes a new recommended adjustment, when SI definitions or conventions change, or when a course adopts a different approved value. Record the revision date, replace values and uncertainties together, and retest every worked conversion. A practical update checklist is:
- Confirm the CODATA edition and publication date.
- Separate exact, defined, and measured quantities.
- Recheck units, uncertainty notation, and significant figures.
- Recalculate the worked examples rather than editing numbers by hand.
- Compare the table with current course or laboratory requirements.
- Save or print the refreshed reference for the next problem-solving session.
For day-to-day study, pair this sheet with How to Solve Physics Problems and use the final-unit check as a required step, not an afterthought. That habit turns a constants table from a list of numbers into a dependable physics study aid.
