Science & Units
Physical Constants Table
Since the 2019 revision of the SI, seven constants are fixed by definition rather than measured. They include the speed of light, the Planck constant, the elementary charge, the Boltzmann constant and the Avogadro constant, and each has been assigned an exact value chosen to keep the older definitions' magnitudes intact. Every unit in the system is now derived from them, which means the kilogram is defined by a constant rather than by a cylinder in a vault.
The consequence for anyone using these numbers is that the seven defining constants have no uncertainty at all. They are not approximately right; they are right by agreement. Everything else is measured against them, and the measured constants carry uncertainties ranging from parts per billion down to the embarrassingly coarse five significant figures of the gravitational constant.
That spread is worth internalising, because it explains an oddity in how precise different calculations can be. The mass of the Earth is known to about five figures because it depends on G, while the mass of an electron is known to eleven. A calculation that mixes them inherits the worse of the two, and quoting eleven digits from a result that involves G is reporting noise.
The third table is the practical one. Standard gravity, the standard atmosphere, absolute zero and the specific heat of water are the values that appear in everyday conversion work on this site, and two of them are exact by convention rather than by measurement. Standard gravity is 9.80665 m/s² exactly, which is why a pound-force converts to newtons without any uncertainty, while actual gravity where you stand varies by about half a percent from equator to pole.
Defining constants — exact by definition, with no uncertainty
| Constant | Symbol | Value | Unit |
|---|---|---|---|
| Speed of light in vacuum | c | 299,792,458 | m/s |
| Planck constant | h | 6.62607015 × 10⁻³⁴ | J⋅s |
| Elementary charge | e | 1.602176634 × 10⁻¹⁹ | C |
| Boltzmann constant | k | 1.380649 × 10⁻²³ | J/K |
| Avogadro constant | Nᴀ | 6.02214076 × 10²³ | 1/mol |
| Luminous efficacy at 540 THz | K꜀d | 683 | lm/W |
| Hyperfine transition of caesium-133 | Δν_Cs | 9,192,631,770 | Hz |
These seven were fixed by definition in the 2019 revision of the SI, which is why they carry no uncertainty. Every other constant is measured against them.
Measured constants — CODATA recommended values
| Constant | Symbol | Value | Unit |
|---|---|---|---|
| Newtonian constant of gravitation | G | 6.67430 × 10⁻¹¹ | m³/(kg⋅s²) |
| Standard acceleration of gravity | g₀ | 9.80665 | m/s² |
| Molar gas constant | R | 8.314462618 | J/(mol⋅K) |
| Stefan–Boltzmann constant | σ | 5.670374419 × 10⁻⁸ | W/(m²⋅K⁴) |
| Electron mass | mₑ | 9.1093837015 × 10⁻³¹ | kg |
| Proton mass | mₚ | 1.67262192369 × 10⁻²⁷ | kg |
| Rydberg constant | R∞ | 10,973,731.568160 | 1/m |
| Fine-structure constant | α | 0.0072973525693 | dimensionless |
| Vacuum permittivity | ε₀ | 8.8541878128 × 10⁻¹² | F/m |
| Atomic mass constant | mᵤ | 1.66053906660 × 10⁻²⁷ | kg |
G is the least precise of these by a wide margin — known to about five significant figures against twelve or more for the rest. That is why the mass of the Earth is known far better than the mass of the Earth in kilograms would suggest.
Constants in everyday use
| Quantity | Symbol | Value | Where it appears |
|---|---|---|---|
| Standard gravity | g₀ | 9.80665 m/s² | Weight, potential energy, pressure conversions |
| Standard atmosphere | atm | 101,325 Pa | Gas law work, tyre and weather pressure |
| Absolute zero | 0 K | −273.15 °C | Every temperature conversion |
| Molar volume at STP | Vₘ | 22.41396954 L/mol | Gas stoichiometry |
| Density of water at 4 °C | ρ | 999.9720 kg/m³ | Volume to mass conversions |
| Specific heat of water | c | 4,184 J/(kg⋅K) | Heating, calorimetry |
| Speed of sound in air at 20 °C | c | 343 m/s | Doppler effect, acoustics |
| Solar constant | S | 1,361 W/m² | Solar panel sizing |
Standard gravity is an exact conventional value, not a measurement of gravity where you are standing. Real gravity varies by about half a percent between the equator and the poles.
How to Use These Tables
- Match precision to the worst input: if a calculation involves G, five significant figures is the honest output, however precise the other inputs are.
- Use standard gravity 9.80665 m/s² for any force or pressure conversion, and do not substitute local gravity unless you are calibrating an instrument.
- Convert temperatures through absolute zero: 0 °C is 273.15 K exactly, and the offset is the whole conversion.
- Check units before substituting: constants are quoted in SI, so a formula mixing inches or pounds has to be converted first.
Common Questions
Why does G have so few significant figures?
Because gravity is very weak and cannot be shielded. Laboratory measurements of the attraction between two masses are dominated by systematic effects, so independent experiments disagree in the fourth or fifth figure. It remains the least precisely known of the fundamental constants.
Is standard gravity the gravity where I am?
No. It is a conventional value of 9.80665 m/s², adopted for calibrations and conversions. Actual gravity varies with latitude and altitude by about half a percent, from roughly 9.780 at the equator to 9.832 at the poles.
What changed in the 2019 SI revision?
Seven constants were assigned exact values, and the kilogram, ampere, kelvin and mole were redefined in terms of them. The kilogram no longer depends on a physical artefact, and units can in principle be realised anywhere with the right apparatus.
Is the speed of light still measured?
No. It has been fixed at 299,792,458 m/s since 1983, and the metre is defined as the distance light travels in 1/299,792,458 of a second. Measuring it now would be measuring your apparatus against the definition.
Why is the density of water not exactly 1,000 kg/m³?
Because it is a measured property of a real substance, and it peaks at 999.9720 kg/m³ near 4 °C. The familiar 1,000 figure is a rounding that is accurate to about three parts in ten thousand, which is why it survives in most practical work.
More Science & Units
Sources
- CODATA recommended values of the fundamental constants — National Institute of Standards and Technology
- SI Brochure — the defining constants of the International System — International Bureau of Weights and Measures
- Standard acceleration of gravity and conventional values — National Institute of Standards and Technology
Filed with Science calculations.