Physical Constants Table
| Constant | Symbol | CODATA value | Uncertainty |
|---|---|---|---|
| Speed of light in vacuum | c | 299 792 458 m/s | — exact |
| Planck constant | h | 6.62607015 × 10⁻³⁴ J·Hz⁻¹ | — exact |
| Elementary charge | e | 1.602176634 × 10⁻¹⁹ C | — exact |
| Boltzmann constant | k | 1.380649 × 10⁻²³ J/K | — exact |
| Avogadro constant | NA | 6.02214076 × 10²³ mol⁻¹ | — exact |
| Newtonian constant of gravitation | G | 6.67430 × 10⁻¹¹ m³·kg⁻¹·s⁻² | ± 0.000 15 |
| Standard acceleration of gravity | g_n | 9.806 65 m/s² | — exact |
| Electron mass | m_e | 9.1093837139 × 10⁻³¹ kg | ± 0.000 000 0028 |
| Proton mass | m_p | 1.67262192595 × 10⁻²⁷ kg | ± 0.000 000 000 52 |
Nine numbers anchor all of physics - and since the 2019 SI redefinition, four of them are no longer measurements at all: the speed of light, the Planck constant, the elementary charge and the Boltzmann constant define the units, so they are exact by law. This table shows all nine verbatim from NIST’s CODATA, with an honest uncertainty column - exact where the value is a definition, a real error bar where scientists are still measuring.
The speed converter above puts any everyday speed on the light scale - a jet, a bullet, the space station - because the gap between human speeds and c is the single most humbling ratio in physics.
How to use
- Enter a speed with its unit; the chips load sound, an airliner, the ISS and highway speed.
- Read the uncertainty column as an honesty meter: — exact means the value defines the unit; ± marks a live measurement.
- Compare G’s error bar with the electron mass’s - gravity is the least precisely known constant in the table despite being the first you meet in school.
Frequently asked questions
Why is the speed of light an exact number?
The metre is defined as the distance light travels in 1/299,792,458 of a second. The speed is exact because it is the ruler: measuring it more precisely would just redefine the metre. The same logic made Planck’s constant, the elementary charge and Boltzmann’s constant exact in the 2019 SI.
Which constant is known worst?
Newton’s gravitational constant G: relative uncertainty 2.2 × 10⁻⁵, thousands of times worse than anything else in the table. Gravity is absurdly weak between lab masses, so torsion-balance experiments fight noise on every front - it is the oldest constant and still the shakiest.
Is g = 9.8 m/s² a measurement?
The standard acceleration gₙ = 9.806 65 m/s² is an agreed convention - a reference value for lift gauges and metrology, not the local value. Actual gravity at your location varies roughly ±0.5% with latitude and altitude; the calculator converts real speeds against light, not this convention.
Why do some constants carry parentheses like 6.674 30(15)?
NIST notation for uncertainty: 6.674 30(15) × 10⁻¹¹ means ±0.000 15 × 10⁻¹¹ - the digits in parentheses apply to the last digits of the value. The table spells the ± form out so nothing hides in the shorthand.