Physical Constants Database Calculator

The Physical Constants Database Calculator provides instant access to seven of the most fundamental constants in physics, with the ability to scale them by any multiplier and express results in scientific notation. These constants — the speed of light, Planck's constant, Boltzmann constant, Avogadro's number, gravitational constant, electron mass, and proton mass — form the bedrock of modern physics and are used in calculations spanning from quantum mechanics to cosmology.

Physical constants are quantities that are universal and unchanging (as far as we know). They are not derived from theory — they are measured experimentally with extraordinary precision. The most recent authoritative values come from the Committee on Data for Science and Technology (CODATA), which periodically reviews all experimental determinations and publishes internationally recommended values. Since the 2019 SI redefinition, several constants have been assigned exact defined values, anchoring the entire system of units.

The speed of light c = 299,792,458 m/s is now an exact defined constant — the meter is defined as the distance light travels in 1/299,792,458 of a second. This constant connects space and time in Einstein's special relativity (E = mc²), sets the maximum speed for information transfer, and appears in Maxwell's equations linking electricity and magnetism: c = 1/√(μ₀ε₀).

Planck's constant h = 6.62607015 × 10⁻³⁴ J·s (exact since 2019) is the quantum of action. It sets the scale at which quantum effects become significant. The energy of a photon is E = hf (frequency times Planck's constant), and Heisenberg's uncertainty principle states ΔxΔp ≥ ℏ/2, where ℏ = h/(2π). Planck's constant now defines the kilogram through the Kibble balance.

The Boltzmann constant k_B = 1.380649 × 10⁻²³ J/K (exact) bridges the microscopic and macroscopic worlds. It connects temperature to the average kinetic energy of particles: ½mv² = (3/2)k_BT. It also appears in the entropy formula S = k_B ln Ω and the Boltzmann distribution, which governs the statistical behavior of atoms, molecules, and photons.

Avogadro's number N_A = 6.02214076 × 10²³ mol⁻¹ (exact) defines the mole — the amount of substance containing exactly this many entities. It connects the atomic scale (individual atoms and molecules) to the laboratory scale (grams, liters). One mole of any substance contains the same number of entities, enabling stoichiometric calculations throughout chemistry.

The gravitational constant G = 6.67430 × 10⁻¹¹ N·m²/kg² determines the strength of gravity. Newton's law of gravitation F = Gm₁m₂/r² uses G, as does Einstein's general relativity. Despite its fundamental importance, G remains the least precisely measured fundamental constant due to the extreme weakness of gravity compared to other forces.

The electron mass m_e = 9.109 × 10⁻³¹ kg and proton mass m_p = 1.673 × 10⁻²⁷ kg are the masses of the two most important subatomic particles. The proton-to-electron mass ratio m_p/m_e ≈ 1836.15 is a dimensionless constant whose value remains unexplained by current theory. These masses determine atomic structure, chemical bonding, and nuclear physics.

The multiplier feature allows you to compute derived quantities. For example, multiplying the speed of light by 3.156 × 10⁷ (seconds per year) gives the light-year distance. Multiplying Boltzmann's constant by room temperature (300 K) gives the thermal energy scale (~4.14 × 10⁻²¹ J). The scientific notation display helps manage the extreme range of scales involved in physics.

The quest to measure physical constants with ever-greater precision drives some of the most sophisticated experiments in modern physics. The speed of light was first measured by Ole Rømer in 1676 using Jupiter's moons, and refined through centuries of increasingly clever experiments until it was fixed by definition in 1983. Planck's constant was first estimated by Max Planck in 1900 while studying black-body radiation, and has been refined to 10⁻⁸ relative uncertainty through experiments with Josephson junctions and the quantum Hall effect. These measurements underpin our entire system of units and our most precise tests of fundamental physics.

The relationships between constants reveal deep structure in physics. The fine-structure constant α = e²/(4πε₀ℏc) ≈ 1/137 combines several constants into a dimensionless number that characterizes the strength of electromagnetism. The Planck units — constructed from G, ℏ, and c — define natural scales of length (1.6 × 10⁻³⁵ m), time (5.4 × 10⁻⁴⁴ s), and mass (2.2 × 10⁻⁸ kg) at which quantum gravity effects become important. Understanding and exploring these constants is essential for any student of physics.