Reference
Scientific & mathematical constants
Values commonly used in formulas, converters, and coursework. Tap copy to grab the numeric string; always cross-check authoritative sources for regulated or mission-critical work.
Mathematical constants
Pi
Dimensionless 3.14159265358979323846 Ratio of a circle's circumference to its diameter.
Euler's Number
Dimensionless 2.71828182845904523536 Base of the natural logarithm.
Golden Ratio
Dimensionless 1.61803398874989484820 Mathematical constant found in nature, art, and optimization.
Tau (2π)
Dimensionless 6.28318530717958647692 One full turn in radians; circumference of a unit circle.
Square Root of 2
Dimensionless 1.41421356237309504880 Diagonal of a unit square; appears throughout geometry and analysis.
Natural Logarithm of 2
Dimensionless 0.69314718055994530941 Common in half-life formulas, binary entropy, and exponential decay.
Euler–Mascheroni Constant
Dimensionless 0.57721566490153286060 Relates the harmonic series to the natural logarithm; used in analytic number theory.
Apéry's Constant
Dimensionless 1.20205690315959428539 Value of the Riemann zeta function at 3; appears in some quantum and statistical models.
Physical & Science constants
Speed of Light in Vacuum
m/s 299,792,458 Exact SI defining constant; upper limit for causal signal speed in vacuum.
Planck Constant
J⋅s 6.62607015 × 10⁻³⁴ Exact SI defining constant; scales quantum action and photon energy E = hf.
Reduced Planck Constant
J⋅s 1.054571817 × 10⁻³⁴ h/2π; appears in Schrödinger equation, angular momentum quantization, and uncertainty relations.
Elementary Charge
C 1.602176634 × 10⁻¹⁹ Exact SI defining constant; magnitude of the electron charge.
Boltzmann Constant
J/K 1.380649 × 10⁻²³ Exact SI defining constant; links microscopic energy to temperature.
Avogadro Constant
mol⁻¹ 6.02214076 × 10²³ Exact SI defining constant; number of entities per mole.
Molar Gas Constant
J/(mol⋅K) 8.31446261815324 Exact in SI (N_A k_B); ideal gas law PV = nRT.
Faraday Constant
C/mol 96,485.33212331001 Charge per mole of electrons (e N_A); electrochemistry and electrolysis.
Vacuum Permittivity
F/m 8.8541878128 × 10⁻¹² Electric constant; relates electric field to charge in free space (SI derived).
Vacuum Permeability
H/m 1.25663706212 × 10⁻⁶ Magnetic constant; Ampère’s law in vacuum (SI derived, historically 4π×10⁻⁷ H/m).
Impedance of Free Space
Ω 376.730313668 μ₀ c; relates E and B amplitudes in a plane electromagnetic wave in vacuum.
Newtonian Constant of Gravitation
m³⋅kg⁻¹⋅s⁻² 6.67430 × 10⁻¹¹ Universal gravitational constant in Newton’s law (CODATA value; finite uncertainty).
Electron Mass
kg 9.1093837015 × 10⁻³¹ Rest mass of the electron.
Proton Mass
kg 1.67262192369 × 10⁻²⁷ Rest mass of the proton.
Neutron Mass
kg 1.67492749804 × 10⁻²⁷ Rest mass of the neutron (slightly larger than the proton).
Fine-Structure Constant
Dimensionless 7.2973525693 × 10⁻³ Coupling strength of electromagnetism; α ≈ 1/137 in many approximations.
Rydberg Constant (Infinite Mass)
m⁻¹ 10,973,731.568160 Spectroscopic constant for hydrogen-like atoms in the infinite nuclear mass limit.
Stefan–Boltzmann Constant
W⋅m⁻²⋅K⁻⁴ 5.670374419 × 10⁻⁸ Total radiated power per area of a black body: P/A = σT⁴.
Wien Displacement Constant
m⋅K 2.897771955 × 10⁻³ λ_max T for blackbody peak wavelength (Wien’s displacement law).
Astronomical constants
Astronomical Unit
m 149,597,870,700 Exact IAU definition; approximate mean Earth–Sun distance scale.
Light-Year
m 9,460,730,472,580,800 Distance light travels in vacuum in one Julian year (365.25 days).
Parsec
m 30,856,775,814,913,670 IAU: (648000/π) astronomical units; about 3.26 light-years.
Solar Mass (nominal)
kg 1.98847 × 10³⁰ IAU nominal solar mass; convenient unit in astrophysics.
Jupiter Mass (nominal)
kg 1.8982 × 10²⁷ Common nominal Jupiter mass for exoplanet masses (about 317.8 Earth masses).
Mean Earth–Moon Distance
m 384,400,000 Rough mean semimajor axis of the lunar orbit (orbit is elliptical; value is approximate).
Earth & Geophysics constants
Standard Gravity
m/s² 9.80665 Conventional nominal acceleration due to gravity (not local g at every latitude).
Earth Mean Radius
m 6,371,000 Approximate mean radius of the Earth (models vary slightly).
Earth Mass
kg 5.9722 × 10²⁴ Approximate mass of the Earth (CODATA / astronomy references).
Standard Atmosphere
Pa 101,325 Conventional mean sea level pressure reference in chemistry and engineering.
Julian Year (seconds)
s 31,557,600 365.25 days; used in definitions such as the light-year.