Scientific and Engineering Constants
Reference table for scientific research, engineering analysis and manufacturing.
1 Scope and conventions
This reference consolidates fundamental physical constants and selected derived constants that are frequently used in scientific research, engineering calculations, metrology, materials science, thermodynamics, electronics, manufacturing and process engineering. Numerical values for fundamental constants follow the CODATA 2022 adjustment published by NIST. Where a value is exact under the present SI definition, it is identified as exact. Values in parentheses denote the standard uncertainty in the final displayed digits.
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| Constant / quantity | Symbol | Recommended value | SI unit | Status / uncertainty | Definition or engineering note |
|---|---|---|---|---|---|
| Speed of light in vacuum | c | 299 792 458 | m·s−1 | Exact | Defined SI constant. |
| Planck constant | h | 6.626 070 15 × 10−34 | J·s | Exact | Quantum of action; E = hν. |
| Reduced Planck constant | ℏ | 1.054 571 817… × 10−34 | J·s | Exact derived | ℏ = h/(2π). |
| Elementary charge | e | 1.602 176 634 × 10−19 | C | Exact | Magnitude of the elementary charge. |
| Boltzmann constant | kB | 1.380 649 × 10−23 | J·K−1 | Exact | Relates temperature to energy scale. |
| Avogadro constant | NA | 6.022 140 76 × 1023 | mol−1 | Exact | Number of specified entities per mole. |
| Molar gas constant | R | 8.314 462 618… | J·mol−1·K−1 | Exact derived | R = NAkB. |
| Atomic mass constant / unified atomic mass unit | mu = u | 1.660 539 068 92(52) × 10−27 | kg | ur = 3.1 × 10−10 | u = (1/12)m(12C). |
| Newtonian gravitational constant | G | 6.674 30(15) × 10−11 | m3·kg−1·s−2 | ur = 2.2 × 10−5 | Universal gravitational constant. |
| Vacuum electric permittivity | ε0 | 8.854 187 8188(14) × 10−12 | F·m−1 | ur = 1.6 × 10−10 | ε0 = 1/(μ0c2). |
| Vacuum magnetic permeability | μ0 | 1.256 637 061 27(20) × 10−6 | N·A−2 (H·m−1) | ur = 1.6 × 10−10 | No longer exact in the post-2019 SI; determined experimentally. |
| Fine-structure constant | α | 7.297 352 5643(11) × 10−3 | 1 | ur = 1.5 × 10−10 | Dimensionless electromagnetic coupling constant. |
| Rydberg constant | R∞ | 10 973 731.568 157(12) | m−1 | ur ≈ 1.1 × 10−12 | Spectroscopic constant. |
| Electron mass | me | 9.109 383 7139(28) × 10−31 | kg | ur = 3.1 × 10−10 | Rest mass of electron. |
| Proton mass | mp | 1.672 621 925 95(52) × 10−27 | kg | ur = 3.1 × 10−10 | Rest mass of proton. |
| Faraday constant | F | 96 485.332 12… | C·mol−1 | Exact derived | F = NAe; charge per mole of elementary charges. |
| Stefan–Boltzmann constant | σ | 5.670 374 419… × 10−8 | W·m−2·K−4 | Exact derived | Radiative heat flux: q = σT4 for an ideal blackbody. |
| Conductance quantum | G0 | 7.748 091 729… × 10−5 | S | Exact derived | G0 = 2e2/h. |
| Magnetic flux quantum | Φ0 | 2.067 833 848… × 10−15 | Wb | Exact derived | Φ0 = h/(2e); fundamental in superconductivity. |
| Josephson constant | KJ | 483 597.848 4… × 109 | Hz·V−1 | Exact derived | KJ = 2e/h. |
| von Klitzing constant | RK | 25 812.807 45… | Ω | Exact derived | RK = h/e2; quantum Hall resistance. |
| Vacuum characteristic impedance | Z0 | 376.730 313 412(59) | Ω | ur = 1.6 × 10−10 | Z0 = μ0c. |
| Bohr radius | a0 | 5.291 772 105 44(82) × 10−11 | m | ur = 1.5 × 10−10 | Characteristic atomic length. |
| Ideal-gas molar volume at 273.15 K and 101.325 kPa | Vm | 22.413 969 54… | L·mol−1 | Derived; pressure / temperature specified | Vm = RT/p under ideal-gas assumptions. |
| Standard acceleration of gravity | g0 | 9.806 65 | m·s−2 | Defined conventional value | Standard gravity; not the local measured g. |
| Standard atmosphere | p0 | 101 325 | Pa | Defined conventional value | Reference pressure; 1 atm. |
| Electron volt | eV | 1.602 176 634 × 10−19 | J | Exact derived unit | Energy acquired by one elementary charge through 1 V. |
| Standard gravitational parameter of Earth | GME | ≈ 3.986 004 418 × 1014 | m3·s−2 | Measured geodetic parameter | Useful in orbital / space engineering; not a universal constant. |
| Standard temperature for thermodynamic reference | T0 | 273.15 | K | Defined reference | 0 °C exactly on the Celsius scale. |
2 Frequently used engineering and manufacturing constants / reference values
Unlike fundamental constants, the following are not universal constants in the strict metrological sense. They are standardized reference quantities or widely used engineering values whose applicability depends on material, temperature, pressure, geometry, process and standard.
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| Quantity | Symbol | Typical / reference value | Unit | Primary engineering use | Qualification |
|---|---|---|---|---|---|
| Standard gravity | g0 | 9.806 65 | m·s−2 | Loads, weight, hydrostatics, mass-force conversion | Conventional standard. |
| Standard atmosphere | p0 | 101 325 | Pa | Pressure reference, gas calculations | Conventional standard. |
| Stefan–Boltzmann constant | σ | 5.670 374 419… × 10−8 | W·m−2·K−4 | Radiation and furnace calculations | Fundamental derived constant. |
| Vacuum impedance | Z0 | 376.730 313 412… | Ω | EMC, antennas, transmission lines | Derived from fundamental constants. |
| Universal gas constant | R | 8.314 462 618… | J·mol−1·K−1 | Thermodynamics, process engineering, reaction engineering | Exact derived from SI-defined constants. |
| Faraday constant | F | 96 485.332 12… | C·mol−1 | Electrolysis, electrochemistry, corrosion, plating | Exact derived from SI-defined constants. |
| Molar volume of ideal gas, 0 °C and 1 atm | Vm | 22.413 969 54… | L·mol−1 | Gas-flow and stoichiometric calculations | Only valid for stated T and p and ideal-gas model. |
| Standard molar volume, 0 °C and 100 kPa | Vm | ≈ 22.711 | L·mol−1 | Alternative industrial gas reference | Pressure differs from 1 atm; always state conditions. |
| Water density near 4 °C | ρ | ≈ 999.97 | kg·m−3 | Hydrostatics, fluid calculations | Temperature / pressure dependent; not a universal constant. |
| Air density, standard sea-level reference | ρair | ≈ 1.225 | kg·m−3 | Aerodynamics, ventilation, loads | Approximate at 15 °C and 101 325 Pa, dry air. |
| Dynamic viscosity of water at 20 °C | μ | ≈ 1.002 × 10−3 | Pa·s | Pumps, piping, Reynolds number | Strongly temperature dependent. |
| Kinematic viscosity of water at 20 °C | ν | ≈ 1.004 × 10−6 | m2·s−1 | Flow and Reynolds-number calculations | Derived from μ/ρ; temperature dependent. |
| Thermal conductivity of pure water at 20 °C | k | ≈ 0.598 | W·m−1·K−1 | Heat transfer | Temperature and composition dependent. |
| Specific heat capacity of water near 20 °C | cp | ≈ 4.182 | kJ·kg−1·K−1 | Thermal systems, heat exchangers | Temperature / pressure dependent. |
| Speed of sound in dry air at 20 °C | a | ≈ 343 | m·s−1 | Acoustics, flow, compressible gas systems | Depends strongly on temperature and humidity. |
3 Symbols, units and reporting practice
- Use SI units in scientific and engineering publications unless a standard or industry convention requires another unit.
- Do not describe every numerical reference as a “constant”: material properties, fluid properties and standard reference conditions are state-dependent.
- For high-accuracy work, reproduce the uncertainty and the CODATA edition used. CODATA values are periodically adjusted.
- For manufacturing calculations, record temperature, pressure, composition, alloy/grade, heat treatment and measurement method whenever a property is not a universal constant.
- Use a multiplication sign (×), scientific notation with explicit powers of ten, and SI unit products such as m·s−1 rather than ambiguous forms such as Nm2.
4 Primary references
- NIST / CODATA, 2022 CODATA Recommended Values of the Fundamental Physical Constants, Mohr, P. J., Newell, D. B., Taylor, B. N., & Tiesinga, E. (2025), Reviews of Modern Physics.
- NIST, CODATA Internationally Recommended 2022 Values of the Fundamental Physical Constants, NIST SP 961 / Physics Laboratory constants database.
- BIPM, The International System of Units (SI), 9th edition, with updates and associated SI Brochure materials.
- ISO 80000 series, Quantities and units, for quantity names and SI presentation.
Editorial note
This table is designed as a publication-quality scientific reference. The values supplied in the original input have been updated to the CODATA 2022 recommendations and corrected where the original list contained exponent, unit, or numerical errors. The next regular CODATA adjustment is scheduled for 2026; values should therefore be checked against the current NIST/CODATA database before use in high-precision work.
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