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The Fundamental Physical Constants Calculator provides instant access to the most important constants in physics, including the speed of light $$c$$, Planck constant $$h$$, gravitational constant $$G$$, elementary charge $$e$$, Boltzmann constant $$k_B$$, Avogadro number $$N_A$$, vacuum permittivity $$\varepsilon_0$$, and vacuum permeability $$\mu_0$$. These constants define the fabric of physical law and connect disparate phenomena — electromagnetism, thermodynamics, gravity, and quantum mechanics — through precise numerical relationships.
Since the 2019 SI redefinition, four constants — $$h$$, $$e$$, $$k_B$$, and $$N_A$$ — are defined to have exact values, anchoring the kilogram, ampere, kelvin, and mole. The speed of light $$c = 299\,792\,458\;\text{m/s}$$ has been exact since 1983. Understanding these constants is essential for dimensional analysis, unit conversions, and verifying physics equations. Select a constant to view its value, SI units, dimensional formula, and related quantities.
Each fundamental constant carries specific SI units and dimensional formula. The calculator stores CODATA 2018 recommended values (updated for the 2019 SI redefinition where applicable):
The multiplier input lets you scale any constant — useful for expressing constants in non-SI units or computing products like $$2\pi c$$.
The Constant Value gives the SI value from CODATA. The Scaled Value multiplies it by your chosen factor. The SI Unit Code and Dimension Code are numeric identifiers for reference: code 1 = m/s [LT⁻¹], 2 = J·s [ML²T⁻¹], 3 = m³kg⁻¹s⁻² [M⁻¹L³T⁻²], 4 = C [IT], 5 = J/K [ML²T⁻²Θ⁻¹], 6 = mol⁻¹ [N⁻¹], 7 = F/m [M⁻¹L⁻³T⁴I²], 8 = H/m [MLT⁻²I⁻²]. The Related Constant Code points to companion constants often used together in formulas.
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Multiplying h by 1/(2π) ≈ 0.1592 gives the reduced Planck constant ℏ ≈ 1.0546 × 10⁻³⁴ J·s, which appears in quantum mechanics as the fundamental quantum of angular momentum.
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G = 6.6743 × 10⁻¹¹ m³ kg⁻¹ s⁻² is the gravitational constant. Its tiny value explains why gravity is the weakest of the four fundamental forces.
Fundamental physical constants are fixed numerical values that appear in the basic equations of physics and cannot be derived from other quantities. They include the speed of light $$c$$, Planck constant $$h$$, gravitational constant $$G$$, elementary charge $$e$$, Boltzmann constant $$k_B$$, and Avogadro number $$N_A$$. Since the 2019 SI redefinition, four of these ($$h, e, k_B, N_A$$) have exact defined values.
$$G$$ is measured with only about 22 parts per million uncertainty because gravity is extremely weak compared to electromagnetic forces. Torsion balance experiments (Cavendish-type) must isolate tiny gravitational forces from much larger environmental disturbances. No known relationship connects $$G$$ to other constants in a way that allows indirect high-precision determination.
The 2019 redefinition fixed the numerical values of $$h$$, $$e$$, $$k_B$$, and $$N_A$$ to be exact, redefining the kilogram, ampere, kelvin, and mole. Previously, the kilogram was defined by a physical artifact (the International Prototype), and $$N_A$$ and $$h$$ had experimental uncertainties. Now all SI base units derive from fixed constants.
Maxwell's equations yield $$c = 1/\sqrt{\mu_0 \varepsilon_0}$$. Before 2019, $$\mu_0 = 4\pi \times 10^{-7}$$ H/m was exact, fixing $$\varepsilon_0$$. After 2019, the fine-structure constant $$\alpha$$ determines $$\mu_0 = 2\alpha h/(e^2 c)$$, giving it a small uncertainty of ~1.5 × 10⁻¹⁰ relative.
Dimensional analysis checks that both sides of a physics equation have the same units (dimensions). Fundamental constants provide the conversion factors between different physical quantities. For example, $$E = mc^2$$ converts mass $$[M]$$ to energy $$[ML^2T^{-2}]$$ using $$c^2$$ with dimensions $$[L^2T^{-2}]$$. Knowing the dimensions of each constant is essential for verifying and constructing physical formulas.
This is an active research question. Laboratory measurements and astrophysical observations constrain any variation to less than about one part in 10¹⁵ per year for $$\alpha$$ (the fine-structure constant). Some theoretical frameworks (string theory, varying-constant cosmologies) allow slow drift, but no confirmed evidence of time variation has been found.
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