Curie Constant Calculator — Magnetic Susceptibility
Compute the Curie constant C, effective magnetic moment μeff, and molar magnetic susceptibility χm for a paramagnetic ion. Enter the Landé g-factor and total angular momentum quantum number J to get the Curie constant in CGS and SI units, plus the susceptibility at any temperature via Curie's law χm = C/T.
K
C = (NA × g² × J(J+1) × μB²) / (3kB) ≈ 0.12503 × g² × J(J+1)
- 1
J(J+1)
2.5 × (2.5 + 1) = 8.75 - 2
g² × J(J+1)
2² × 8.75 = 35 - 3
Curie constant C
0.12503 × 35 = 4.37591C ≈ 0.12503 × g² × J(J+1) cm³·K/mol — the prefactor equals NAμB²/(3kB) in CGS units.
How does this calculator work?
The Curie constant C ≈ 0.12503 × g² × J(J+1) cm³·K/mol, where g is the Landé g-factor and J is the total angular momentum quantum number. Molar magnetic susceptibility χm = C/T. Effective magnetic moment μeff = g√(J(J+1)) in units of μB. For pure-spin 3d ions set g = 2 and J = S.
Formula
How this is calculated
Curie's law describes the magnetic susceptibility of an ideal paramagnet: the molar susceptibility χm is inversely proportional to the absolute temperature T, χm = C/T, where C is the Curie constant. C encapsulates the magnetic properties of the ion: the Avogadro-number prefactor NA, the square of the Landé g-factor g which measures how the orbital and spin angular momenta couple to the external field, and J(J+1) from the total angular momentum quantum number J. In CGS-Gaussian units the formula reduces to the remarkably compact C ≈ 0.12503 × g² × J(J+1) cm³·K/mol, where the coefficient 0.12503 equals (NA × μB²)/(3kB) evaluated with CGS constants.
The effective magnetic moment μeff = g√(J(J+1)) × μB is the root-mean-square moment per atom in units of the Bohr magneton μB. It is what is directly measured from the slope of a 1/χm vs T graph: slope = 1/C = 1/(0.12503 × μeff²/μB²). For a pure spin system with orbital angular momentum quenched (common in 3d transition metals), L = 0, J = S, and g ≈ 2. For lanthanide (4f) ions, both L and S contribute and the full J formalism is required.
This calculator uses the CGS-Gaussian unit convention, which remains the standard for tabulating magnetic susceptibilities in chemistry and solid-state physics. The SI Curie constant equals the CGS value multiplied by 4π × 10⁻⁶ when using volume susceptibility, but conventions vary — the CGS cm³/mol form avoids this ambiguity. Deviations from pure Curie law (such as Curie-Weiss behaviour at low temperature due to magnetic exchange interactions) are not modelled here.
Frequently asked questions
Fe³⁺ in high-spin configuration has S = 5/2 and L = 0 (half-filled d-shell), so J = S = 5/2 and g ≈ 2. C = 0.12503 × 4 × (5/2 × 7/2) = 0.12503 × 4 × 8.75 ≈ 4.38 cm³·K/mol. The effective moment μeff = 2√8.75 ≈ 5.92 μB, which matches the experimentally observed value.
Curie's law χm = C/T applies to ideal non-interacting paramagnets. The Curie-Weiss law χm = C/(T − θ) adds a Weiss temperature θ to account for magnetic exchange interactions between spins. Positive θ indicates ferromagnetic coupling; negative θ indicates antiferromagnetic coupling. This calculator models the pure Curie case (θ = 0).
In the CGS-Gaussian system (the most common for magnetism), C has units of cm³·K/mol and susceptibility χm has units of cm³/mol (sometimes written as emu/mol). In SI, C has units of m³·K/mol and χm has units of m³/mol. Converting: C_SI = 4π × 10⁻⁶ × C_CGS (for molar susceptibility in the volume definition). The CGS form is used here to match standard literature tables.
TG we-Calculate Editorial Team. (2026). Curie Constant Calculator — Magnetic Susceptibility [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/curie-constant-calculator
TG we-Calculate Editorial Team. "Curie Constant Calculator — Magnetic Susceptibility." TG we-Calculate. 2026. https://we-calculate.com/calculator/curie-constant-calculator.
TG we-Calculate Editorial Team, "Curie Constant Calculator — Magnetic Susceptibility," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/curie-constant-calculator
@misc{wecalculate_curie_constant_calculator, title = {Curie Constant Calculator — Magnetic Susceptibility}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/curie-constant-calculator}}, year = {2026}, note = {TG we-Calculate} }
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