About

Curie's Law describes the magnetic susceptibility χ of paramagnetic materials as inversely proportional to absolute temperature T. The relationship χ = C ÷ T holds only above the Curie or Néel temperature, where thermal agitation dominates over magnetic ordering. Applying this formula at or near T = 0 K produces a divergence that has no physical meaning. Misidentifying the regime (ferromagnetic vs. paramagnetic) or using Celsius instead of Kelvin yields errors that propagate into incorrect material characterizations, flawed MRI contrast agent dosing calculations, or wrong sensor calibrations.

This calculator solves for any one of the four variables in the extended Curie relation M = C ⋅ H ÷ T. It assumes the linear (low-field, high-temperature) regime where the Langevin function approximates to its first-order term. For dense or strongly interacting systems, consider the Curie - Weiss modification χ = C ÷ (T − θ), which this tool also supports as an optional correction.

Formulas

The fundamental Curie's Law relates magnetic susceptibility to temperature:

χ = CT

The extended form with an applied magnetic field H gives the magnetization:

M = C ⋅ HT

The Curie constant itself is derived from fundamental quantities:

C = n ⋅ μ² ⋅ μ₀3 ⋅ k_B

The Curie - Weiss modification for interacting systems:

χ = CT − θ

Where χ = magnetic susceptibility (dimensionless, volume), C = Curie constant (K), T = absolute temperature (K), M = magnetization (A/m), H = applied magnetic field strength (A/m), n = number density of magnetic moments (m⁻³), μ = magnetic moment per atom (A⋅m²), μ₀ = vacuum permeability = 4π × 10⁻⁷ H/m, k_B = Boltzmann constant = 1.380649 × 10⁻²³ J/K, and θ = Weiss constant (K), positive for ferromagnetic interactions, negative for antiferromagnetic.

Reference Data

Material	Type	Curie Constant C (K)	χ at 300 K (10⁻³)	Effective Moment μ_eff (μ_B)	Electron Config
Gadolinium (III) ion	Paramagnetic	7.88	26.3	7.94	[Xe] 4f⁷
Iron (III) ion	Paramagnetic	4.38	14.6	5.92	[Ar] 3d⁵
Manganese (II) ion	Paramagnetic	4.38	14.6	5.92	[Ar] 3d⁵
Chromium (III) ion	Paramagnetic	1.88	6.27	3.87	[Ar] 3d³
Copper (II) ion	Paramagnetic	0.375	1.25	1.73	[Ar] 3d⁹
Nickel (II) ion	Paramagnetic	1.00	3.33	2.83	[Ar] 3d⁸
Cobalt (II) ion	Paramagnetic	1.88	6.27	3.87	[Ar] 3d⁷
Titanium (III) ion	Paramagnetic	0.375	1.25	1.73	[Ar] 3d¹
Vanadium (III) ion	Paramagnetic	1.00	3.33	2.83	[Ar] 3d²
Dysprosium (III) ion	Paramagnetic	14.17	47.2	10.65	[Xe] 4f⁹
Erbium (III) ion	Paramagnetic	11.48	38.3	9.58	[Xe] 4f¹¹
Neodymium (III) ion	Paramagnetic	1.64	5.46	3.62	[Xe] 4f³
Cerium (III) ion	Paramagnetic	0.80	2.67	2.54	[Xe] 4f¹
Europium (III) ion	Paramagnetic	0.00	0.00	0.00	[Xe] 4f⁶ (J=0)
Aluminium (metal)	Paramagnetic	0.0063	0.021	-	Pauli para.
Platinum (metal)	Paramagnetic	0.0085	0.028	-	Pauli para.

Frequently Asked Questions

Curie's Law contains T in the denominator. At 0 °C (273.15 K), the formula produces a finite, physical result. But if you mistakenly use 0 as the temperature value, you get division by zero. More fundamentally, susceptibility is proportional to 1÷T where T represents absolute thermal energy. Celsius has an arbitrary zero point that does not correspond to zero thermal energy. Always convert: T_K = T_°C + 273.15.

Curie's Law is valid only in the paramagnetic regime, i.e., above the Curie temperature T_C for ferromagnets or the Néel temperature T_N for antiferromagnets. Below these critical temperatures, cooperative magnetic ordering dominates and χ no longer follows the simple C÷T relationship. For example, iron has T_C = 1043 K. The formula also fails at very low temperatures where quantum saturation effects appear and the Langevin function cannot be linearized.

Curie's Law (χ = C÷T) assumes non-interacting magnetic moments. The Curie-Weiss Law (χ = C÷(T − θ)) adds a Weiss constant θ that accounts for exchange interactions between neighboring moments. When θ > 0, interactions are ferromagnetic. When θ < 0, they are antiferromagnetic. When θ = 0, the Curie-Weiss Law reduces to Curie's Law.

The Curie constant is proportional to μ², where the effective magnetic moment μ_eff = g √J(J+1) μ_B. For transition metal ions where orbital angular momentum is quenched, this simplifies to μ_eff ≈ √n(n+2) μ_B, where n is the number of unpaired electrons. Fe³⁺ with 5 unpaired electrons has μ_eff ≈ 5.92 μ_B, while Cu²⁺ with 1 unpaired electron has μ_eff ≈ 1.73 μ_B.

Yes, but only approximately. Above T_C, a ferromagnet enters the paramagnetic state and its susceptibility follows the Curie-Weiss Law with θ ≈ T_C. Pure Curie's Law (without the θ correction) will overestimate the susceptibility because it ignores the residual exchange interactions. For accurate work above T_C, always use the Curie-Weiss form and plot 1÷χ vs. T to extract both C and θ from the linear fit.

This calculator uses SI units throughout. The applied field H is in A/m (amperes per meter), and magnetization M is also in A/m. The susceptibility χ is the dimensionless volume susceptibility (M÷H). If you have CGS data (Oersted for H, emu/cm³ for M), convert using 1 Oe = 79.577 A/m. The Curie constant C has units of K (Kelvin) when χ is dimensionless.