Curie's Law Calculator — Paramagnetic Susceptibility
Use Curie's law χ = C/T to find the magnetic susceptibility of a paramagnetic material at any temperature, then compute the magnetization for a given applied flux density.
K
K
T
Dimensionless — χ = C / T
- 1
Temperature reciprocal
1 ÷ 300 = 0.00333333 - 2
Magnetic susceptibility χ
0.3 × 0.00333333 = 0.001000χ = C / T — susceptibility grows as temperature falls.
How does this calculator work?
Curie's law χ = C/T states that a paramagnetic material's susceptibility is inversely proportional to absolute temperature. Enter the material's Curie constant C (in K), temperature T (K) and applied flux density B (T); the calculator returns χ = C/T and magnetization M = χB/μ₀. Larger C or lower T → stronger magnetism.
Formula
How this is calculated
Paramagnetic materials contain unpaired electron spins that partially align with an external magnetic field. At high temperatures, thermal agitation randomises the spins and weakens the net magnetization — this is the physics behind Curie's law: the volume magnetic susceptibility χ = M/H is inversely proportional to the absolute temperature T, with the Curie constant C encoding both the ion density and their effective magnetic moment via C = μ₀ × n × g² × μ_B² × J(J+1) / (3k_B). A larger C (more ions or more angular momentum) gives a stronger response; a higher T suppresses it.
Given B and T, the calculator derives H = B/μ₀, then χ = C/T, then M = χH. The induced flux density μ₀M is typically in the micro-tesla range for common paramagnets in a 1 T magnet. The chart plots χ against temperature, tracing the characteristic 1/T hyperbola that collapses toward zero as T rises.
Curie's law is valid only above the material's magnetic ordering temperature. Below the Curie point (ferromagnets) or Néel temperature (antiferromagnets), spin exchange interactions dominate and the linear M-vs-H relation breaks down. Typical paramagnetic salts have C ≈ 0.1–8 K; weakly paramagnetic metals such as aluminium have C ~ 10⁻⁵ K. The related Curie–Weiss law χ = C/(T − θ) adds an interaction term θ for materials near ordering.
Frequently asked questions
C encodes the density and size of the magnetic moments in the material. In SI units C = μ₀ × n × g² × μ_B² × J(J+1) / (3k_B), where n is the number of magnetic ions per m³, g the Landé g-factor, μ_B the Bohr magneton, J the total angular momentum quantum number and k_B the Boltzmann constant. Materials with more unpaired electrons or higher J (like Gd³⁺ with J = 7/2) have larger C and stronger paramagnetic response.
Gadolinium salts are among the strongest: χ ≈ 0.026 at 300 K (C ≈ 7.9 K). Iron(III) salts give χ ≈ 10⁻², manganese(II) salts ≈ 10⁻³. Weakly paramagnetic metals (aluminium, platinum) have χ in the 10⁻⁵ range. Diamagnets (copper, water) have small negative χ not described by Curie's law.
The Curie–Weiss law χ = C/(T − θ) adds a Weiss temperature θ that reflects interactions between magnetic moments. For an ideal paramagnet θ = 0, recovering Curie's law. A positive θ indicates ferromagnetic tendency; negative θ signals antiferromagnetism. Near T = θ the law predicts a divergence marking the onset of long-range magnetic order.
TG we-Calculate Editorial Team. (2026). Curie's Law Calculator — Paramagnetic Susceptibility [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/curies-law-calculator
TG we-Calculate Editorial Team. "Curie's Law Calculator — Paramagnetic Susceptibility." TG we-Calculate. 2026. https://we-calculate.com/calculator/curies-law-calculator.
TG we-Calculate Editorial Team, "Curie's Law Calculator — Paramagnetic Susceptibility," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/curies-law-calculator
@misc{wecalculate_curies_law_calculator, title = {Curie's Law Calculator — Paramagnetic Susceptibility}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/curies-law-calculator}}, year = {2026}, note = {TG we-Calculate} }
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