Radius Ratio Calculator
For NaCl the radius ratio is 0.563536, between 0.414 and 0.732, so each ion has six neighbours in the rock-salt structure.
Na⁺ 1.02 Å, Mg²⁺ 0.72 Å, Ca²⁺ 1.00 Å, Zn²⁺ 0.74 Å (six-fold).
Cl⁻ 1.81 Å, O²⁻ 1.40 Å, F⁻ 1.33 Å, S²⁻ 1.84 Å.
0.56353591160221
Full answer, then cut to fewer decimals (not rounded):
- 0.56353591160221
- 0.5635359116022
- 0.563535911602
- 0.56353591160
- 0.5635359116
- 0.563535911
- 0.56353591
- 0.5635359
- 0.563535
- 0.56353
- 0.5635
- 0.563
- 0.56
- 0.5
- Predicted coordination number
- 6
- Coordination polyhedron
- octahedral
- Typical structure
- NaCl (rock salt)
Step-by-step solution
- r_c/r_a = 1.02 ÷ 1.81 = 0.5635359116
- Limits: 0.155 (CN 3), 0.225 (CN 4), 0.414 (CN 6), 0.732 (CN 8), 1 (CN 12)
Radius Ratio Formula
r_c / r_a → coordination number
limits 0.155 (3), 0.225 (4), 0.414 (6), 0.732 (8), 1.0 (12)
Worked Example
Sodium chloride: Na⁺ 1.02 Å and Cl⁻ 1.81 Å:
- r_c/r_a = 1.02 ÷ 1.81 = 0.5635359116
- Limits: 0.155 (CN 3), 0.225 (CN 4), 0.414 (CN 6), 0.732 (CN 8), 1 (CN 12)
Coordination polyhedron: octahedral · Typical structure: NaCl (rock salt)
GATE tip
Electroneutrality fixes the formula: in CaF₂, Ca²⁺ has 8 F⁻ neighbours and each F⁻ has 4 Ca²⁺, the ratio of their coordination numbers matching 1 : 2.
More Processing and Materials Calculators
-
Polymer Molecular Weight Calculator
Mₙ = Σ xᵢMᵢ, M_w = Σ xᵢMᵢ² / Σ xᵢMᵢ
xᵢ number fraction; PDI = M_w/Mₙ ≥ 1; DP = Mₙ/m₀
Example: Fractions of 10, 20, 30 and 40 kg/mol with number fractions 0.1, 0.3, 0.4 and 0.2: Number-average molecular weight Mₙ = 27000 g/mol.
-
Rule of Mixtures Calculator
Isostrain: E_c = V_fE_f + V_mE_m
isostress: 1/E_c = V_f/E_f + V_m/E_m
Example: Carbon fibre (230 GPa) in epoxy (3.5 GPa) at 60 % fibre volume: Longitudinal modulus (isostrain) E_c = 139.4 GPa.
-
Rolling Calculator
Δh_max = μ²R, L = √(RΔh)
F ≈ σ̄ w L (no friction hill); true strain ln(h₀/h₁)
Example: Rolling 25 mm plate to 20 mm with 300 mm radius rolls and μ = 0.1: Draft Δh = 5 mm.
-
Chvorinov's Rule Calculator
t = B (V/A)ⁿ
B mould constant, n ≈ 2; riser modulus ≥ 1.2 × casting modulus
Example: A 200 × 100 × 50 mm block with B = 2 s/mm² and n = 2: Solidification time t = 6.80272 min.
Frequently asked questions
Where do the limits come from?
Each limit is the ratio at which the cation just touches all its anion neighbours in that polyhedron; for octahedral coordination it is √2 − 1 = 0.414.
Is the rule always right?
It is a guide: covalent bonding and polarisation can change the structure, as in ZnS, which is tetrahedral despite a ratio near 0.4.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Radius Ratio Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/radius-ratio-calculator/
IEEE
Scientific Converters, "Radius Ratio Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/radius-ratio-calculator/