Packing efficiency (PE) = (Volume occupied by atoms in cell) / (Total volume of cell) × 100%

Simple Cubic (SC)

$r = \frac{a}{2}; \quad Z = 1$

$PE = \frac{1 \times \frac{4}{3}\pi r^3}{a^3} = \frac{\frac{4\pi}{3} \times \frac{a^3}{8}}{a^3} = \frac{\pi}{6} \approx 52.4\%$

BCC

$r = \frac{a\sqrt{3}}{4}; \quad Z = 2$

$r^3 = \frac{a^3 \cdot 3\sqrt{3}}{64}$

$PE = \frac{2 \times \frac{4\pi}{3} \times \frac{3\sqrt{3}a^3}{64}}{a^3} = \frac{\pi\sqrt{3}}{8} \approx 68.0\%$

FCC

$r = \frac{a\sqrt{2}}{4}; \quad Z = 4$

$r^3 = \frac{a^3 \cdot 2\sqrt{2}}{64} = \frac{a^3\sqrt{2}}{32}$

$PE = \frac{4 \times \frac{4\pi}{3} \times \frac{a^3\sqrt{2}}{32}}{a^3} = \frac{\pi\sqrt{2}}{6} \approx 74.05\%$

Summary

$SC < BCC < FCC = HCP$ $52.4\% < 68\% < 74\%$