How to calculate spin-only magnetic moments without using a calculator? Here is a mnemonic and heuristic that comes to the rescue:

Mnemonic and Heuristic for Estimating Spin-only Magnetic Moments

Abstract follows.

A mnemonic and heuristic for estimating spin-only magnetic moments of free atoms and ions, and based on a continued fractions algorithm, are presented. Chemistry teachers and students might find these useful as problem-solving strategies for lectures and test sessions where calculators might not be permitted or available.