We perform first principles calculations on work functions of single wall carbon nanotubes, which can be divided into two classes according to tube diameter (D). For class I tubes (D > 1 nm), work functions lie within a narrow distribution (approximately 0.1 eV) and show no significant chirality or diameter dependence. For class II tubes (D < 1 nm), work functions show substantial changes, with armchair tubes decreasing monotonically with diameter, while zigzag tubes show the opposite trend. Surface dipoles and hybridization effects are shown to be responsible for the observed work function change.