Swimming velocities and breathing rates were measured for migrating gray whales ( Eschrichtius robustus (Lilljeborg, 1861)) at Costa Azul, Baja California, to compare swimming effort of southbound whales, northbound whales without calves, and northbound mothers and calves. From December 2004 to May 2005, whales were followed using a theodolite to determine swimming velocity. Binoculars were used to count whale blows and their timings were recorded to determine breathing rates. Individual whale breathing rates (BR) were divided by their swimming velocity (V) to derive a comparative index of swimming effort in units of breaths per kilometre. There were significant differences in mean BR, V, and swimming effort among the three migrating groups (p < 0.05). Southbound migrating whales averaged a swimming effort of 7.4 breaths·km–1 (V = 1.9 m·s–1, BR = 0.8 breaths·min–1). Northbound whales without calves showed the lowest swimming effort of the three migrating groups (4.7 breaths·km–1, V = 1.8 m·s–1, BR = 0.5 breaths·min–1). Northbound mothers and calves had the same swimming velocity (V = 1.2 m·s–1), but BR and swimming effort were calculated separately yielding a swimming effort of 7.6 breaths·km–1 (BR = 0.5 breaths·min–1) for mothers and 10.1 breaths·km–1 (BR = 0.7 breaths·min–1) for calves. Cost of transport was calculated for northbound calves, yielding a range based on 1.5% and 3% tidal volumes of 0.25–0.34 and 0.51–0.58 J·kg–1·m–1, respectively.