The head of an ax should be smooth. Any blemishes on the surface are likely to be points of weakness where the ax will crack or chip over time. The handle should be made from a straight-grained hardwood, ideally hickory. Hickory stands out for its durability and shock absorbing capacity.
A hatchet is a small ax. To swing an ax requires two hands, chopping smaller pieces of wood with a hatchet uses one hand.
Safety is paramount when using an axe: