The most informal bow is a bend of about 15 degrees. To greet customers or to thank someone (the business bow) you bend about 30 degrees. For the most formal bow (deep respect, gratitude, or a formal apology) you bend 45 degrees while looking at your feet.
When you bow:
- your feet must be together
- men keep their hands at their sides (fingers together)
- women keep their hands on the front of their thighs (fingers together)
- the whole upper body must move forward, not just the head
The custom of bowing has been around a long time. It most likely started its life as prostration, the attitude of slaves: lying down on the floor in front of their master. In other words, this form of politeness started its life as a sign of submission.
Others believe the Japanese bow originates from the days of the Samurai. When two Samurai warriors met, they would bow their heads, revealing the backs of their necks to each other, which indicated that they trusted each other not to cut their head off.
In the same vein, when people shake hands, they normally do so with the right hand: the right hand was historically the hand with which you wielded your sword. Offering your hand to someone was a sign of peace and good faith, showing that your hand was empty of a weapon.
The custom of doffing one's hat, also, is similar to bowing, in the sense that, again, you reveal one of the most vulnerable parts of your body to another and show that you trust the person you are thus greeting.
In European cultures bowing is historically an exclusively male custom. Women have instead traditionally performed a curtsy: bending the knees as one leg draws backwards ("scraping" the floor), while the upper body stays upright. Think of the curtain calls of ballet dancers. The depth of the bow or curtsy, as in the Japanese bow, shows the degree of respect.