Is there a standard height and depth for stairs?
The general rule (in the US) is 7-11 (a 7 inch rise and 11 inch run) (17.78cm-27.94cm).  More exactly, no more than 7 3/4 inches (19.7cm) for the riser (vertical) and a minimum of 10 inches (25.4cm) for the tread (horizontal or step).  You can find some more information here as well on other stair-related dimensions.

To calculate if the steps will be within the Building Codes specs :  2 times the step riser height + 1 tread width equals between 24 and 25 in inches (60.96cm and 63.5cm).

example:  (2 x 7.5") + 10 = 25 (2 x 19.05cm + 10 = 48.1cm)