Sd: effective cone area

Sd is the area of the piston the driver behaves as. It is not the area of the visible cone, and it is not computed from the frame diameter.

The convention is to measure to the middle of the surround, because the inner half of the surround moves with the cone and the outer half does not. For a circular driver, if d is the diameter measured from the middle of the surround on one side to the middle on the other, then S_d = \pi d^2/4.

Why it matters

Sd appears everywhere. It converts cone motion into air motion: the volume of air a driver can move is V_d = S_d \times x_{max}, and that product, not either factor alone, sets how loud the driver can play at low frequencies.

It also enters Vas squared, which is why an error in Sd is so damaging to a derived parameter set.

The practical consequence

Displacement volume is what you are really buying. Two drivers with the same S_d \times x_{max} move the same air and, at low frequencies, can produce the same maximum output, whatever their nominal sizes. A 12-inch driver with 6 mm of travel and a 10-inch with 9 mm are close to equivalent.

This is also why four small drivers can substitute for one large one: area adds. Four 6.5-inch cones have roughly the area of one 13-inch. They will not behave identically higher up, where spacing between them starts to matter, but for bass the arithmetic is simply additive.

A caution

Manufacturers are inconsistent about Sd. Some quote to the middle of the surround as they should, some to the inner edge, and some appear to use the nominal frame size. A figure that looks generous usually is.