The surface area \( S \) of a sphere can be calculated using the formula:
\[ S = 4\pi r^2 \]
where \( r \) is the radius of the sphere. The radius is half of the diameter, so for a sphere with a diameter of 40 inches, the radius is:
\[ r = \frac{40}{2} = 20 \text{ inches} \]
Now, substitute the radius into the surface area formula:
\[ S = 4\pi (20)^2 \]
Calculating \( (20)^2 \):
\[ (20)^2 = 400 \]
Now substitute that value back into the formula:
\[ S = 4\pi \times 400 = 1600\pi \]
Thus, the surface area of the sphere is:
\[ \boxed{1600\pi} \text{ square inches.} \]