Assumes a circular pipe cross-section. The relationship between internal diameter and cross-sectional area for a circle is:

\(A = k_c \cdot D^2\)

Solving for the diameter:

\begin{equation}\label{eq:pipe-sizing-diameter} D = \sqrt{\frac{A}{k_c}} \end{equation}

Symbols

\(D\)	Minimum required internal pipe diameter \([\unit{ \inch}]\)
\(A\)	Cross-sectional area (from \eqref{eq:pipe-sizing-area}) \([\unit{ \inch\squared}]\)
\(k_c\)	Circle area factor (0.78 \(\approx \pi/4\)) \([\unit{ \unitless}]\)

Note

The factor \(k_c = 0.78\) is an industry-standard rounded approximation of \(\pi / 4 \approx 0.7854\) used in U.S. customary compressed air pipe sizing practice. The resulting diameter is the minimum internal (bore) diameter; the next larger standard nominal pipe size should be selected for the actual installation.