What hydraulic radius is
Hydraulic radius describes how efficiently a channel or conduit shape conveys flow. It is not a physical radius but a ratio that compares how much cross-sectional area is available to flow against how much of the channel boundary is in contact with (and creates friction against) the fluid.
The formula
Hydraulic radius is calculated as R = A / P, where A is the cross-sectional area of flow and P is the wetted perimeter – the length of the channel boundary that is actually touching the fluid. A larger hydraulic radius generally means less relative friction loss and more efficient flow, which is why it is a core input to Manning’s equation for open-channel flow.
For quick reference: a full circular pipe of diameter D has R = D/4, and a wide rectangular channel of depth d approaches R ≈ d. Use the direct area/perimeter inputs above for any channel shape.