Hydraulic Radius Calculator

Hydraulic radius Rh is the flow cross-sectional area divided by the wetted perimeter, Rh = A / P, measured in metres here. It summarises how efficiently a channel or pipe carries flow, and larger values generally mean less resistance per unit of area.

For a full round pipe the area is pi times (d/2) squared and the wetted perimeter is pi times d. Dividing area by perimeter cancels the pi and leaves d divided by 4, so a 0.2 m pipe gives Rh = 0.05 m regardless of the fluid.

It is the length of the cross-section boundary that is actually in contact with the fluid. An open channel wets the bottom and the two sides but not the free surface on top, while a duct flowing full wets all four walls.

Both have area width times depth, but the perimeters differ. An open channel has a free surface, so its wetted perimeter is width plus two depths. A full duct is sealed and flowing full, so its perimeter is twice the sum of width and depth.

Three: a full round pipe defined by diameter, an open rectangular channel defined by width and flow depth, and a full rectangular duct defined by width and height. Trapezoidal, triangular and partially full pipe shapes are not covered here.

Yes. The circular option treats the pipe as completely full, so it uses the whole circle for area and perimeter. A partly full pipe has a smaller wetted perimeter and a different hydraulic radius that this tool does not compute.

Enter every dimension in metres. Area then comes out in square metres, wetted perimeter in metres, and hydraulic radius in metres. If your data is in millimetres or feet, convert to metres first for consistent results.

It appears in open-channel flow through Manning's equation and the Chezy formula, and in pipe flow through the hydraulic diameter, which is four times the hydraulic radius. Engineers use it to size drains, culverts, sewers and ducts.

No. The formulas run in your browser as you type, so nothing you enter leaves your device and the calculator keeps working if you go offline.