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Hydraulic Radius Calculator

Find the hydraulic radius of a channel.

How it is calculated

The hydraulic radius is the flow area divided by the wetted perimeter: Rh = A ÷ P. A is the cross-sectional area of the water, in length squared (m²), and P is the wetted perimeter, the length of channel boundary in contact with the water, in length units (m). Rh comes out in the same length unit you used, shown by the tool only as "units" because it does not convert anything. Use consistent units, for example square metres with metres. The perimeter must be above zero and the area cannot be negative. The tool does not work out A or P from a shape. You must find them first: for a rectangular channel with width b and depth y, A = b × y and P = b + 2y, and the free water surface is not counted in P.

Worked example

A rectangular channel is 2 m wide and carries water 0.8 m deep. Flow area: A = 2 × 0.8 = 1.6 m². Wetted perimeter: the bed plus two sides, P = 2 + 2 × 0.8 = 3.6 m. Hydraulic radius: 1.6 ÷ 3.6 = 0.4444 units, which is 0.4444 m here. Notice that this is less than the 0.8 m depth, because the two side walls add friction length.

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Common mistakes

  • Counting the free water surface in the wetted perimeter. Only the bed and sides touching the water count; the top surface is open to air.
  • Using the full channel perimeter instead of the wetted part. A pipe or channel that is half full has a wetted perimeter much smaller than its whole boundary.
  • Mixing units, such as area in square feet and perimeter in metres. The ratio then has no meaning, so convert first.
  • Confusing hydraulic radius with the geometric radius. For a circular pipe flowing full Rh equals one quarter of the diameter, not half.
  • Entering depth for the area. The area field takes the whole cross-section of water, such as width times depth, not the depth alone.

About this calculator

This calculator finds the hydraulic radius, Rh = A/P, of an open channel or partially filled pipe — the cross-sectional area of flow (A) divided by the wetted perimeter (P), the length of the channel boundary actually in contact with the water. It's a key input to open-channel flow equations like Manning's equation, since a larger hydraulic radius means less frictional drag per unit of flow area and therefore faster, more efficient flow for the same slope and roughness.

Civil and hydraulic engineers use it to design canals, culverts, storm drains, and sewer pipes that carry the expected flow without overtopping or excessive friction losses; irrigation engineers use it to size channels for efficient water delivery; and students in fluid mechanics courses use it as a standard building block before applying Manning's or Chézy's equations.

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Comments (1)

  • Editorial team

    A full circular pipe makes a handy test of your inputs, because its hydraulic radius is always a quarter of the diameter. For a 0.5 m pipe the area is about 0.19635 and the perimeter about 1.5708, and the tool returns 0.1250. If your own full-pipe numbers do not reproduce a quarter of the diameter, recheck the units. Which channel shape are you working with: pipe, rectangle, trapezoid?

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