Weir Flow Calculator

Weir flow calculator: flow from head

A weir flow calculator estimates how much water passes over a weir from the width of the crest and the depth of water above it. It uses Q = 3.33 × L × H^1.5 for a rectangular, sharp-crested weir, with L and H in feet and Q in cubic feet per second. A 3 ft crest with 0.5 ft of head gives 3.53 cfs.

The head is raised to the power 1.5, so flow rises faster than depth.

The formula in plain words

Take the head in feet and raise it to the 1.5 power, which is the head times its own square root. Multiply by the crest length. Multiply by 3.33. The result is cubic feet per second. For gallons per minute, multiply by 448.83.

Worked example, a pond overflow

A rectangular notch is 3 ft wide, and water stands 0.5 ft above the crest.

• H^1.5: 0.5 × √0.5 = 0.3536
• Q: 3.33 × 3 × 0.3536 = 3.53 cfs
• In gpm: 3.53 × 448.83 = 1,585 gpm

Worked example, how head changes flow

Keep the 3 ft crest and change the head.

• 0.25 ft: 3.33 × 3 × 0.125 = 1.25 cfs
• 0.5 ft: 3.53 cfs
• 1.0 ft: 3.33 × 3 × 1 = 9.99 cfs

Doubling the head from 0.5 to 1.0 ft multiplies the flow by 2.83, not 2. That is the 1.5 power at work.

Flow by crest length and head

Crest length	Head 0.25 ft	Head 0.5 ft	Head 1.0 ft
2 ft	0.83 cfs	2.35 cfs	6.66 cfs
3 ft	1.25 cfs	3.53 cfs	9.99 cfs
5 ft	2.08 cfs	5.89 cfs	16.65 cfs
10 ft	4.16 cfs	11.77 cfs	33.30 cfs

Working backwards from flow

If you know the flow and want the head, rearrange the formula: H = (Q ÷ (3.33 × L))^(2/3). For 10 cfs over a 6 ft crest, 10 ÷ 19.98 = 0.5005, and raising that to the 2/3 power gives about 0.63 ft. Check it forward: 3.33 × 6 × 0.63^1.5 = 9.99 cfs, close to 10.

How to measure

• Measure the crest length across the opening in feet.
• Measure the head from the crest’s top edge to the water surface.
• Take the head upstream, out of the drawdown zone, with a staff gauge or a ruler fixed to a post.
• The crest should be sharp and level, and the water should fall freely past it.

Common mistakes

• Measuring the head at the crest itself. The surface dips there, so the reading is too low.
• Using inches. The formula wants feet, so 6 inches is 0.5 ft.
• Applying it to a V-notch or a broad weir.
• Ignoring end contractions. When water squeezes in at the sides, the real flow is lower than this formula shows.
• Treating the result as exact. Approach velocity and submerged weirs change the answer.

Dams and spillways are safety structures. A licensed engineer should design them, and permits are often required.

Sizing a notch for a target flow

You can also use the formula to size a weir. Say a pond overflow must pass 10 cfs with no more than 0.5 ft of water over the crest. With H = 0.5, H^1.5 is 0.3536, so the crest length is L = 10 ÷ (3.33 × 0.3536) = 8.49 ft. A notch 8.5 ft wide handles it, and a narrower one raises the water higher.

Treat that as a starting figure. Debris, vegetation and ice can block a notch, and the design flow comes from the storm you plan for, which an engineer works out.

Related pages

For open channels, use the Manning equation calculator. For a simple conversion of flow units, see the flow rate calculator, and for pipe crossings, the culvert calculator.