In short: for a suppressed rectangular weir, flow rate is Q = 1.84 × L × H1.5 (SI units); for a 90° V-notch, it is Q = 1.40 × H2.5. Both take a single measured head and turn it into a flow rate — no separate flow meter needed. Use the calculator above for any head, crest length or notch angle.
These figures are planning aids based on published weir formulas. For regulatory monitoring or billing-grade measurement, confirm with a licensed engineer and a calibrated gauge.
How to calculate weir flow rate
A weir turns a flow-rate measurement into a much simpler height measurement. Water backs up behind a fixed obstruction — a straight crest or a notch — and spills over it. Because the shape of the crest is fixed and known, the depth of water flowing over it (the head, H) is all that is needed to work out how much water is passing, using an empirical formula developed from lab measurements.
This calculator converts your head (and, for a rectangular weir, your crest length) into meters, applies the matching formula, and returns the flow rate in GPM, liters per second, cubic meters per second and cubic feet per second. Orifice flow uses a related but distinct formula for flow through a submerged opening rather than over a free crest — use that instead if your opening is fully submerged.
Worked example. Take a suppressed rectangular weir 2 ft (0.6096 m) long with a measured head of 6 in (0.1524 m). H1.5 = 0.15241.5 ≈ 0.0595. Multiply: Q = 1.84 × 0.6096 × 0.0595 ≈ 0.0667 m³/s, which is about 66.7 L/s or 1,057.7 GPM. That is exactly what the calculator shows with its default values.
Suppressed vs. contracted. "Suppressed" means the weir crest runs the full width of the approach channel, so there is no side contraction. If your weir is narrower than the channel, each side contraction shortens the effective crest length by about 0.1 × H — enter that reduced length instead of the physical crest length.
Why the head measurement is so sensitive
Both weir formulas raise the head to a power greater than one, so small errors in reading H turn into much larger errors in the calculated flow. For a rectangular weir (H1.5), doubling the head roughly 2.8×s the flow. For a V-notch weir (H2.5), doubling the head roughly 5.7×s the flow. That steeper relationship is exactly why V-notch weirs are favored for low, variable flows: the same small change in flow shows up as a bigger, easier-to-read change in H.
Practically, this means the head gauge matters more than almost anything else in the setup. Read it upstream of the drawdown curve — the point where the water surface starts curving down toward the crest — at a distance of at least three to four times the maximum expected head, using a staff gauge or stilling well referenced to the exact elevation of the crest.
Rectangular weir flow by head (2 ft crest)
Flow rate for a suppressed rectangular weir with a 2 ft (0.61 m) crest, using Q = 1.84 × L × H1.5.
| Head (H) | Flow (L/s) | Flow (GPM) |
|---|---|---|
| 2 in / 51 mm | 12.8 | 204 |
| 4 in / 102 mm | 36.3 | 576 |
| 6 in / 152 mm (default) | 66.7 | 1,058 |
| 8 in / 203 mm | 102.7 | 1,629 |
| 10 in / 254 mm | 143.6 | 2,276 |
| 12 in / 305 mm | 188.7 | 2,991 |
90° V-notch weir flow by head
Flow rate for a 90° V-notch weir, using Q = 1.40 × H2.5. Notice how much faster flow grows with head compared with the rectangular weir above.
| Head (H) | Flow (L/s) | Flow (GPM) |
|---|---|---|
| 2 in / 51 mm | 0.81 | 12.9 |
| 4 in / 102 mm | 4.61 | 73.0 |
| 6 in / 152 mm (default) | 12.7 | 201 |
| 8 in / 203 mm | 26.1 | 413 |
| 10 in / 254 mm | 45.5 | 722 |
| 12 in / 305 mm | 71.8 | 1,138 |
Worked examples
Small channel monitoring, rectangular
1,057.7 GPM
A 2 ft rectangular weir with a 6 in head — the calculator's defaults — passes about 1,057.7 GPM (66.7 L/s), the same flow verified in the worked example above.
Low-flow spring monitoring, 90° V-notch
413 GPM
A 90° V-notch weir with an 8 in head passes about 413 GPM (26.1 L/s) — Q = 1.40 × 0.20322.5 ≈ 0.0261 m³/s.
Custom 60° notch, Cd 0.58
408 GPM
A 60° V-notch with a 10 in head and Cd = 0.58 passes about 408 GPM (25.7 L/s), using the general formula Q = (8/15) · Cd · √(2g) · tan(θ/2) · H2.5.
What else affects the result
Aeration of the nappe. The sheet of water falling over the crest (the nappe) needs air underneath it. If the space behind the falling sheet isn't vented to atmospheric pressure, a partial vacuum forms and pulls more flow over the crest than the formula predicts. Always confirm the nappe is fully ventilated.
Downstream submergence. Both formulas assume free, uncontrolled discharge — the downstream water level stays below the crest. If tailwater rises above the crest and "drowns" the weir, actual flow will be higher than these formulas show, and a submergence correction is needed.
Crest condition. The formulas assume a sharp, square-edged crest, typically a thin plate or a beveled edge on the downstream side. A rounded, worn or fouled crest behaves like a broad-crested weir instead and needs a different discharge coefficient.
Approach velocity. In a narrow or fast-moving approach channel, the water already carries some velocity (and kinetic energy) before it reaches the weir, which the basic formulas above ignore. For channels where the approach cross-section is more than a few times the flow area over the weir, this effect is small enough to disregard — see channel flow if you need to size the approach channel itself.
Frequently asked questions
What is the formula for weir flow rate?
Flow over a rectangular (suppressed) weir follows the Francis formula, Q = 1.84 × L × H1.5, where L is the crest length and H is the head in meters, giving Q in cubic meters per second. A 90° V-notch weir follows Q = 1.40 × H2.5. For a V-notch of any other angle, the general formula Q = (8/15) × Cd × √(2g) × tan(θ/2) × H2.5 applies, using a discharge coefficient Cd typically between 0.58 and 0.62.
How do I measure the head (H) on a weir?
Measure H vertically from the crest of the weir (its lowest edge) up to the water surface, taken upstream of the weir at a distance of at least three to four times the maximum expected head, clear of the drawdown curve where the water surface starts to dip toward the crest. A staff gauge or stilling well gives the most repeatable reading.
Rectangular or V-notch — which is more accurate for small flows?
A V-notch weir is generally more accurate at low flows. Because its discharge varies with H to the power of 2.5 instead of 1.5, a small change in flow produces a larger, more measurable change in head, giving better resolution than a rectangular weir at the same low flow rate.
Does the crest length matter for a V-notch weir?
No. A V-notch weir's discharge depends only on the head and the notch angle, not on any crest length, which is why the calculator hides the length field once you switch to a V-notch.
What if my V-notch isn't exactly 90°?
Switch to the custom V-notch option, enter the actual notch angle and a discharge coefficient (0.58–0.62 is typical for a sharp-edged notch), and the calculator uses the general V-notch formula instead of the fixed 90° constant.
Do I need to correct for end contractions on a rectangular weir?
This calculator assumes a suppressed rectangular weir — one that spans the full width of the channel, so there are no side contractions. If your weir does not extend the full channel width, each side contraction effectively shortens the crest by about 0.1 × H, and you should enter that reduced effective length instead.
Sources & references
- Francis, J. B. (1883). Lowell Hydraulic Experiments (4th ed.) — rectangular sharp-crested weir formula.
- Kindsvater, C. E., & Carter, R. W. (1959). Discharge characteristics of rectangular thin-plate weirs. Journal of the Hydraulics Division, ASCE, 85(HY6), 1–36.
- U.S. Bureau of Reclamation. Water Measurement Manual — weir and flume discharge tables.
John Mac, PE
Water Systems Specialist · Austin, Texas
Texas-licensed Professional Engineer with 13+ years in residential water systems and 180+ completed projects. Writes and reviews the calculators on watercalculator.us. Read full bio
Texas PE (2016) · BS Civil Engineering, Hydraulics (2013)