Weir Flow Calculator
Head over crest to V-notch or rectangular flow.
What it does
Streams and ditches get measured with boards, not meters. A weir plate with a sharp notch turns upstream depth into flow through a power law: small head changes swing discharge fast. One reading beats wading with a current meter.
The tool above applies the standard V-notch and rectangular formulas in imperial or metric. Enter head, and crest length for rectangular, then read cfs with gpm or liters per second with cubic meters per day.
The USBR Water Measurement Manual and USGS streamgaging references publish these same forms: 2.5 times head to the 2.5 for a 90-degree V in cubic feet per second, 3.33 times length times head to the 1.5 for suppressed rectangular. Metric constants mirror them exactly.
Use it for ditches, springs, and plant checks with a clean plate. Sediment, algae, tilt, and drowned nappes all read low, so clean the crest, level it, vent it, and measure head well upstream.
How to use
- Pick imperial (in, cfs) or metric (cm, L/s).
- Pick V-notch or rectangular weir.
- Enter head over the crest.
- Enter crest length for rectangular.
- Read flow plus gpm or daily volume.
- Verify crest condition before trusting it.
Formula
- H
- Head over the crest in inches (cm metric).
- L
- Crest length in ft (m metric), rectangular only.
Metric mirrors with meters: 1380 x H^2.5 L/s for V-notch and 1840 x L x H^1.5 L/s for rectangular. GPM multiplies cfs by 448.8; cubic meters per day multiply L/s by 86.4.
Worked example
Example: 6 in over V-notch
6 inches of head over a 90-degree V-notch weir.
- 90-degree V-notch with 6 in of head.
- Feet: 6 / 12 = 0.5 ft.
- Flow: 2.5 x 0.5^2.5 = 0.44 cfs.
- GPM: 0.44 x 448.8 = 198 gpm.
- Keep the crest sharp, level, and vented.
Reference table
| Head | Flow | GPM |
|---|---|---|
| 2 in | 0.03 cfs | 13 gpm |
| 4 in | 0.16 cfs | 72 gpm |
| 6 in | 0.44 cfs | 198 gpm |
| 8 in | 0.91 cfs | 407 gpm |
| 12 in | 2.50 cfs | 1,122 gpm |
Limits
- Standard 90-degree V and suppressed rectangular only.
- Free-flow nappes assumed; drowned weirs differ.
- Head must be read upstream, not at the crest.
- Sediment and algae void the math.
Common mistakes
- Reading head at the crest instead of upstream.
- Using V-notch constants on other angles.
- Ignoring drowned downstream levels.
- Skipping crest cleaning and leveling.
- Mixing inches with the foot-based formula.
Try it yourself
Quick checks. Answers sit tucked under each question.
Flow over a V-notch at 3 in of head?
Head is 0.25 ft. Flow is 2.5 x 0.25^2.5 = 0.08 cfs, or 35 gpm.
Flow over a 2 ft rectangular weir at 4 in?
Head is 0.333 ft. Flow is 3.33 x 2 x 0.333^1.5 = 1.28 cfs, or 575 gpm.
Questions
What is a weir for measuring flow?
A sharp-crested plate with a V or rectangular opening that meters open-channel flow from upstream head. Measure head upstream at least three depths back, to the crest level.
V-notch or rectangular: which one?
Small flows read best on a 90-degree V-notch; larger flows suit rectangular weirs with a measured crest length. V-notch stays sensitive at trickles where rectangles go vague.
What is the V-notch constant?
About 2.5 for a 90-degree V in cfs with feet (1380 in L/s with meters). Other angles use their own constants, so confirm the notch angle before borrowing the math.
When does the formula hold?
Fully contracted, level, sharp crest with free nappe and air under it. Drowned, tilted, or rounded crests read low and need corrections outside this page.
Can I get MGD for plant reporting?
Yes, roughly: this 0.44 cfs equals about 0.29 MGD. The metric path reports cubic meters per day the same way for plant math.
What ruins weir accuracy?
Sediment buries the crest, algae rounds the edge, and debris skews the head. Clean monthly, relevel yearly, and log readings with dates.