Stream Discharge Calculator (Float Method, Q = A·v)
Estimate river or stream discharge from width, depth, and surface float velocity.
Returns flow in cubic meters per second (cumecs) and cubic feet per second.
Measuring how much water a river actually carries
Discharge is the volume of water flowing past a point per second. It is the number hydrologists, flood forecasters, and water-rights regulators care about most, because it drives everything downstream: flood risk, how much can be withdrawn for irrigation, how a pollutant gets diluted, whether a culvert is big enough. The float method is the simplest field technique for estimating it without instruments, and it rests on one equation:
Q = A × v
Where Q is discharge (volume per time), A is the cross-sectional area of the flowing water, and v is the average velocity. Area is width times average depth for a roughly rectangular channel.
The float method, step by step
- Pick a straight, uniform reach of the stream with no big eddies or obstructions.
- Measure the width across the surface.
- Measure depth at several points across the width and average them. (More points means a better average for an irregular bottom.)
- Mark off a known length along the bank, say 10 meters. Drop a float (an orange, a stick, a partly filled bottle) in the current and time how long it takes to travel that length. Surface velocity = distance / time. Repeat a few times and average.
- Multiply: Q = width × average depth × velocity × correction factor.
Why the correction factor matters
A float rides the surface, where water moves fastest. The water near the bed and banks is slowed by friction, so the average velocity through the whole cross-section is less than the surface velocity. You multiply the surface speed by a correction factor to get the mean:
- About 0.85 for a smooth-bottomed channel (concrete, sand)
- About 0.75 for a rough or rocky streambed
- About 0.80 as a general default
Skipping this correction is the single most common mistake in float-method measurements, and it overestimates discharge by 15 to 25 percent.
Units and what the numbers mean
This calculator reports discharge in both cubic meters per second (m³/s, called cumecs) and cubic feet per second (cfs), the unit used by the US Geological Survey for streamflow. For scale:
| Discharge | Example |
|---|---|
| Under 0.03 m³/s (1 cfs) | A small creek you can step across |
| 0.3 m³/s (about 10 cfs) | A modest stream |
| 30 m³/s (about 1,000 cfs) | A small river |
| 1,000-3,000 m³/s | The Thames in flood, the Colorado at high water |
| About 209,000 m³/s | The Amazon, the largest river discharge on Earth |
When to use a better method
The float method is a field estimate, good to maybe plus or minus 20 percent. For anything official, hydrologists use a current meter (a propeller or electromagnetic sensor) at many points across the cross-section, or an Acoustic Doppler Current Profiler towed across the channel. Stream gauging stations relate water height (stage) to discharge through a calibrated rating curve, so a simple height reading gives discharge continuously. And where you know the channel slope and roughness instead of velocity, Manning’s equation predicts the velocity directly. But for a quick estimate with a tape measure, a stopwatch, and an orange, Q = A × v with a velocity correction is hard to beat.
A worked example
A stream is 4 m wide with an average depth of 0.5 m, so the cross-sectional area is 2 m². A float covers a 10 m reach in 12.5 seconds, giving a surface velocity of 0.8 m/s. The streambed is gravelly, so use a correction of 0.75 for the mean velocity: 0.8 × 0.75 = 0.6 m/s.
Q = 2 × 0.6 = 1.2 m³/s, which is about 42 cubic feet per second. A modest stream, the kind that might drive a small mill or supply a village.