In short: streamflow (discharge) is the cross-sectional area of a channel multiplied by the mean water velocity through it, Q = A × V. A stream 15 ft wide and 1.5 ft deep, flowing at 2 ft/s, carries about 45 cubic feet per second (cfs) — roughly 20,200 gallons per minute. Enter your own width, depth and velocity above for an instant estimate.
This is a planning-grade estimate from a simplified rectangular section. For flood studies, water rights or gauge calibration, use a certified hydrographer and the USGS mid-section method.
How to calculate streamflow
Streamflow, also called discharge, is the volume of water passing a cross-section of a channel per unit of time. It depends on just two things: how big the wetted cross-section is, and how fast the water is moving through it. The relationship is the area-velocity equation:
This calculator treats the channel as a simple rectangle — width times average depth — then multiplies by velocity to get discharge, converting the result into whatever flow unit you need. That single multiplication is exactly what a stream gauge does at a larger scale, just with a more detailed cross-section built from several measured verticals instead of one.
Worked example. Take the calculator's default stream: 15 ft wide, 1.5 ft deep, flowing at a measured mean velocity of 2 ft/s. The cross-sectional area is 15 × 1.5 = 22.5 ft². Multiply by velocity: 22.5 × 2 = 45 ft³/s, or 45 cfs. Converting, that is about 20,197 gallons per minute, 1.27 m³/s, or roughly 29.1 million gallons per day.
Two ways to get velocity. Average velocity means you already have a mean velocity reading, from a current meter or wading rod, and can multiply directly. The float method instead times a floating object across a known distance at the surface, then applies a correction coefficient (below) because surface water moves faster than the average through the whole section.
Why the float method needs a correction coefficient
Water in an open channel does not move at one uniform speed. Friction against the streambed and banks slows the water nearest those surfaces, so velocity is highest somewhere near the surface at mid-channel and lowest at the edges and bottom. A current meter placed at about 0.6 of the depth from the surface reads close to the true mean velocity directly — that is the basis of the standard mid-section gauging method.
A floating object, by contrast, only ever reports surface velocity, which runs faster than the section's true mean. To correct for this, hydrographers multiply the timed surface velocity by a coefficient, commonly around 0.85 for a fairly regular natural channel — rougher, shallower or weedier channels pull the coefficient down toward 0.80, while smooth, deep, uniform channels push it up toward 0.90. This calculator applies whichever coefficient you choose before computing discharge, so both methods can be compared on the same footing. See our methodology page for the full method notes.
Float-method correction coefficients by channel type
Typical multipliers used to convert surface velocity to mean velocity. Pick the closest description, or measure a few verticals with a current meter if precision matters.
| Channel description | Coefficient | 45 cfs example becomes |
|---|---|---|
| Rough, weedy, or shallow bed | 0.80 | 42.4 cfs |
| Typical natural channel (default) | 0.85 | 45.0 cfs |
| Smooth, deep, uniform channel | 0.90 | 47.6 cfs |
Worked examples
Small creek, direct reading
5.76 cfs
A 6 ft wide, 0.8 ft deep creek flowing at 1.2 ft/s has an area of 4.8 ft², giving 5.76 cfs — about 2,585 GPM or 0.163 m³/s.
Medium stream, float method
159 cfs
A 25 ft wide, 2.5 ft deep stream with a 3.0 ft/s surface velocity and a 0.85 coefficient (mean 2.55 ft/s) carries about 159 cfs — roughly 71,500 GPM or 103 MGD.
Flood-stage river
10,800 cfs
A 150 ft wide river running 12 ft deep at 6 ft/s carries about 10,800 cfs — roughly 306 m³/s or 21,400 acre-ft per day.
What else affects the result
Natural cross-sections aren't rectangles. Width times average depth overstates area for a channel with sloped banks or an uneven bed. Certified stream gauging divides the channel into several verticals — often 20 or more for a wide river — each with its own measured depth and velocity, and sums the sub-areas (the USGS mid-section method).
Velocity varies across the section. Even with an accurate area, a single velocity reading is only representative if it is taken near the 0.6-depth point, or averaged from readings at 0.2 and 0.8 of the depth in deeper channels. A surface-only reading, uncorrected, will noticeably overstate discharge.
Flow is rarely steady. Discharge changes with rainfall, snowmelt and season, sometimes by an order of magnitude within a single day during a storm. A one-time measurement describes flow at that moment only — long-term stream gauges log continuously for this reason.
Frequently asked questions
How do you calculate streamflow?
Streamflow (discharge) is calculated as Q = A × V, where A is the cross-sectional area of the channel and V is the mean water velocity through that section. For a simple rectangular section, area is width times average depth. A stream 15 ft wide, 1.5 ft deep, flowing at 2 ft/s has an area of 22.5 ft² and a discharge of 45 cubic feet per second (cfs).
What is the float method, and why multiply by 0.85?
The float method estimates velocity by timing a floating object across a known distance, which measures the faster-moving surface velocity, not the mean velocity through the whole cross-section. Friction against the bed and banks slows water below the surface, so surface velocity is multiplied by a correction coefficient, typically about 0.85 for a natural channel, to approximate the true mean velocity.
How accurate is a simple width times depth cross-section?
Treating a channel as a rectangle (width × average depth) gives a reasonable estimate for a fairly uniform section, but natural channels are irregular, so the true area is usually somewhat less than width times average depth. For gauging-quality accuracy, the USGS mid-section method divides the channel into several verticals, each with its own depth and velocity, and sums the sub-areas.
What is a normal streamflow rate for a small creek versus a river?
As a rough order of magnitude, a small creek often runs at roughly 1 to 10 cfs, a medium stream 10 to a few hundred cfs, and a small river several hundred to a few thousand cfs, with major rivers running into the tens of thousands of cfs. Actual flow varies enormously with rainfall, snowmelt and season, so these ranges are only a general sense of scale.
What units is streamflow measured in?
In the United States, streamflow is most often reported in cubic feet per second (cfs), the standard USGS gauging unit. It is also expressed in gallons per minute (GPM) for smaller flows, cubic meters per second or liters per second in metric contexts, million gallons per day (MGD) for water-supply planning, and acre-feet per day for water-rights and irrigation accounting.
Sources & references
- Rantz, S. E., and others (1982). Measurement and Computation of Streamflow. U.S. Geological Survey Water-Supply Paper 2175.
- World Meteorological Organization (2010). Manual on Stream Gauging, WMO-No. 1044.
- International Organization for Standardization. ISO 748: Hydrometry — Velocity-area methods.
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)