River Discharge Calculator
River discharge (Q) is the volume of water flowing past a stream cross-section per unit time. The standard USGS method for measuring discharge is the area-velocity method: Q = A * v, where A is the cross-sectional area of the stream channel (width times average depth) and v is the mean flow velocity. This method is applied at multiple subsections across the channel, with the total discharge being the sum of all subsection contributions. This calculator provides a simplified single-section estimate for educational and preliminary assessment purposes.
River discharge formula
A = Width (ft) * Average depth (ft) [cross-section area in ft2]
Q (cfs) = A * Mean velocity (ft/s)
Q (m3/s) = Q (cfs) * 0.028317
Daily volume (Mgal) = Q (cfs) * 86400 (s/day) * 7.48052 (gal/ft3) / 1,000,000
This simplified calculation assumes a uniform rectangular cross-section and uniform velocity. Real channels have irregular cross-sections and velocity profiles; the USGS uses multiple measurement verticals to account for this variation.
Streamflow measurement context
- The USGS operates over 8,000 stream gauges across the US, providing continuous real-time discharge data at waterdata.usgs.gov.
- Stream discharge varies with season: snowmelt streams peak in spring; rain-dominated streams peak in winter; intermittent streams may have zero discharge in dry months.
- 1 cubic foot per second (cfs) equals 449 gallons per minute or approximately 2 acre-feet per day.
- The USGS defines "bankfull discharge" as the flow that fills the channel to the top of the banks, approximately the 1.5-year recurrence interval flood for many streams.
- For design purposes, always use certified USGS gauge data or licensed hydrological assessments rather than simplified field estimates.
Frequently asked questions
What is river discharge?
River discharge (Q) is the volume of water flowing past a cross-section of a stream per unit time, typically measured in cubic feet per second (cfs) or cubic meters per second (m3/s). It is the primary measure of streamflow used by the USGS National Water Information System (NWIS).
How does the USGS measure streamflow?
USGS hydrographers measure streamflow by wading across a stream and taking velocity measurements at multiple verticals using an acoustic Doppler current profiler (ADCP) or mechanical current meter. The cross-section is divided into subsections, and Q is the sum of A*v for each subsection.
What is mean velocity and how is it measured?
Mean velocity in a stream cross-section is typically measured at 0.6 of the depth from the surface (for shallow streams) or averaged from measurements at 0.2 and 0.8 of the depth. The USGS standard method uses a current meter or ADCP to measure point velocities across the channel.
What is a typical river discharge range?
Discharge varies enormously. A small headwater stream might flow at 1 to 10 cfs. The Mississippi River at its mouth averages about 600,000 cfs. During floods, rivers can exceed 1,000 times their base flow. The Amazon River averages about 7 million cfs, the world's largest by discharge.
How does discharge relate to flood risk?
USGS stream gauges continuously measure stage (water surface elevation), which is converted to discharge using a rating curve. Flood stage thresholds are set by the National Weather Service based on historical discharge data and downstream impacts. Real-time data is available at waterdata.usgs.gov.
Official sources
- USGS: National Water Information System.
- USGS: Streamflow: How Water Flows in Streams.
- NOAA: National Weather Service River Forecasting.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.