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The USGS Water Science School

How Streamflow is Measured
Part 3: The stage-discharge relation

Introduction 1: Measuring stage 2: Discharge measurement 3: Stage-discharge relation

Streamgages continuously measure stage, as stated in the "Measuring Stage"" section. This continuous record of stage is translated to river discharge by applying the stage-discharge relation (also called rating). Stage-discharge relations are developed for streamgages by physically measuring the flow of the river with a mechanical current meter or ADCP at a wide range of stages; for each measurement of discharge there is a corresponding measurement of stage. The USGS makes discharge measurements at most streamgages every 6 to 8 weeks, ensuring that the range of stage and flows at the streamgage are measured regularly. Special effort is made to measure extremely high and low stages and flows because these measurements occur less frequently. An example of a stage-discharge relation is shown in the diagram below. The stage-discharge relation depends upon the shape, size, slope, and roughness of the channel at the streamgage and is different for every streamgage.

A typical stage-discharge relation; here, the discharge of the river is 40 cubic feet per second (ft3/s) when the stage is 3.30 feet (ft). The dots on the curve represent concurrent measurement of stage and discharge.

The development of an accurate stage-discharge relation requires numerous discharge measurements at all ranges of stage and streamflow. In addition, these relations must be continually checked against on-going discharge measurements because stream channels are constantly changing. Changes in stream channels are often caused by erosion or deposition of streambed materials, seasonal vegetation growth, debris, or ice. An example of how erosion in a stream channel increases a cross-sectional area for the water, allowing the river to have a greater discharge with no change in stage, is shown in the diagram below. New discharge measurements plotted on an existing stage-discharge relation graph would show this, and the rating could be adjusted to allow the correct discharge to be estimated for the measured stage.

Erosion of part of a channel results in an increased cross-sectional area in the diagram on the right and the potential for conveying a larger quantity of water at the same stage..

Converting stage information to streamflow information

Most USGS streamgages transmit stage data by satellite to USGS computers where the stage data are used to estimate streamflow using the developed stage-discharge relation (rating) (see diagram below). The stage information is routinely reviewed and checked to ensure that the calculated discharge is accurate. In addition, the USGS has quality-control processes in place to ensure the streamflow information being reported across the country has comparable quality and is obtained and analyzed using consistent methods.

Most of the stage and streamflow information produced by the USGS is available in near real time through the National Water Information System (NWIS) World Wide Web site ( In addition to real-time streamgage data, the NWIS Web site also provides access to daily discharges and annual maximum discharges for the period of record for all active and discontinued streamgages operated by the USGS.

A typical stage-discharge relation; here, the discharge of the river is 40 cubic feet per second (ft3/s) when the stage is 3.30 feet (ft). The dots on the curve represent concurrent measurement of stage and discharge.

Streamflow summary

Streamgaging involves obtaining a continuous record of stage, making periodic discharge measurements, establishing and maintaining a relation between the stage and discharge, and applying the stage-discharge relation to the stage record to obtain a continuous record of discharge. The USGS has provided the Nation with consistent, reliable streamflow information for over 115 years. USGS streamflow information is critical for supporting water management, hazard management, environmental research, and infrastructure design. For more information on USGS streamgaging, go to the USGS Web site at The National Streamflow Information Program offers more information on this topic., Go to the USGS Office of Surface Water Web site for more information on surface-water activities, and the USGS WaterWatch site gives you current streamflow conditions nationwide or in your area.

Sources and more information

Related topics:

How the stream height (stage) relates to the amount of water flowing in a stream
Real-time USGS streamflow data

Learn about the water cycle, with a diagram in over 60 languages.The water cycle: Streamflow

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