River Discharge Calculator
Estimate the flow rate of a river or channel from its width, mean depth and current speed — the volume of water passing each second.
How it works
Q = A × v = width × mean depth × mean velocity
Discharge is the volume of water flowing past a cross-section each second, and by continuity it equals the channel's cross-sectional area times the mean flow velocity. The mean depth and mean velocity matter, not the maxima: real channels are deeper and faster in the middle than at the banks, so field measurements average several verticals across the width. Discharge is the key quantity in flood forecasting, water supply and hydro-power because it captures the total flow, not just how fast the surface looks.
Worked example
A river 10 m wide with a mean depth of 2 m has a cross-sectional area of 20 m². Flowing at a mean velocity of 1.5 m/s, its discharge is Q = 20 × 1.5 = 30 m³/s — about 30,000 litres per second, or 1,060 cubic feet per second.
Sources: Discharge (hydrology) — Wikipedia
Frequently asked questions
Why use mean velocity rather than surface speed?
Friction with the bed and banks slows the flow, so water at the surface and centre moves faster than near the boundaries. The mean velocity across the whole cross-section is typically around 80–90% of the surface speed, and using surface speed alone would overestimate discharge.
How is river discharge measured in practice?
Hydrologists divide the channel into vertical segments, measure depth and velocity in each with a current meter or acoustic profiler, and sum the segment discharges. Permanent gauging stations infer discharge from water level using a calibrated stage–discharge rating curve.
What is the difference between discharge and velocity?
Velocity is how fast the water moves (m/s); discharge is how much water passes per second (m³/s). A narrow, fast stream and a wide, slow river can carry the same discharge — the product of area and velocity is what counts.
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This calculator is for educational purposes. Double-check important results before acting on them.