Tool · free
River discharge calculator (mid-section method)
For each measurement vertical, enter the distance from the bank, the depth and the water velocity. The calculator computes the discharge Q using the mid-section method - summing the products of depth, velocity and assigned width for each vertical.
| Distance from bank [m] | Depth [m] | Velocity [m/s] |
|---|
Fill in at least two verticals (distance, depth, velocity).
How we calculate
Each vertical i is assigned a width "strip" w: for interior verticals it is half the distance to the left neighbour and half to the right (w = (x[i+1] − x[i−1]) / 2), and for the outermost ones - half the distance to the single neighbour. The discharge is the sum over all verticals:
Q = Σ (depth × velocity × w)
To estimate the banks more accurately, add outer verticals with depth 0 right at the bank - the calculator then naturally "closes" the cross-section.
Frequently asked questions
What do I enter as "distance from the bank"?
The distance of the measurement vertical from a fixed point on the bank (e.g. from a tape stretched across the channel), in metres, increasing. If you measure depth 0 right at the bank, you can add such a vertical at the start and end of the table - this improves the estimate at the edges.
What velocity do I enter for a vertical?
The mean velocity in that vertical - from a current meter, most often at 0.6 of the depth from the surface, or the average of measurements at 0.2 and 0.8 of the depth. This is the value meant to represent the whole vertical.
How many verticals are needed?
The more, the more accurate - especially in a channel with an uneven bed. A few to a dozen verticals is a typical field range. The calculator gives a result from 2 verticals, but with 2-3 treat it as very rough.
What method is the result calculated with?
The mid-section method - a standard velocity-area method used e.g. by the USGS and compliant with ISO 748. Each vertical is assigned half the distance to its neighbouring verticals as its width "strip".
A single Q measurement is a snapshot - the regime shows in a series
Repeated discharge measurements at the same cross-section build a picture of the river’s regime - floods, low flows, seasonality. In LimnoLog you record every result (also offline), and a chart emerges from the series.
Open the app → Explore LimnoLog features →Read more