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] | Actions |
|---|
Fill in at least two verticals (distance, depth, velocity).
How we calculate
Each vertical i gets its own width "strip" w. For an interior vertical the strip reaches halfway to the neighbour on the left and on the right: w = (x[i+1] − x[i−1]) / 2. An outermost vertical gets half the distance to its single neighbour. The discharge is the sum over all verticals:
Q = Σ (depth × velocity × w)
The first and last rows of the table set the limits of the cross-section - the calculator computes discharge only between them. The strip between an outermost vertical and the bank is not included in the result until you enter the bank as a vertical. At a sloping bank, add a vertical at the water’s edge at both ends: depth 0, velocity may be left empty. At a vertical wall (quay, culvert), enter a vertical at the wall with its actual depth and take the velocity as a fraction of the neighbouring vertical’s velocity - this is how USGS computes it. Enter depth 0 only where the bed really reaches the water surface.
Frequently asked questions
What do I enter as "distance from the bank"?
The distance of the vertical from a fixed point, e.g. from the start of a tape stretched across the channel, in metres. Row order does not matter - the calculator sorts them. The first and last rows should lie at the water’s edges: at a sloping bank with depth 0, at a vertical wall with the depth at the wall. Without them the strips at the banks are not included in the result.
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?
Enough that no partial section carries more than 10 % of the discharge (ideally no more than 5 %) - this is the criterion of ISO 748:2021 (clause 7.1.2): 10 % as the limit, 5 % as the recommendation. The standard also gives a recommended minimum number of verticals: at least 15 for a channel narrower than 0.5 m, 20 for 0.5-5 m and 22 for a wider channel. In the mid-section method the USGS usually divides the cross-section into about 25-30 partial sections. Place the verticals more densely where it is deeper and faster. The calculator gives a result from 2 verticals, but below the standard’s recommended minimum treat it as a rough estimate, not a measurement for a series.
What method is the result calculated with?
The mid-section method - a standard velocity-area method used e.g. by the USGS and described in ISO 748 (clause 8.1.3 of the 2021 edition). 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 measurements at the same cross-section add up to the river’s regime: floods, low flows, seasonality. In LimnoLog you record every result (also offline), and a chart emerges from the series.
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