River Discharge Calculator (Velocity–Area Method)
Estimate river or stream discharge from cross‑section measurements using the standard velocity–area method. Supports SI and US customary units, multiple verticals, and automatic panel calculations.
Using SI units: width in metres, depth in metres, velocity in m/s. Discharge will be in m³/s.
Cross‑Section & Panels
Enter measurements for each vertical (panel). The calculator will compute panel area and discharge, then sum them to get total river discharge.
Optional. Click “Apply width to all” to fill blank widths.
| # | Panel width (m) | Depth (m) | Mean velocity (m/s) | Area (m²) | Panel Q (m³/s) |
|---|
Tip: For a simple rectangular channel with nearly uniform depth and velocity, you can use a single panel.
Worked example
Suppose you measure a small river using 4 panels with equal width 1.5 m. Depth and mean velocity at each vertical are:
| Panel | Width (m) | Depth (m) | Velocity (m/s) | Area (m²) | Q (m³/s) |
|---|---|---|---|---|---|
| 1 | 1.5 | 0.6 | 0.40 | 0.90 | 0.36 |
| 2 | 1.5 | 0.8 | 0.55 | 1.20 | 0.66 |
| 3 | 1.5 | 0.7 | 0.50 | 1.05 | 0.53 |
| 4 | 1.5 | 0.5 | 0.35 | 0.75 | 0.26 |
| Total discharge | 1.81 m³/s | ||||
Enter these values in the table above (4 panels, width 1.5 m, depths and velocities as listed) and the calculator will return a total discharge of approximately 1.81 m³/s.
River discharge formula (velocity–area method)
River discharge (also called streamflow) is the volume of water passing through a cross‑section of a river per unit time.
Basic definition
For a uniform channel:
Q = A × v
where:
- Q = discharge (m³/s or ft³/s)
- A = cross‑sectional area of flow (m² or ft²)
- v = mean flow velocity (m/s or ft/s)
Velocity–area method with panels
Real rivers have non‑uniform depth and velocity. The standard hydrometric approach is to divide the cross‑section into n panels and sum their contributions:
Q = Σ (Ai × vi) for i = 1 … n
with:
- Ai = area of panel i (panel width × average depth)
- vi = mean velocity in panel i
Typical units
- SI: width (m), depth (m), velocity (m/s) → Q in m³/s
- US customary: width (ft), depth (ft), velocity (ft/s) → Q in ft³/s (cfs)
How to measure river discharge in the field
- Select a straight, stable reach. Avoid bends, backwaters, and rapidly changing bed conditions.
- Lay out a cross‑section. Stretch a tape across the river perpendicular to flow and mark verticals at regular spacing.
- Measure depth at each vertical. Use a wading rod or sounding line to measure from surface to bed.
-
Measure velocity. Use a current meter or
ADCP. For wading measurements, common practice is:
- Single‑point method at 0.6 depth for shallow flows.
- Two‑point method at 0.2 and 0.8 depth; mean velocity is the average of the two.
- Compute panel area and discharge. For each panel, multiply width × average depth to get area, then area × mean velocity to get panel discharge.
- Sum all panels. The sum is the total discharge at that cross‑section.
Limitations and good practice
- Increase the number of panels where depth or velocity changes rapidly.
- Avoid measuring during rapidly rising or falling stages unless necessary.
- Repeat measurements to check consistency and estimate uncertainty.
- Use rating curves (stage–discharge relationships) for continuous monitoring once enough measurements are collected.
Frequently asked questions
Is this calculator suitable for large rivers?
Yes, as long as you have representative depth and velocity data across the cross‑section. For large rivers, measurements are often made from a boat using an ADCP; you can still aggregate those data into panels and enter them here.
Can I use average depth and velocity for the whole river?
For very simple, nearly uniform channels, you can approximate Q with a single panel using the overall average depth and velocity. However, for natural rivers with complex profiles, using multiple panels gives more reliable results.
How accurate is the velocity–area method?
When performed according to hydrometric standards (sufficient panels, calibrated instruments, stable cross‑section), uncertainties of ±5–10% are typical. Errors increase if the cross‑section is poorly chosen or if velocity measurements are sparse.