Stream Power Erosion Potential Calculator

How stream power links river flow and erosion

Stream power describes the rate at which flowing water can expend energy along a river channel. When a reach carries more water, drops more steeply, or squeezes the flow into a tighter width, it has greater capacity to move sediment, scour its bed, and cut into its banks. This makes stream power useful for river engineering, restoration planning, field classes, and preliminary screening. It is not a replacement for a full hydraulic model, but it provides a physically grounded first indication of whether a reach may be gentle, active, or strongly erosive.

This calculator uses the three variables in the classic stream-power relationship: discharge Q, slope S, and channel width B. It reports total stream power per unit channel length and unit stream power. Total stream power rises with larger flow and steeper slope. Unit stream power divides that value by width, allowing reaches of different sizes to be compared on a more equal basis. For erosion screening, the unit value is often especially informative because a narrower channel concentrates the same flow energy.

Field measurements for stream-power inputs

Discharge Q (m³/s) is the volumetric flow rate through the reach. With gauged data, it is often the most readily available input. In ungauged settings, it may come from a rating curve, a regional estimate, or a selected design flow such as bankfull, a seasonal flow, or a flood scenario. Choose a value that represents the event of interest. A channel that is stable during ordinary flow can become erosive during a storm, so selecting the discharge is part of the assessment rather than a mere data-entry step.

Channel slope S (m/m) is the representative energy gradient of the reach. It is dimensionless, although written as metres per metre. Because slope directly multiplies stream power, modest measurement differences can matter. Use a reach-scale slope rather than the steepest isolated riffle unless that feature is specifically under study. Low-gradient rivers may have slopes of only a few thousandths, whereas mountain channels can be much steeper.

Channel width B (m) is the active width across which flow energy is distributed. Width appears only in the unit stream-power calculation: a wider channel spreads the same total power over more area, while a constricted channel concentrates it. For planning work, decide whether width represents bankfull, flood-stage, or the current active channel. Combining a flow at one stage with a width measured at another stage can distort the comparison.

• Use one consistent flow scenario for discharge, slope, and width.
• Enter slope as a decimal ratio, such as 0.002, rather than as a percent.
• Use a width appropriate to the modeled stage; restoration, levees, and constrictions can materially change unit stream power.

Computing total and unit stream power

This stream-power calculator applies the hydraulic relationship directly: water density and gravity convert the discharge-and-slope combination into total power per unit channel length, then channel width converts that value to power per unit area. Discharge and slope therefore increase both outputs in direct proportion, while width changes only the unit result.

It implements total stream power $\Omega$ and unit stream power $\omega$. Total stream power represents the energy rate available along the reach; unit stream power indicates how concentrated that energy is over channel width. This concentration is why channel narrowing can raise local erosion potential even if upstream discharge remains unchanged.

The total stream power per unit channel length is

Formula: Ω = ρ g Q S

$$\Omega =\rho gQS$$

where $\rho$ is water density (approximately 1000 kg/m³), $g$ is gravitational acceleration (9.81 m/s²), $Q$ is discharge, and $S$ is channel slope. Dividing by channel width $B$ gives unit stream power:

Formula: ω = Ω / B

$$\omega =\frac{\Omega }{B}$$

The result panel reports $\Omega$ in watts per metre and $\omega$ in watts per square metre. Increasing Q or S raises both measures linearly. Increasing B leaves total power per channel length unchanged but lowers unit power by distributing the energy across a wider channel.

Stream-power example using the default reach

For a reach with discharge of 50 m³/s, slope of 0.002, and width of 20 m, total stream power is 1000 × 9.81 × 50 × 0.002 = 981. Dividing by width gives 981 / 20 = 49.05 W/m². At this page’s display precision, the reach has Ω = 981 W/m and ω = 49.1 W/m², which the calculator labels moderate erosion potential.

The example illustrates the formula’s sensitivity. Doubling discharge while holding slope and width fixed doubles total and unit stream power. Halving width at the same discharge and slope does not alter total stream power, but it doubles unit stream power because the energy is concentrated into a narrower channel. These are the scenario comparisons this calculator is designed to support.

Unit stream-power categories for erosion screening

Unit stream power is associated with a river’s capacity to entrain sediment and erode its bed or banks. Lower values can favour weaker transport and deposition, moderate values can indicate active transport, and very high values can accompany steep channels, floods, or constrained sections where scour and bank retreat warrant attention. The bands below are only screening labels, but they help compare sites and show why identical discharge can act differently in wide and narrow reaches.

These bands should not be used in isolation. Bed material, vegetation, bank cohesion, revetments, flood duration, and sediment supply all influence a real channel response. A gravel-bed river with strong banks may respond differently from a sandy channel with weak banks at the same calculated power. The estimate remains useful because it supplies a consistent physical comparison: more water and slope increase the result, while more width reduces the unit value.