The height of the jump is derived from the application of the equations of conservation of mass and momentum. There are several methods of predicting the height of a hydraulic jump.
They all reach common conclusions that:
* The ratio of the water depth before and after the jump depend solely on the ratio of velocity of the water entering the jump to the speed of the wave over-running the moving water.
* The height of the jump can be many times the initial depth of the water.
For a known flow rate  as shown by the figure below, the approximation that the momentum flux is the same just up- and downstream of the energy principle yields an expression of the energy loss in the hydraulic jump. Hydraulic jumps are commonly used as energy dissipators downstream of dam spillways.
; Applying the continuity principle
In fluid dynamics, the equation of continuity is effectively an equation of conservation of mass. Considering any fixed closed surface within an incompressible moving fluid, the fluid flows into a given volume at some points and flows out at other points along the surface with no net change in mass within the space since the density is constant. In case of a rectangular channel, then the equality of mass flux upstream () and downstream () gives:
:  or  
with  the fluid density,  and  the depth-averaged flow velocities upstream and downstream, and  and  the corresponding water depths.
; Conservation of momentum flux
For a straight prismatic rectangular channel, the conservation of momentum flux across the jump, assuming constant density, can be expressed as:
In rectangular channel, such conservation equation can be further simplified to dimensionless M-y equation form, which is widely used in hydraulic jump analysis in open channel flow.
Jump height in terms of flow
Dividing by constant  and introducing the result from continuity gives
which, after some algebra, simplifies to:
where  Here  is the dimensionless Froude number, and relates inertial to gravitational forces in the upstream flow. Solving this quadratic yields:
Negative answers do not yield meaningful physical solutions, so this reduces to:
:  so
known as Bélanger equation. The result may be extended to an irregular cross-section.
This produces three solution classes:
* When , then  (i.e., there is no jump)
* When , then  (i.e., there is a negative jump – this can be shown as not conserving energy and is only physically possible if some force were to accelerate the fluid at that point)
* When , then  (i.e., there is a positive jump)
This is equivalent to the condition that . Since the  is the speed of a shallow gravity wave, the condition that  is equivalent to stating that the initial velocity represents supercritical flow (Froude number > 1) while the final velocity represents subcritical flow (Froude number < 1).
;Undulations downstream of the jump 
Practically this means that water accelerated by large drops can create stronger standing waves (undular bores) in the form of hydraulic jumps as it decelerates at the base of the drop. Such standing waves, when found downstream of a weir or natural rock ledge, can form an extremely dangerous "keeper" with a water wall that "keeps" floating objects (e.g., logs, kayaks, or kayakers) recirculating in the standing wave for extended periods.