The Streeter–Phelps equation determines the relation between the dissolved oxygen concentration and the biological oxygen demand over time and is a solution to the linear first order differential equation
This differential equation states that the total change in oxygen deficit (D) is equal to the difference between the two rates of deoxygenation and reaeration at any time.
The Streeter–Phelps equation, assuming a plug-flow stream at steady state is then
where
* is the saturation deficit, which can be derived from the dissolved oxygen concentration at saturation minus the actual dissolved oxygen concentration ().  has the dimensions .
* is the deoxygenation rate, usually in .
* is the reaeration rate, usually in .
* is the initial oxygen demand of organic matter in the water, also called the ultimate BOD (BOD at time t=infinity). The unit of  is . 
* is the oxygen demand remaining at time t, . 
* is the initial oxygen deficit .
* is the elapsed time, usually .
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 lies typically within the range 0.05-0.5  and  lies typically within the range 0.4-1.5 .
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The Streeter–Phelps equation is also known as the DO sag equation. This is due to the shape of the graph of the DO over time.