Dissolved Oxygen Sag Calculator

Work out dissolved oxygen sag instantly with clear inputs, formula shown and shareable results.

About Dissolved Oxygen Sag Calculator

The Streeter-Phelps model balances deoxygenation from BOD decay against reaeration from the atmosphere, producing a dissolved oxygen sag curve. The critical point, where oxygen is lowest, occurs where the two rates are equal. The self-purification ratio kr/kd indicates how quickly a river recovers; below 1 the sag is deep and prolonged.

Formulas

Streeter-Phelps deficit

D(t) = kd L0 / (kr - kd) x (e^(-kd t) - e^(-kr t)) + D0 e^(-kr t)

Critical time

t_c = 1/(kr - kd) x ln(kr/kd x (1 - D0 (kr - kd) / (kd L0)))

Worked example

With the default values below, Dissolved Oxygen Sag Calculator returns Minimum Dissolved Oxygen of 4.4058. Change any input above and every figure here is recalculated in your browser.

Inputs used

Initial Oxygen Deficitminimum 0 mg/L: 2 mg/L
Ultimate BOD After Mixingminimum 0 mg/L: 15 mg/L
Deoxygenation Rate Constantminimum 0 per day: 0.23 per day
Reaeration Rate Constantminimum 0 per day: 0.4 per day

Results

Minimum Dissolved Oxygen: 4.4058
Critical Oxygen Deficit: 4.6942
Time To Critical Point: 2.6449
Self-Purification Ratio: 1.7391

Step by step

1Values used
2Streeter-Phelps deficit
3Critical time
4Minimum Dissolved Oxygen= 4.4058
5Critical Oxygen Deficit= 4.6942
6Time To Critical Point= 2.6449
7Self-Purification Ratio= 1.7391

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
Dissolved oxygen is a statutory water quality standard protecting aquatic life. Modelling for consent purposes must use calibrated rate constants and approved methods.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Dissolved oxygen is a statutory water quality standard protecting aquatic life. Modelling for consent purposes must use calibrated rate constants and approved methods.

Frequently Asked Questions

What dissolved oxygen do fish need?

Salmonids need above 6-7 mg/L, coarse fish above 4-5 mg/L, and below about 3 mg/L most fish suffer or die. Consent conditions are set to protect the designated use of the water body.

What controls the reaeration rate?

Turbulence, depth and temperature. A shallow, fast, rocky reach reaerates many times faster than a deep, slow, impounded one, which is why impoundments worsen oxygen sag.