Operator calculator
Food-to-Microorganism (F/M) Ratio calculator
Compare the BOD you feed each day to the biomass in the aeration tank.
Calculator
F/M ratio
0.25 lb BOD/day per lb MLVSS
- 1. Food = 4 × 180 × 8.34 = 6,004.8 lb BOD/day
- 2. Microorganisms = 1.2 × 2,400 × 8.34 = 24,019.2 lb MLVSS
- 3. F/M = 6,004.8 ÷ 24,019.2 = 0.25
For instructional use. Results assume the standard conversion factors shown on this page. Actual field calculations may need chemical strength, density, temperature, and other adjustments, so check your plant’s procedures.
Formula and inputs
F/M = [flow (MGD) × BOD (mg/L) × 8.34] ÷ [tank volume (MG) × MLVSS (mg/L) × 8.34]
| Input | Unit |
|---|---|
| Influent flow | MGD |
| Influent BOD | mg/L |
| Aeration tank volume | MG |
| MLVSS | mg/L |
| Result: F/M ratio | lb BOD/day per lb MLVSS |
Conversion factors used: 8.34 lb per gallon of water (cancels in the ratio).
When to use it
The F/M ratio tells you whether the activated sludge has too much or too little food for its microorganisms, which drives settling and treatment quality.
Both the food (BOD) and the microorganisms (MLVSS) are converted to pounds with the pounds formula, then divided.
Applies to: Wastewater Treatment.
Exam tip: Both 8.34 factors cancel, but write them anyway so you do not drop a unit conversion.
Study guides
Build the math skill behind the calculator
Water Operator Math Made Simple walks through the formulas step by step.
Water Operator Math Made Simple
A Step-by-Step Guide to the Math Every Water Operator Needs to Know