Water and wastewater math formula sheet
Print this page (Ctrl+P or Share → Print) to keep a one-page copy. Each formula links to a calculator with a worked example.
| 01 | Pounds Formula | lbs/day = Flow (MGD) × Concentration (mg/L) × 8.34 lbs/gal |
|---|---|---|
| 02 | Detention Time | Detention time (hr) = Tank volume (gal) ÷ Flow (gal/hr) Rectangular volume = L × W × D × 7.48 gal/ft³ |
| 03 | F/M Ratio | F/M = (Flow MGD × BOD mg/L × 8.34) ÷ (Aeration volume MG × MLVSS mg/L × 8.34) |
| 04 | MCRT / Sludge Age | MCRT (days) = lbs solids in aeration + clarifier ÷ (lbs/day WAS + lbs/day effluent TSS) |
| 05 | SVI | SVI (mL/g) = 30-min settled volume (mL/L) × 1,000 ÷ MLSS (mg/L) |
| 06 | Chlorine Dose and Feed | Dose (mg/L) = Demand + Residual Feed (lbs/day) = Flow MGD × Dose × 8.34 ÷ (% available ÷ 100) |
| 07 | Surface Overflow Rate | SOR (gpd/ft²) = Flow (gpd) ÷ Surface area (ft²) Area = 0.785 × D² |
| 08 | Weir Overflow Rate | WOR (gpd/ft) = Flow (gpd) ÷ Weir length (ft) Weir length = 3.1416 × D |
| 09 | Percent Removal | % Removal = (In − Out) ÷ In × 100 |
| 10 | Pipe Volume | Volume (gal) = 0.785 × (D in ÷ 12)² × Length (ft) × 7.48 |
| 11 | Flow Rate (Q = A × V) | Q (ft³/s) = A (ft²) × V (ft/s) Q (gpm) = Q (ft³/s) × 448.8 |
| 12 | CT Value | CT (mg·min/L) = Residual (mg/L) × Contact time (min) |
Conversions
| Water weight | 1 gal = 8.34 lbs | |
|---|---|---|
| Volume | 1 ft³ = 7.48 gal · 1 MG = 1,000,000 gal | |
| Flow | 1 MGD = 694.4 gpm · 1 ft³/s = 448.8 gpm = 0.646 MGD | |
| Time | 1 day = 24 hr = 1,440 min | |
| Pressure | 1 psi = 2.31 ft of water · 1 ft of water = 0.433 psi | |
| Circles | Area = 0.785 × D² · Circumference = 3.1416 × D | |
| Concentration | 1 mg/L = 1 ppm · 1% = 10,000 mg/L |