The Activated Sludge Calculator computes F/M ratio, Solids Retention Time (SRT), Hydraulic Retention Time (HRT), and Organic Loading Rate for biological wastewater treatment. Used by environmental engineers and plant operators for activated sludge system design and process optimization.
0.278
kg BOD/(kg MLSS·day)
18
days
7.2
hours
0.833
kg BOD/(m³·day)
2
0.278
kg BOD/(kg MLSS·day)
18
days
7.2
hours
0.833
kg BOD/(m³·day)
2
The calculator for activated sludge process parameters computes the four key design and operational variables that define the performance of a biological wastewater treatment system: the Food-to-Microorganism (F/M) ratio, Solids Retention Time (SRT), Hydraulic Retention Time (HRT), and Organic Loading Rate (OLR). These parameters govern microbial community composition, effluent quality, and sludge production in the most widely deployed biological treatment technology worldwide.
The F/M ratio expresses the daily mass of substrate (BOD or COD) applied per unit mass of active biomass (MLVSS) in the aeration basin:
F/M = (Q × S₀) / (V × MLVSS) (kg BOD/kg MLVSS·day)
where Q is influent flow rate (m³/day), S₀ is influent BOD (mg/L), V is aeration basin volume (m³), and MLVSS is mixed liquor volatile suspended solids (mg/L). Low F/M (0.05–0.15 kg/kg·day) produces high-quality, well-settling sludge; high F/M (0.3–0.6 kg/kg·day) results in dispersed growth, poor settling, and lower treatment efficiency but higher process stability. The detention time calculator provides the HRT calculation as a standalone tool.
SRT (also called Mean Cell Residence Time or sludge age) is the average time microorganisms remain in the system:
SRT = (V × MLSS) / (Q_w × X_w + Q_e × X_e) (days)
where Q_w is waste sludge flow rate and X_w is its suspended solids concentration. SRT determines which microbial populations can survive in the system. Nitrifying bacteria require SRT of at least 10–15 days at 20°C; general BOD removal requires only 3–5 days. Long SRT produces more stable, mineralized sludge with lower volume but requires larger aeration basins. SRT is the primary control variable operators adjust by changing the waste sludge rate. Use this online calculator to find the correct waste rate for a target SRT.
HRT is the average time wastewater spends in the aeration basin:
HRT = V / Q (hours or days)
Typical HRT ranges from 4–8 hours for conventional activated sludge to 18–24 hours for extended aeration systems. OLR expresses the substrate loading per unit basin volume:
OLR = (Q × S₀) / V (kg BOD/m³·day)
Design OLR typically ranges 0.3–1.0 kg BOD/m³·day for conventional systems. Excessive OLR causes oxygen depletion and process upset. The relationship F/M = OLR / MLVSS links all three parameters. The E-factor calculator and specialized chemistry calculators category provide complementary environmental and process chemistry tools.
Process performance is monitored through the Sludge Volume Index (SVI) — the volume (mL) occupied by 1 gram of sludge after 30 minutes of settling:
Sludge bulking is commonly caused by filamentous bacteria that proliferate at high F/M ratios or under nutrient-deficient conditions. Selector reactors — small high-F/M zones at the inlet — suppress filamentous growth by favoring floc-forming organisms. The green chemistry metrics calculator and process mass intensity calculator provide related environmental performance metrics for industrial processes.
The key activated sludge parameters are calculated as:
$$\text{F/M} = \frac{Q \times S_0}{V \times X}$$
Where F/M is the food-to-microorganism ratio (kg BOD per kg MLSS per day), $$Q$$ is the influent flow rate, $$S_0$$ is the influent BOD concentration, $$V$$ is the aeration tank volume, and $$X$$ is the mixed liquor suspended solids (MLSS) concentration.
$$\text{SRT} = \frac{V \times X}{Q_w \times X_w}$$
Where SRT (sludge age) is the average time biomass remains in the system, $$Q_w$$ is the waste sludge flow rate, and $$X_w$$ is the waste sludge concentration.
$$\text{HRT} = \frac{V}{Q}$$
$$\text{OLR} = \frac{Q \times S_0}{V \times 1000}$$
The F/M ratio classifies the process type: extended aeration (<0.1), conventional (0.1–0.3), moderate rate (0.3–0.6), or high rate (>0.6). Lower F/M means more complete treatment and better sludge settling but requires larger reactor volumes.
An F/M of 0.1–0.3 with SRT of 5–15 days characterizes conventional activated sludge with 85–95% BOD removal. Extended aeration (F/M < 0.1, SRT > 20 days) achieves near-complete oxidation with minimal excess sludge. High-rate systems (F/M > 0.6, SRT < 3 days) achieve 60–80% removal in smaller reactors but produce more sludge requiring further stabilization. The OLR should typically be below 1.0 kg BOD/(m³·day) for conventional systems.
Inputs
Results
F/M = (10000×250)/(3000×3000) = 0.278, SRT = (3000×3000)/(50×10000) = 18 days, HRT = 7.2 hours
Inputs
Results
F/M = 0.05, very low loading. SRT = 100 days (very high), HRT = 24 hours. Nearly complete oxidation.
The food-to-microorganism ratio (F/M) expresses the mass of organic matter (BOD) applied per unit mass of microorganisms (MLSS) per day. It determines the metabolic state of the biomass: low F/M means organisms are starved (endogenous respiration dominates), while high F/M means organisms are well-fed (active growth phase). F/M = Q×S₀/(V×X).
Mixed Liquor Suspended Solids (MLSS) is the concentration of suspended solids in the aeration tank, consisting of active biomass, inert organic matter, and inorganic matter. Typical MLSS for conventional activated sludge is 2,000–4,000 mg/L. MLVSS (volatile fraction) represents the organic/biological portion, typically 70–85% of MLSS.
SRT is controlled by adjusting the waste sludge flow rate (Qw). Increasing Qw removes biomass faster, decreasing SRT. Decreasing Qw allows biomass to accumulate, increasing SRT. Operators adjust Qw daily based on SRT targets, MLSS measurements, settling characteristics, and effluent quality. Automated SRT control systems are increasingly common.
Nitrification requires SRT ≥ 1/μmax of nitrifying bacteria, which depends on temperature. Minimum SRT: 4-5 days at 20°C, 8-12 days at 15°C, 15-20 days at 10°C. Design SRT is typically 2-3 times the minimum to provide a safety factor. Ensure sufficient alkalinity (7.14 mg CaCO₃ per mg NH₃-N oxidized) and dissolved oxygen (>2 mg/L).
BOD (Biochemical Oxygen Demand) measures biologically degradable organic matter over 5 days. COD (Chemical Oxygen Demand) measures all oxidizable organic matter chemically. BOD/COD ratio indicates biodegradability: >0.5 is readily biodegradable, <0.3 may need specialized treatment. F/M typically uses BOD, but some designs use COD, especially for industrial wastewaters.
Sludge settleability is characterized by the Sludge Volume Index (SVI). At optimal F/M (0.1-0.3), floc-forming bacteria dominate and SVI is 80-150 mL/g (good settling). At very low F/M (<0.05), pin floc may form (poor settling). At high F/M (>0.5), dispersed growth or bulking filaments may dominate (poor settling, SVI > 200). Filamentous bulking is the most common settling problem.
Oxygen demand depends on BOD removed and nitrification: O₂ = a'(S₀-Se)Q + b'XV + 4.57×(NH₃-N oxidized)×Q, where a' ≈ 0.5 kg O₂/kg BOD and b' ≈ 0.06 kg O₂/(kg VSS·day). Total oxygen demand typically ranges from 1.0-2.0 kg O₂ per kg BOD removed for carbonaceous treatment, plus 4.57 kg O₂ per kg ammonia nitrogen nitrified.
Filamentous bulking (SVI > 200) is caused by: low dissolved oxygen (<1 mg/L), low F/M (encourages filamentous organisms), nutrient deficiency (N or P limitation), low pH (<6.5), septic wastewater (high sulfide), and slowly biodegradable substrates. Solutions include increasing DO, adjusting F/M, adding selectors, nutrient supplementation, or chlorinating return sludge.
A selector is a small initial contact zone (HRT 10-30 minutes) where return sludge contacts influent wastewater at high F/M. This favors floc-forming bacteria over filamentous organisms because floc formers have higher maximum growth rates at high substrate concentrations. Selectors can be aerobic, anoxic, or anaerobic and effectively prevent most types of filamentous bulking.
For design: choose target F/M and SRT based on treatment objectives, then calculate required V from known Q and S₀. For operation: measure Q, V, X, and S₀ to compute current F/M and SRT, then adjust Qw to maintain target values. The calculator serves both purposes: designers input desired parameters and solve for unknowns, while operators verify current conditions.
Municipal wastewater effluent targets: BOD < 20-30 mg/L, TSS < 20-30 mg/L, NH₃-N < 1-5 mg/L (if nitrification required), total nitrogen < 10-15 mg/L (if nutrient removal required), total phosphorus < 0.5-2 mg/L. Conventional activated sludge achieves 85-95% BOD removal; advanced systems with nutrient removal achieve >95% BOD and >80% nitrogen/phosphorus removal.
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