Ontario Water Operator Exam: Essential Math Formulas and Practice Problems

Guidance reviewed September 13, 2026.

Prepare for Your Specific Exam

Calculation content varies by certification area and level. Use the current need-to-know document for your exam; this practice guide does not define an exam weighting or an exhaustive formula list.

OWWCO’s exam preparation guidance links formula/conversion tables and identifies the exams using WPI content. OIT exams continue to use Ontario content. Confirm the permitted resources for your specific exam with OWWCO before your sitting.

Practise selecting the right relationship, tracking units and checking whether the result makes sense. Having a reference table does not replace understanding how to use it.

Useful Unit Conversions

Use consistent units throughout a calculation. Check the applicable reference table and show each conversion.

15 Worked Formula Examples

1. Chlorine Dosage

Dose (mg/L) = Demand (mg/L) + Residual (mg/L)

Example: Chlorine demand = 2.1 mg/L, target residual = 0.4 mg/L. Dose = 2.1 + 0.4 = 2.5 mg/L

2. Chemical Mass Required

Mass (kg/day) = Flow (m³/day) × Dose (g/m³) ÷ 1,000

Example: Flow = 8,000 m³/day, dose = 2.5 mg/L. Mass = 8,000 × 2.5 ÷ 1,000 = 20 kg/day

3. Volume of a Cylinder

V = π × r² × h (where r = radius, h = height)

Example: Tank diameter = 10 m, depth = 4 m. r = 5 m. V = 3.14159 × 25 × 4 = 314.2 m³

4. Volume of a Rectangle

V = L × W × H

Example: Reservoir 20 m × 15 m × 5 m deep. V = 20 × 15 × 5 = 1,500 m³

5. Flow Rate (Velocity Method)

Q = A × V (flow = cross-sectional area × velocity)

Example: Pipe diameter = 0.3 m, velocity = 1.5 m/s. A = π × (0.15)² = 0.0707 m². Q = 0.0707 × 1.5 = 0.106 m³/s

6. Hydraulic Retention Time

HRT (hours) = Volume (m³) × 24 / Flow (m³/day)

Example: Tank volume = 500 m³, flow = 2,000 m³/day. HRT = 500 × 24 / 2,000 = 6 hours

7. CT Value

CT = C (mg/L) × T (minutes)

Example: Chlorine residual = 0.8 mg/L, contact time = 25 minutes. CT = 0.8 × 25 = 20 mg·min/L

This CT example is arithmetic only. Required disinfection CT depends on the target organism, log reduction, disinfectant, temperature and pH. Use the approved effective contact time and applicable CT tables; nominal tank detention time is not automatically effective contact time.

8. Percent Solution

% = (mass of solute / mass of solution) × 100

Example: 5 kg of alum dissolved in 95 kg of water. % = (5 / 100) × 100 = 5%

9. Pump Efficiency

Efficiency (%) = (Water Power / Input Power) × 100

Water power (kW) = Flow (m³/s) × Head (m) × 9.81 kN/m³

10. Fluoride Dosage

Solution feed (L/day) = Active ingredient required (kg/day) ÷ Active ingredient concentration (kg/L)

For example, 10 kg/day of required active ingredient from a solution containing 0.20 kg active ingredient per litre requires 10 ÷ 0.20 = 50 L/day. For fluoride, express the dose and solution concentration on the same fluoride basis.

11. Weir Overflow Rate

Weir overflow rate (m³/m·day) = Flow (m³/day) / Weir length (m)

12. Surface Overflow Rate

SOR (m³/m²·day) = Flow (m³/day) / Surface area (m²)

13. Sludge Volume Index (SVI)

SVI = (Settled sludge volume mL/L × 1,000) / MLSS (mg/L)

SVI uses the 30-minute settled volume and is reported in mL/g. Interpret it alongside plant trends, solids concentration and clarifier performance; one range does not establish process health.

14. Food-to-Microorganism Ratio

F:M = BOD applied (kg/day) / MLVSS in aeration basin (kg)

15. Percent Removal

% Removal = ((Influent - Effluent) / Influent) × 100

Example: Influent BOD = 250 mg/L, effluent BOD = 15 mg/L. % Removal = ((250 - 15) / 250) × 100 = 94%

Practice Problem: Full Calculation Scenario

A water treatment plant treats 12,000 m³/day. The raw water has a chlorine demand of 1.6 mg/L and the target residual at the point of entry is 0.6 mg/L. The plant uses a sodium hypochlorite solution containing 12% available chlorine by mass (density 1.17 kg/L). How many litres of hypochlorite solution are required per day?

Step 1: Calculate the chlorine dose. Dose = 1.6 + 0.6 = 2.2 mg/L

Step 2: Calculate the mass of chlorine required. Mass = 12,000 m³/day × 2.2 g/m³ ÷ 1,000 = 26.4 kg/day

Step 3: Calculate the volume of hypochlorite solution. The available chlorine concentration is 12% by mass. Mass of solution = 26.4 kg ÷ 0.12 = 220 kg. Volume = 220 kg ÷ 1.17 kg/L = 188 litres/day