Chemical feed rate math trips up more water operators than any other topic on the certification exam. The core formula is simple: mg/L × flow (MGD) × 8.34 = lbs/day. Three numbers multiplied together. But that simplicity hides a stack of assumptions that fall apart the moment you stop feeding a dry chemical at 100% strength into a flow measured in exact million-gallon increments.
In real treatment, you are feeding a liquid chemical that is 12.5% concentration with a specific gravity of 1.17, into a flow that your meter reads in gallons per minute, and you need to set a pump in milliliters per minute. Every unit conversion is a place where mistakes happen. This guide walks through the feed rate math from first principles, explains where the 8.34 factor comes from, and shows how to adjust for the chemicals you actually use.
The Core Conversion: mg/L to Pounds per Day
The foundation of all chemical dosing math is the pounds formula: lbs/day = dose (mg/L) × flow (MGD) × 8.34. The 8.34 factor is the weight of one gallon of water in pounds. It appears because mg/L is a weight-per-volume concentration, and you need to convert it to a weight-per-weight basis to get pounds of chemical per day.
Here is why 8.34 works. One mg/L is the same as one part per million by weight in water, because one liter of water weighs one kilogram (1,000,000 milligrams). One million gallons of water weighs 8.34 million pounds (1,000,000 gallons × 8.34 lbs/gallon). So 1 mg/L × 1 MGD = 8.34 lbs/day. The factor is a unit bridge between metric concentration and US volumetric flow.
This formula works perfectly when the chemical is 100% pure and the solution has the same density as water. If you are feeding dry calcium hypochlorite at 65% available chlorine, or liquid sodium hypochlorite at 12.5% trade percent, or alum solution with a specific gravity of 1.33, the formula needs adjustments. The 8.34 factor assumes water density, so any chemical heavier than water throws the calculation off.
A practical example: you need to dose 2.0 mg/L of chlorine into a flow of 0.5 MGD. The pounds formula gives you 2.0 × 0.5 × 8.34 = 8.34 lbs/day of pure chlorine. If you are feeding 65% calcium hypochlorite, you need 8.34 / 0.65 = 12.8 lbs/day of the actual chemical product. If you are feeding 12.5% sodium hypochlorite solution, the calculation changes again because you are feeding a liquid, not a powder, and the density is not 8.34 lbs/gallon.
lbs/day = dose (mg/L) × flow (MGD) × 8.34
Where 8.34 = weight of one gallon of water (lbs).
This assumes 100% chemical purity and SG = 1.0.
Adjust for concentration: lbs/day ÷ decimal concentration.
Adjust for SG: multiply 8.34 by specific gravity for liquid chemicals.
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Chemical Concentration: Trade Percent vs Weight Percent
When the label on a jug of sodium hypochlorite says 12.5%, it means 12.5% available chlorine by weight of the solution. This is often called trade percent. It does not mean that 12.5% of the liquid volume is pure chlorine. The distinction matters because dosing calculations require you to know how much active ingredient is in each gallon, not just the percentage on the label.
Sodium hypochlorite at 12.5% trade strength contains about 1.25 lbs of available chlorine per gallon. You get this by multiplying the solution density (about 10.0 lbs/gallon at 12.5% strength) by the decimal concentration (0.125): 10.0 × 0.125 = 1.25 lbs Cl₂/gallon. Compare that to 8.34 lbs/gallon for water. The higher density of the bleach solution means each gallon carries more chemical than you would calculate using straight water math.
Degradation is the other trap. Sodium hypochlorite loses strength over time, faster in heat and sunlight. A jug that tests 12.5% when it arrives at the plant might be 10% by the time you use it three weeks later. Many operators test incoming chemical strength with a titration kit and adjust feed rates accordingly. If you are dosing based on the label and the chemical has degraded to 10%, you are underdosing by 20%.
Calcium hypochlorite is sold as a granular product at 65% or 68% available chlorine. The remaining 32-35% is calcium and other inert compounds. When you dissolve it in a solution tank, the solution strength depends on how much you dissolve per gallon. A common mix is one pound per gallon, which gives you a solution of about 7.8% available chlorine (0.65 lbs Cl₂ / 8.34 lbs water). The solution behaves like a dilute bleach with a specific gravity close to 1.0.
Specific Gravity: When 8.34 Is Not 8.34
Specific gravity is the ratio of a chemical's density to the density of water. Water has an SG of 1.0 and weighs 8.34 lbs/gallon. A chemical with an SG of 1.2 weighs 8.34 × 1.2 = 10.0 lbs/gallon. This matters every time you calculate feed rates for liquid chemicals, because the pounds formula assumes you are pumping something that weighs 8.34 lbs/gallon. If the chemical is heavier, each gallon you pump delivers more pounds than the formula predicts.
Common specific gravity values in water treatment: sodium hypochlorite (12.5%) is about 1.17 to 1.20. Ferric chloride solution (38-42%) runs 1.39 to 1.44. Alum solution (48.5%) is about 1.33. Polymer emulsions range from 1.0 to 1.15. Fluorosilicic acid (23-25%) is about 1.23. Caustic soda (50%) is about 1.53. Each of these chemicals requires a different density adjustment in feed calculations.
To adjust the pounds formula for SG: gallons/day = lbs/day ÷ (8.34 × SG × concentration). For example, you need 50 lbs/day of available chlorine and you are feeding 12.5% sodium hypochlorite with SG of 1.18. Gallons per day = 50 ÷ (8.34 × 1.18 × 0.125) = 50 ÷ 1.23 = 40.7 gallons/day. If you ignored SG and used plain 8.34, you would calculate 50 ÷ (8.34 × 0.125) = 47.9 gallons/day. That is 18% too high. You would be overfeeding.
The practical takeaway: always look up the SG of every liquid chemical you feed. Chemical suppliers include it on the safety data sheet (SDS) in Section 9. If you cannot find it, measure it with a hydrometer. A $15 hydrometer can prevent thousands of dollars in chemical overfeed or underfeed over a year.
Sodium hypochlorite (12.5%): 1.17–1.20
Ferric chloride (38-42%): 1.39–1.44
Alum solution (48.5%): 1.33
Caustic soda (50%): 1.53
Fluorosilicic acid (23-25%): 1.23
Polymer emulsions: 1.00–1.15
Feed Pump Calibration: Trust but Verify
A chemical feed pump rated for 10 gallons per hour at maximum stroke and speed will almost never deliver exactly 10 gallons per hour in the field. Diaphragm pumps lose output as back pressure increases, tubing wears, check valves foul, and diaphragms fatigue. A pump that was accurate six months ago might be delivering 15-20% less chemical today without any obvious sign of failure.
The bucket-and-stopwatch test is the simplest calibration method. Disconnect the discharge line from the injection point, route it into a graduated container, and run the pump at its normal setting for a measured time period. If the pump is set for 500 mL/min and you collect 425 mL in one minute, the pump is delivering 85% of its setpoint. Adjust the stroke or speed to compensate, or note the correction factor and apply it to your dosing calculations.
Common causes of pump output loss include worn tubing (peristaltic pumps lose accuracy as tubing stretches), fouled or worn check valves (diaphragm pumps rely on check valves to prevent backflow; if they leak, output drops), crystallized chemical in the pump head, and excessive back pressure from clogged injection quills. Preventive maintenance schedules should include tubing replacement every 6-12 months, check valve inspection quarterly, and a calibration verification at least monthly.
For critical applications like chlorine disinfection, calibrate weekly. The difference between 2.0 mg/L and 1.6 mg/L of chlorine residual can be the difference between compliant disinfection and a boil-water advisory. Write the calibration result in your plant log so you can track drift over time. A pump that consistently reads low is telling you something is wearing out.
Common Feed Rate Mistakes
The most frequent mistake is calculating for 100% chemical when you are feeding a solution. If you need 8.34 lbs/day of chlorine and you are feeding 12.5% sodium hypochlorite, you need to divide by 0.125 to get the product feed rate. Operators who skip this step underdose by a factor of eight. The residual is near zero, the compliance sample fails, and nobody can figure out why.
The second most common mistake is ignoring specific gravity. Liquid alum at 48.5% and SG 1.33 weighs 11.1 lbs/gallon, not 8.34. If you calculate gallons per day using 8.34 in the denominator, you will overfeed by about 33%. Over a year, that is a significant chemical cost and can cause downstream problems like low pH or high aluminum residual.
Unit confusion is the third trap. The pounds formula uses flow in million gallons per day (MGD). If your flow meter reads in gallons per minute (GPM), you must convert: MGD = GPM × 1440 ÷ 1,000,000. If your meter reads in cubic feet per second (CFS), convert with: MGD = CFS × 0.6463. Getting the flow units wrong is an order-of-magnitude error that produces absurd feed rates.
Finally, many operators set a feed rate once and forget to recalculate when conditions change. Flow varies seasonally. Source water quality changes. Chemical concentration degrades. Temperature affects reaction kinetics. A feed rate that was correct in July may be wrong in January. Build a habit of recalculating whenever flow, dose target, or chemical strength changes. Use a logbook or spreadsheet to track all three variables so you can spot when a recalculation is needed.
1. Calculating for 100% chemical when feeding a dilute solution.
2. Ignoring specific gravity on liquid chemicals.
3. Using the wrong flow units (GPM vs MGD vs CFS).
Each of these produces an error of 30% or more in the feed rate.