# Conversion factor

A conversion factor changes something to a different version or form. A factor is something that brings results or a cause, while conversion is an action of changing the "version" of a thing.

In mathematics, specifically algebra, a conversion factor is used to convert a measured quantity to a different unit of measure without changing the relative amount. To accomplish this, a ratio (fraction) is established that equals one (1). In the ratio, the conversion factor is a multiplier that, when applied to the larger unit, converts the larger unit into the smaller unit, by multiplication with the measured amount.

24 hrs/1 day = 1 or 43,560 square feet/1 acre = 1
3 days = 3 × 24 hours = 72 hours  (conversion factor is 24)
Note: If a=b, then a/b=1 and b/a=1

Days are converted, to hours, by multiplying the days by the conversion factor as 24. The conversion can be reversed by dividing, the hours, by 24 to get days; however, the reciprocal 1/24 could be considered the reverse conversion factor for an hours-to-days conversion, where 1/24 ~= 0.0416666666667. Hence, the term "conversion factor" is the multiplier which yields the result, not a divisor from that viewpoint. To yield hours, the conversion factor is 24, not 1/24, so: hours = days × 24 (multiplying by the factor).

## Common conversion factors for water and wastewater

For water treatment or reservoirs, there are several conversion factors which are commonly used:

• Since 1 day = 24 hours = 1440 minutes, therefore 15 minutes (1 day/1440 minutes) = 15/1440 ~= 0.010416667 ~= 0.01 days.
• 1 million gallons per day (MGD) = 3.069 acre feet per day (ac-ft/day) = 1.55 cubic feet per second (cfs) = 694 gallons per minute (gpm)
• 1 gallon = 3785 milliliters = 3.785 liters = 8.34 pounds of water.

Examples of conversions:

1. 55 gallons of water (8.34 pound/1 gallon)   = 458.7 pounds.
2. a hose running 20 gpm for 1 day (1440 minutes/1 day) = 28,800 gallons/day.
3. a one-ton truck can carry 2000 pounds (1 gallon/8.34 pounds) = 240 gallons (water).