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

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, specifically algebra

Algebra

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...

, 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

Water treatment

Water treatment describes those processes used to make water more acceptable for a desired end-use. These can include use as drinking water, industrial processes, medical and many other uses. The goal of all water treatment process is to remove existing contaminants in the water, or reduce the...

 or reservoir

Reservoir

A reservoir , artificial lake or dam is used to store water.Reservoirs may be created in river valleys by the construction of a dam or may be built by excavation in the ground or by conventional construction techniques such as brickwork or cast concrete.The term reservoir may also be used to...

s, 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).