# Water Quality Mathematical Expressions & Relationships Reference Sheet

Water Quality Mathematical Expressions &
Relationships
A Collection of Water Quality Mathematical Expressions and
Relationships
Gram (g), kilogram (Kg), milligram (mg), microgram (ug) - These are units of mass
(weight) in the metric system. The basic unit is the gram (0.002205 lb.). 1000 grams
equals 1 kilogram (2.205 lb). A milligram is 1/1000th of a gram (i.e. 1000 mg equal 1 g).
A microgram is 1/1000th of a milligram and 1/1,000,000th of a gram (i.e.1000 ug equals
1 mg and 1,000,000 ug equals 1g).
Meter (M), centimeter (cm) - these are selected metric units of length. We can consider
the basic unit of length to be the meter (1.094 yards; 39.37 inches). 1 centimeter (0.3937
inches) is 1/100th of a meter (i.e. 100 centimeters equal 1 meter).
Liter (L), milliliter (ml), microliter (ul) - these are metric units of volume and they
work like the units of mass and length described above. If we say that the basic unit of
volume is the liter (1.057 quarts), then a milliliter equals 1/1000th of a liter and a
microliter equals 1/1,000,000th of a liter. So, there are 1000mL in 1 liter, 1000uL in 1
milliliter and 1,000,000mL in 1 liter. There are a couple of secrets. One is that 1 milliliter
equals 1 cubic centimeter (cc; imagine a cube 1 centimeter to a side). Another, it is
assumed that 1 milliliter of water equals 1 cubic centimeter of water, which weighs
1gram! (Red Herring: "A pint's a pound the world around.") In any case, the assumed
mass of 1 liter of water equals 1 kilogram, 1000 grams, 1,000,000 milligrams or
1,000,000,000 micrograms.
Parts per million (ppm) - this is a generic unit of measure in the sense that it can
represent a lot different units of measure (e.g. mg/L, ug/ml, mg/Kg, lb/acre), therefore a
ppm equals one part of something per million parts of something else. So if you have
water quality data in mg/L, that data is equivalent to ppm (i.e. 50mg Calcium/L = 50 mg
Calcium per 1,000,000 mg/L of water = 50 ppm Calcium). By the way, if you have soil
test data in parts per million you can convert that to lb/Acre by multiplying by 2. It is
assumed that an acre furrow slice (8" thick) of soil weighs 2,000,000 pounds.
Parts per billion (ppb) - similar in concept to ppm except they are smaller and
consequently there can be more of them, 1 ppm = 1000 ppb If you have 0.010 mg lead/L
this equals 0.010 ppm lead or 10 ppb lead (0.010 ppm x 1000ppb/ppm).
Milliequivalents per liter (meq/L) - meq/L is another method of expressing
concentration, when the analytes are dissolved and disassociated in solution. meq/L is
also equal to millimoles of charge per liter (mM+/L or mM-/L depending on valence). A
mole contains 6.022 x 1023 molecules; for example a mole of calcium contains 6.022 x