# Formulas & Terms to Know

FORMULAS, UNITS, ABBREVIATIONS

Units and Unit Conversions:
 MASS: 1 kg = 1,000 g g = gram 1 kg = 2.20 lb kg = kilogram 1 lb = 454 g lb = pound 1 US (short) t = 2,000 lb t = ton (mt = metric ton) 1 metric (long) t = 1,000 kg = 1 Mg Mg = mega gram LENGTH: 1′ = 12″ inch = in = “ 1 mile = 5,280′ foot = ft = ‘ 1 km = 1000 m yard = yd = 3 ft 1 m = 100 cm = 1, 000 mm meter = m 1 m = 3.28′ = 39.4″ = 1.09 yd centimeter = cm 1 in = 2.54 cm = 25.4 mm mm = millimeter AREA: 1 ac = 43,560 ft2 ac = acre 1 mi2 = 640 ac mi2 = square mile 1 ha = (100 m)2 = 10,000 m2 = 2.47 ac ha = hectare VOLUME: 1 L = 1,000 cm3 = 106 mm3 AF = Acre-Foot 1 AF = 43,560 ft3 gal = U.S. fluid gallon 1 ft3 = 7.48 gal L = liter 1 m3 = 106 cm3 = 1,000 L cm3 = cubic centimeter 1 gal = 3.78 L DENSITY (water, 20°C): 1 cm3 = 1 g 1 L = 1,000 g = 1 kg METRIC PREFIXES: T = tera = 1012 d = deci = 10-1 G = giga = 109 c = centi = 10-2 M = mega = 106 m = milli = 10-3 k = kilo = 103 µ = micro = 10-6 h = hecto = 102 n = nano = 10-9 da = deka = 101 p = pico = 10-12
Unit Symbols and Abbreviations in Soils and Hydrology:
 V = volume PD = particle density A = area BD = bulk density d = depth PS = pore space (usually in %) Q = discharge CEC = cation exchange capacity v = velocity BS = base saturation (usually in %) τ = (tau) travel time L = length Θv = (theta) water content by volume q = groundwater flow rate Θw = (theta) water content by weight K = hydraulic conductivity ψ = (psi) water potential i = hydraulic gradient
Some Useful Common Atomic Weights (ionic valence shown if commonly ionic):
 H+ = 1 Na+ = 23 C = 12 Mg+2 = 24 N = 14 Al+3 = 27 O-2 = 16 Cl– = 37 S = 32 K+ = 39 Ca+2 = 40
Formulas You Should Know:
Area of a circle  =  π r2 (r = radius, π = 3.14)
Volume of a cylinder  =
π r2 h (h = height of cylinder)
Density  =  m/v (m = mass, v = volume)

Performing Basic Unit Conversions by Factor-Labeling:
NOTE:  In fractions or ratios, numerator (N)
denominator (D)

The speed of light (c) is 3.0 x 108 m per sec.  How many mi/hr is this?

3.0 x 108 m     x     3.28 ft     x    1 mi     x     60 sec     x     60 min     =     6.7 x 108 mi
——————-         ————       ————–     ————-         ————          ——————-     =     670 million mi/hr
sec                    1 m           5,280 ft          1 min               1 hr                      hr

How to do it:
1)  Write the initial value to be converted clearly as a fraction (ratio) showing initial units.
2)  Begin by looking at the initial unit in the numerator (N) {m} and the desired final unit {mi}.
3)  Multiply your initial fraction by a conversion factor equality
(i.e., 3.28 ft = 1 m), arranged so the appropriate unit cancels out (m in the N cancels with m in the D).
4)  Continue to add conversion factors, canceling units until you arrive at the desired unit.
5)  Repeat this process, now looking at the desired units in the D.
6)  If you set this up correctly, all units should cancel except the desired ones (in this case mi in the N and hr in the D).
7)  Multiply and divide the actual numeric values in the N and the D to obtain the numeric answer.

Concentration Calculations:
Concentrations are ratios of amounts (number, mass or volume), with the “amount of interest” in the N and the “entire amount” in the D.  This ratio can be expressed in a couple of different ways.
Assume we have 234 marbles, all the same size; 79 are blue, 3 are red and the rest are various colors.

Simple ratio:
The concentration of blue marbles is 79/234 which equals 0.338.  The concentration of red marbles is 3/234 which equals 0.013.  This means there is 0.338 blue marble for every one marble, and 0.013 red marble for every one marble.

Percent:
This unit assumes we have 100 in the D.  It shows the “amount of interest” per 100 of the “entire amount.”  To get it we multiply the simple ratio by 100:
% Blue marbles = 0.338 x 100 = 33.8% (there are 33.8 blue marbles per 100 marbles)
% Red marbles = 0.013 x 100 = 1.3% (there are 1.3 red marbles per 100 marbles)

Parts per Million (ppm):
This is the same as percent but it is per ‘million’ rather than per ‘cent.’  To get it we multiply the simple ratio by 1,000,000.
ppm blue marbles = 0.338 x 106 = 338,000 (there are 338,000 blue marbles per 1,000,000 marbles)
ppm red marbles = 0.013 x 106 = 13,000 (there are 13,000 red marbles per 1,000,000 marbles)

Parts per Million (ppm) is used a lot in soil and water chemistry to express concentrations where amounts of interest are low, especially using metric mass units.  Note that in % and ppm the units should be the same in the N and the D since it is a ratio.  Common metric ppm units include:
1 mg/L = 1 mg/kg = 10-3 g/103 g = 1 g/106 g = 1 ppm (since 1 L weighs 1 kg)
1 µg/mL = 1 µg/g = 10-6 g/g = 1 g/106 g = 1 ppm (since 1 mL weighs 1 g)
* Note that
1 µg/kg = 10-6 g/103 g = 1 g/109 g = 1 ppb (part per billion, which equals 1,000 ppm)

TERMS, GLOSSARIES

Hydrologic Glossary (PDF)