## Useful Unit Conversions

Conversion factors are from the Bureau of Reclamation's Metric Manual, 1978, by L.D. Pedde, W.E. Foote, L.F. Scott, D.L. King, and D.L. McGalliard, U.S. Government Printing Office, Washington DC.

English weights and volumes are avoirdupois units, and English volumes are based on fluid ounces.

Click on the topic to go directly to specific conversions or calculations:

 pico = p = 10-12 nano = n = 10-9 micro = µ = 10-6 = 0.000001 milli = m = 10-3 = 0.001 centi = c = 10-2 = 0.010 hecto = h = 10+2 = 100 kilo = k = 10+3 = 1,000 mega = M = 10+6 = 1,000,000 giga = G = 10+9 tera = T = 10+12

 1.0 inch = 0.0254 m = 2.54 cm = 25.4 mm 1.0 foot (ft) = 0.30480 m = 30.480 cm = 304.8 mm 1.0 yard (yd) = 0.91440 m = 91.440 cm = 914.4 mm 1.0 mile (mi) = 1,760 yd = 5,280 ft = 63,360 in = 1.6093 km = 1,609.3 m = 160,934 cm 1.0 cm = 0.010 m = 10 mm = 0.03281 ft = 0.3937 in 1.0 meter (m) = 100 cm = 1,000 mm = 1.0936 yd = 3.2808 ft = 39.370 in 1.0 km = 1,000 m = 100,000 cm = 0.62137 mi = 1,093.61 yd = 3,280.83 ft = 39,370 in
 1.0 gram (g) = 1,000 mg = 1,000,000 µg = 1.000 cm3 deionized H2O at STP 1.0 kg = 1,000 g = 2.204622 lb = 35.27396 oz 1.0 ounce (oz) = 0.06250 lb = 28.34953 g = 0.0283495 kg 1.0 pound (lb) = 16 oz = 0.45359 kg = 453.59 g

 1.0 hour = 3,600 s 1.0 day = 1,440 min = 86,400 s 1.0 week = 168 hr = 10,080 min = 604,800 s

 Celsius to Fahrenheit: °F = (°C x 1.80) + 32 Fahrenheit to Celsius: °C = (°F - 32) x 0.5556 Kelvin to Celsius: °C = °K - 273.15 Celsius to Kelvin:  °K = °C + 273.15 STP - standard temperature and pressure = 273 °K at 1 atm

 1.0 in2 = 0.00064516 m2 = 6.4516 cm2 = 645.16 mm2 1.0 ft2 = 0.1111 yd2 = 144 in2 = 0.092903 m2 = 929.03 cm2 = 92,903 mm2 1.0 yd2 = 9 ft2 = 1,296 in2 = 0.836127 m2 = 8,361.27 cm2 = 836,127 mm2 1.0 acre = 0.0015625 mi2 = 4,840 yd2 = 43,560 ft2 = 4,046.87 m2= 0.404687 ha 1.0 mi2 = 640 acres = 27.878 x 106 ft2 = 2,589,988 m2 = 258.99 ha 1.0 cm2 = 100 mm2 = 0.1550 in2 1.0 m2 = 10,000 cm2 = 1.1959 yd2 = 10.7369 ft2 = 1,550.0 in2 1.0 hectare (ha) = 100 m x 100 m = 10,000 m2 = 0.00385901 mi2 = 2.47104 acres = 11,959.9 yd2 1.0 km2 = 100 ha = 1,000,000 m2 = 0.3860 mi2 = 247.104 acres

 1.0 fluid oz = 1.8047 in3 = 0.029574 L = 29.574 mL 1.0 in3 = 0.5541 oz = 0.016387 L = 16.387 mL 1.0 pint = 16.0 fluid oz = 0.47318 L = 473.18 mL 1.0 quart = 2.0 pt = 32.0 fluid oz = 0.94635 L = 946.35 mL 1.0 gallon = 4.0 qt = 8.0 pt = 128 fluid oz = 3.7854 L 1.0 ft3 = 7.4805 gal = 0.028317 m3 = 28.317 L 1.0 acre-ft = 1233.489 m3 = 1.233 X 106 L = 325,851 gal 1.0 cm3 = 1.0 mL deionized H2O at STP = 0.001 L 1.0 liter (L) = 0.001 m3 = 1,000 mL = 0.264172 gal = 1.0567 qt = 2.1134 pt 1.0 m3 = 1,000 L = 8.1071 x 10-4 acre-ft = 35.315 ft3 = 264.17 gal
 1.0 gal/min (gpm) = 0.0044191 acre-ft/d = 0.0022280 cfs = 192.5 ft3/d = 3.7854 L/min = 0.063090 L/s = 227.124 L/hr = 5,451 L/d 1.0 ft3/s (cfs) = 1.98347 acre-ft/d = 448.831 gal/min = 646,317 gal/d = 0.0283169 m3/s = 28.3169 L/s = 2.4466 x 106 L/d = 2,446.6 m3/d = 1,699.01 L/min = 101,941 L/hr 1.0 acre-ft/d = 0.504167 cfs = 325,851 gal/d = 14.2764 L/s = 856.584 L/min = 51,395 L/hr = 1.23348 x 106 L/d = 1,233.482 m3/d 1.0 m3/s = 1,000 L/s = 35.315 ft3/s = 264.17 gal/s 1.0 L/s = 1,000 mL/s = 0.0010 m3/s = 0.035315 ft3/s = 0.264172 gal/s
 1 atmosphere (atm) = 760 mm Hg (torr) = 29.9213 in Hg = 14.7 lb/in2 = 101.325 kPa 1.0 pascal (Pa) = 1.0 N/m2 = 1.45038 x 10-4 lb/in2 = 0.00750064 mm Hg 1.0 bar = 100.0 kPa = 100,000 N/m 1.0 in of Hg = 25.4 mm of Hg = 3,386.38 Pa (at 0 °C) = 3,376.85 Pa (at 16 °C) 1.0 mm of Hg = 0.0393701 in of Hg = 0.0013158 atm =133.322 Pa = 0.019339 lb/in2 1.0 in of water = 249.0817 Pa (at 4 °C) = 248.8400 Pa (at 16 °C) 1.0 lb/in2 = 0.068046 atm = 51.71509 mm of Hg = 6.89476 kPa

 Force: 1.0 newton (N) = 1.0 kg-m/s2 = 105 dynes Energy: 1.0 joule (J) = 1.0 N-m = 1.0 W-s = 0.239006 cal = 107 erg = 0.73756 ft-lb 1.0 eV (electronvolt) = 1.60219 x 10-19 J, 1.0 cal = 4.184 J Radiation: 1.0 becquerel (Bq) = 1 disintegration per second 1.0 curie (Ci) = 3.7 x 1010 Bq = 3.7 x 104 rutherfords (rd) 1.0 pCi = 0.010 Bq, 1.0 rd = 1.0 x 106 Bq Radiation Exposure: 1.0 gray (Gy) = 1.0 J/kg = 0.010 rad (radiation absorbed dose)

 1.0 mg/L = 0.001 g/L = 1,000 µg/L = 1,000,000 ng/L 1.0 µg/L = 0.001 mg/L = 1,000 ng/L 1.0 ng/L = 0.001 µg/L = 0.000001 mg/L 1.0 percent = 1.0 g/100g = 10 o/oo (parts per thousand) = 10 g/kg = 10,000 mg/kg (also applies to units/L for dilute waters with low TDS and ρ ~ 1.0 g/cm3) 1.0 g/kg = 0.10 percent = 1,000 mg/kg 1.0 mg/kg = 0.0010 g/kg = 0.00010 percent = 1,000 µg/kg 1.0 µg/kg = 0.001 mg/kg = 1,000 ng/kg

Molar and Equivalent Weights for Major Ions
Compound Name Chemical Formula Molecular Weight, mg/mMole1 Equivalent Weight, mg/meq1 Approximate Conductivity Factor,  µS/cm per mg/L2
Carbonate CO32- 60.0094 30.0047 2.82
Bicarbonate HCO3- 61.0171 61.0171 0.715
Hydroxide OH- 17.0073 17.0073 5.56
Calcium Carbonate CaCO3 100.0874 50.0437 N/A
Sulfate SO42- 96.0636 48.0318 1.54
Chloride Cl- 35.4527 35.4527 2.14
Calcium Ca2+ 40.078 20.039 2.60
Magnesium Mg2+ 24.3050 12.1525 3.82
Sodium Na+ 22.9898 22.9898 2.13
Potassium K+ 39.0983 39.0983 1.84

1 Data from 76th edition of the CRC Handbook of Chemistry and Physics
2 Data from 20th edition of APHA-AWWA-WEF Standard Methods for The Examination of Water and Wastewater

Calculations to Check Water Analyses3
Anion-Cation Balance

Because most natural waters are electroneutral, the sum of cations (positive ions) should equal the sum of anions (negative ions) when the concentrations are calculated in milliequivalents per liter, meq/L. This means that existing water quality data for major ions may be independently checked for accuracy.

1.   Calculate sum of anions, Σanions in meq/L, using the conversions in the above table:

Σanions = [OH-] + [CO32-] + [HCO3-] + [SO42-] + [Cl-], meq/L

2.   Calculate sum of cations, Σcations in meq/L, using the conversions in the above table:

Σcations= [Ca2+] + [Mg2+] + [Na+] + [K+], meq/L

3.   Calculate ion balance percent:

Ion Balance Percent = {(Σcations - Σanions) ÷ (Σcations + Σanions)} x 100

4.   Ion balance percent should be near zero depending on the concentration of the water:

If (Σcations + Σanions) is 0 to 6.0 meq/L, ion balance may be:   ± 0.2 meq/L
If (Σcations + Σanions) is 6.0 to 20.0 meq/L, ion balance may be:   ± 2.0 percent
If (Σcations + Σanions) is 20 to 600 meq/L, ion balance may be:   ± 5.0 percent

Measured TDS and Calculated TDS

Total dissolved solids (TDS) is determined by weighing a sample after evaporation and then drying at 180 °C (EPA Method 160.1). The measured TDS, TDSm, should be close to calculated TDS, TDSc, determined by adding all major ions concentrations in mg/L.

1.   Calculate TDSc from sum of major ions, Σ(ions) in mg/L, using analysis results:

TDSc = Σ(ions)
= [OH-] + [CO32-] + [HCO3-] + [SO42-] + [Cl-] + [Ca2+] + [Mg2+] + [Na+] + [K+]

2.  The ratio of TDSM to TDSC should range from 1.0 to 1.2:

1.0 < (TDSM/TDSC) < 1.2

Measured EC and Calculated EC

The measured conductivity, ECM, should be close to calculated conductivity, ECC, determined by summing the product of each major ion concentration in mg/L times the approximate conductivity factors for each ion seen in the table above.

1.   Calculate ECc from individual ion concentrations in mg/L, denoted as Ci, multiplied by the "Approximate Conductivity Factor, µS/cm per mg/L", denoted as Fi, for each of the major ions:

ECc = Σ(Ci * Fi)
= ([CO32-]*2.82) + ([HCO3-]*0.715)+([SO42-]*1.54) + ([Cl-]*2.14) +
([Ca2+]*2.60) + ([Mg2+]*3.82) + ([Na+]*2.13) + ([K+]*1.84)

2.  The ratio of ECc to ECm should range from 0.9 to 1.1:

0.9 < (ECc/ECm) < 1.1

3.  Method 1030E, from 20th edition of APHA-AWWA-WEF Standard Methods for The Examination of Water and Wastewater

Atmospheric Partial Pressures for O2 and CO2
1 2 3 4 5
0 0 sea level 0.2070 0.000326
5,280 1,609 Denver CO 0.1741 0.000274
10,400 3,170 Leadville CO 0.1421 0.000224

Empirical equations4 for estimating pO2 and pCO2
pO2 (atm) = 0.20704 - (6.239 x 10-6) x (elevation, ft)
pCO2 (atm) = 3.262 x 10-4 - (9.9297 x 10-9) x (elevation, ft)

4 These equations are based on simple linear regression of U.S. standard atmosphere data from 76th edition of the CRC Handbook of Chemistry and Physics. These equations do not take into account local changes in atmospheric pressure from weather systems. More accurate estimates may be obtained by measuring local atmospheric pressure (absolute, in mm Hg) and then adjusting sea level values for pO2 and pCO2

J. Carl Dealy, TFFIP Manager
(209) 836-6236