Lecture 02
Unit Systems and Conversions
Experience shows that a lack of facility in the skills of unit manipulation is responsible
for confusion and delay in acquiring competence in precision farming. This handout
review units and unit conversion related to global positioning systems, precision farming
and crop management.
Various units and their conversion factors are given below. A complete list of units and
unit conversions from SI (System International) to non-SI units (English units) are
presented on pages 2 and 3.
Length
Mass
1 in = 2.54 cm
1 kg = 103 gm
1 ft = 12 in = 30. 48 cm
1 gm = 10-3 kg
1 yd = 3 ft = 91.44 cm
1 kg = 2.205 lbs
1 m = 1.0936 yd = 3.281 ft = 39.37 in
1 lbs = 454 gm
1 mi = 5280 ft = 1760 yd
1 oz = 28.4 gm
1 mi = 1.609 km
1 ton = 2000 lbs
1 light year = 9.461 x 1015 m
1 mt = 2205 lbs
Area
Volume
1 in2 = 6.4516 cm2
1 in3 = 16.39 cm3
1 ft2 = 9.29 x 10-2 m2
1 ft3 = 1728 in3
1 cm2 = 10-4 m2
1 gal = 4 qt = 8 pt = 128 oz = 231 in3
1 acre = 43, 560 ft2
1 gal = 3.786 lit
1 mi2 = 6430 acres = 2.59 km2
1 lit = 1000 cm3 = 10-3 m3
Time
Speed
1 h = 60 min = 3600 sec
1 ft/sec = 0.3048 m/sec
1 d = 24 h = 1440 min = 8.64 x 104 sec
1 mi/h = 0.4470 m/sec
1 y = 365.24 d = 3.156 x 107 sec
1 mi/h = 1.467 ft/sec
Speed of light = 186,300 mi/sec (in vaccum)
Speed of light = 300,000,000 m/sec
Unit systems and conversions. Fall Semester 2015.
Raj Khosla
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Conversion Factors for SI and non-SI Units
To convert Column 1
into Column 2,
multiply by
Length
0.621
1.094
3.28
1.0
3.94 x 10-2
10
Column 1 SI Unit
Column 2 non-SI Unit
To convert Column 2
into Column 1,
multiply by
kilometer, km (103 m)
meter, m
meter, m
micrometer, μm (10-6m)
millimeter, mm (10-3m)
nanometer, nm (10-9m)
mile, mi
yard, yd
foot, ft
micron, μ
inch, in
Angstrom, Å
1.609
0.914
0.304
1.0
25.4
0.1
hectare, ha
square kilometer, km2 (103 m)2
square kilometer, km2 (103 m)2
square meter, m2
square meter, m2
square millimeter, mm2 (10-3m)2
Acre
Acre
square mile, mi2
Acre
square foot, ft2
square inch, in2
0.405
4.05 x 10-3
2.590
4.05 x 103
9.29 x 10-2
645
cubic meter, m3
cubic meter, m3
cubic meter, m3
liter, L (10-3m3)
liter, L (10-3m3)
liter, L (10-3m3)
liter, L (10-3m3)
liter, L (10-3m3)
liter, L (10-3m3)
acre-inch
cubic foot, ft3
cubic inch, in3
bushel, bu
quart (liquid), qt
cubic foot, ft3
Gallon
ounce (fluid), oz
pint (fluid), pt
102.8
2.83 x 10-2
1.64 x 10-5
35.24
0.946
28.3
3.78
2.96 x 10-2
0.473
gram, g (10-3 kg)
gram, g (10-3 kg)
kilogram, kg
kilogram, kg
kilogram, kg
megagram, Mg (tonne)
tonne, t
pound, lb
ounce (avdp), oz
pound, lb
quintal (metric), q
ton (2000 lb), ton
ton (U.S.), ton
ton (U.S.), ton
454
28.4
0.454
100
907
0.907
0.907
kilogram per hectare, kg ha-1
kilogram per cubic meter, kg m-3
kilogram per hectare, kg ha-1
kilogram per hectare, kg ha-1
kilogram per hectare, kg ha-1
liter per hectare, L ha-1
tonnes per hectare, t ha-1
megagram per hectare, Mg ha-1
megagram per hectare, Mg ha-1
meter per second, m s-1
pound per acre, lb acre-1
pound per bushel, bu-1
bushel per acre, 60 lb wheat
bushel per acre, 56 lb corn
bushel per acre, 48 lb barley
gallon per acre
pound per acre, lb acre-1
pound per acre, lb acre-1
ton (2000 lb) per acre, ton acre-1
mile per hour
1.12
12.87
67.19
62.71
53.75
9.35
1.12 x 10-3
1.12 x 10-3
2.24
0.447
Area
2.47
247
0.386
2.47 x 10-4
10.76
1.55 x 10-3
Volume
9.73 x 10-3
35.3
6.10 x 104
2.84 x 10-2
1.057
3.53 x 10-2
0.265
33.78
2.11
Mass
2.20 x 10-3
3.52 x 10-2
2.205
0.01
1.10 x 10-3
1.102
1.102
Yield and Rate
0.893
7.77 x 10-2
1.49 x 10-2
1.59 x 10-2
1.86 x 10-2
0.107
893
893
0.446
2.24
Unit systems and conversions. Fall Semester 2015.
Raj Khosla
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To convert Column 1
into Column 2,
multiply by
Specific Surface
10
1000
Density
1.00
Pressure
9.90
10
2.09 x 10-2
1.45 x 10-4
Column 1 SI Unit
Column 2 non-SI Unit
To convert Column 2
into Column 1,
multiply by
square meter per kilogram, m2 kg-1
square meter per kilogram, m2 kg-1
square centimeter per gram, cm2 g-1
square millimeter per gram, mm2 g-1
0.1
0.001
megagram per cubic meter, Mg m-3
gram per cubic centimeter, g cm-3
1.00
mega pascal, Mpa (106 Pa)
mega pascal, Mpa (106 Pa)
pascal, Pa
pascal, Pa
Atmosphere
Bar
pound per square foot, lb ft-2
pound per square inch, lb ft-2
0.101
0.1
47.9
6.90 x 103
Kelvin, K
Celsius, ºC
Celsius, ºC
Fahrenheit, ºF
1.00 (ºC + 273)
5/9 (ºF – 32)
British thermal unit, Btu
calorie, cal
Erg
foot-pound
calorie per square centimeter langley)
Dyne
calorie per square centimeter
minute (irradiance), cal cm-2 min-1
1.05 x 103
4.19
10-7
1.36
4.19 x 104
10-5
698
milligram per square meter second,
mg m-2 s-1
milligram (H2O) per square meter
second, mg m-2 s-1
milligram per square meter second,
mg m-2 s-1
milligram per square meter second,
mg m-2 s-1
gram per square decimeter hour,
g dm-2 h-1
micromole (H2O) per square centimeter second, μmol cm-2 s-1
milligram per square centimeter
second, mg cm-2 s-1
milligram per square decimeter hour,
mg dm-2 h-1
27.8
radian, rad
degrees (angle), °
1.75 x 10-2
siemen per meter, S m-1
tesla, T
millimho per centimeter, mmho cm-1
gauss, G
0.1
10-4
cubic meter, m3
cubic meter per hour, m3 h-1
cubic meter per hour, m3 h-1
hectare-meters, ha-m
hectare-meters, ha-m
hectare-centimeters, ha-cm
acre-inches, acre-in
cubic feet per second, ft3 s-1
U.S. gallons per minute, gal min-1
acre-feet, acre-ft
acre-inches, acre-in
acre-feet, acre-ft
102.8
101.9
0.227
0.123
1.03 x 10-2
12.33
Temperature
1.00 (K – 273)
(9/5 ºC) + 32
Energy, Work, Quantity of Heat
9.52 x 10-4
0.239
107
0.735
2.387 x 10-5
105
1.43 x 10-3
joule, J
joule, J
joule, J
joule, J
joule, per square meter, J m-2
newton, N
watt per square meter, W m-2
Transpiration and Photosynthesis
3.60 x 10-2
5.56 x 10-3
10-4
35.97
Plane Angle
57.3
Electrical Conductivity, Electricity, and Magnetism
10
104
Water Measurement
9.73 x 10-3
9.81 x 10-3
4.40
8.11
97.28
8.1 x 10-2
Unit systems and conversions. Fall Semester 2015.
Raj Khosla
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180
104
2.78 x 10-2
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To convert Column 1
into Column 2,
multiply by
To convert Column 2
into Column 1,
multiply by
Column 1 SI Unit
Column 2 non-SI Unit
1
centimole per kilogram, cmol kg-1
1
0.1
1
gram per kilogram, g kg-1
milligram per kilogram, mg kg-1
milliequivalents per 100 grams,
meq 100 g-1
percent, %
parts per million, ppm
bequerel, Bq
bequerel per kilogram, Bq kg-1
gray, Gy (absorbed dose)
sievert, Sv (equivalent dose)
curie, Ci
picocurie per gram, pCi g-1
rad, rd
rem (roentgen equivalent man)
3.7 x 1010
37
0.01
0.01
Oxide
P2O5
K2O
CaO
MgO
0.437
0.830
0.715
0.602
Concentrations
Radioactivity
2.7 x 10-11
2.7 x 10-2
100
100
Plant Nutrient Conversion
Elemental
2.29
P
1.20
K
1.39
Ca
1.66
Mg
Unit systems and conversions. Fall Semester 2015.
Raj Khosla
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Prefixes for decimal fractions and multiples:
Decimal fraction
Prefix
Abbreviation
Example
10-18
Atto
a
atto-meter
10-15
Femto
f
femto-meter
10-12
Pico
p
pico-gram 9pg)
10-09
Nano
n
nano-meter (nm)
10-06
Micro

micro-gram (g)
-03
Milli
m
milli-meter (mm)
10-02
Centi
c
centi-meter (cm)
10-01
Deci
d
deci-liter (dl)
101
Deka
da
deca-gram (dag)
102
Hecto
h
hecto-liter (hl)
103
Kilo
k
kilo-grams (kg)
106
Mega
M
mega-byte (Mb)
109
Giga
G
giga-hertz (Ghz)
1012
Tera
T
tera-grams (Tg)
10
Unit systems and conversions. Fall Semester 2015.
Raj Khosla
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Example calculations:
1. GPS satellite signals are broadcast at the speed of light. The speed of light in vacuum is 186,000
miles/second. Calculate speed of light in meters/second.
Answer:
2. Calculate in miles, km, feet, and meter that the GPS signal will travel in 1 micro second ( sec) and 1
nano second (n sec). Given that 1 micro second is 1 millionth part of a second, 1 nano second is 1
billionth part of a second.
Answer:
3. Larry’s field is 100 acres in size. His average grain yield was 60 bushels of wheat per acre. Using
units and unit conversions from the tables, calculate and show:
(i)
(ii)
(iii)
The size of Larry’s field in hectares
Average grain yield in kg/hectare
Total grain yield of Larry’s farm in metric tonnes.
Answer:
Unit systems and conversions. Fall Semester 2015.
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How to create or calculate your own conversion factors.
Lets work with the example above. The unit table shows that for converting bushel per acre of wheat (60
lbs) to kg per hectare, you simply multiply the bushels per acre x 67.19.
How do we get 67.19 as conversion factor?
Converting Latitude/Longitude Coordinates:
Latitudes and Longitudes are measured in Degrees, Minutes and Seconds units. However depending
upon the GPS system you are using, such units may be intermingled together and may be reported in
various different ways. Such as:
DM.m = Degrees, Minutes, Decimal Minutes (ex. 45o22.6333’);
D.d = Degrees, Decimal Degrees (ex. 45.3772o);
DMS = Degrees, Minutes, Seconds (ex. 45o22'38");
Fractions of degrees are broken down into minutes and seconds. Each minute represents 1/60th of a
degree and each second represents 1/60th of a minute (or 1/3600th of a degree).
It is therefore important for you to know and learn how to convert Latitude and Longitude from one unit
format to another.
Below are the steps of converting from an angle in degrees-minutes-seconds to decimal degrees and back
to degrees-minutes-seconds.
EXAMPLES:
D = Degrees
M = Minutes
S = Seconds
.m = Decimal Minutes
.s = Decimal Seconds
Unit systems and conversions. Fall Semester 2015.
Raj Khosla
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Process for Converting Latitude/Longitude Coordinates:
1) DMS to DM.m (45o22'38" -- ??):
- Divide S by 60 to get .m (38/60=.6333’)
- Add .m to M to get M.m (22+.6333=22.6333’)
Answer: 45o22.6333’
2) DM.m to D.d (45o 22.6333’ -- ??):
- Divide M.m by 60 to get .d (22.6333/60=.3772)
- Add .d to D to get D.d (45+.3772=45.3772o)
Answer: 45.3772o
3) D.d to DM.m (45.3772 -- ??):
- Multiply .d by 60 to get M.m (.3772*60=22.6333’)
Answer: 45o22.6333’
4) DM.m to DMS (45o22.6333’ -- ??):
- Multiply .m by 60 to get S(.6333*60=38”)
Answer: 45o22'38"
Converting UTC (Universal Time Coordinated) to a regular daily clock time:
Converting UTC to…
Eastern Standard Time (EST)
UTC – 5 hours = EST
Central Standard Time (CST)
UTC – 6 hours = CST
Mountain Standard Time (MST)
UTC – 7 hours = MST
Pacific Standard Time (PST)
UTC – 8 hours = PST
When “Daylight-Saving Time” in effect, the conventional becomes…
Eastern Daylight Time (EDT)
UTC – 4 hours = EDT
Central Daylight Time (CDT)
UTC – 5 hours = CDT
Mountain Daylight Time (MDT)
UTC – 6 hours = MDT
Pacific Daylight Time (PDT)
UTC – 7 hours = PDT
Unit systems and conversions. Fall Semester 2015.
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Example: Convert 172356 UTC time to a normal Daily clock time for Mountain Time Zone (Use
Mountain Standard Time):
Example: Convert MST of 6:00pm to UTC time.
Calculating distance between a measured GPS position data and a reference benchmark.
Example 1: Let say you are measuring the location of a landmark (for e.g., a statue) at CSU and there is a
geodetic-benchmark point close to the landmark. You positioned your GPS unit on the landmark and
started recording real-time data. After recording data for a few minutes, you took the mean of your
measured data points. Now you want to know the distance between the benchmark and your landmark
mean data point.
Benchmark information:
LAT:
LON:
40o 34.3796’ NORTH
-105o 04.9663’ WEST
Note the unit/format: “Degree.Min.min”
Estimated mean of the measured data:
LAT:
LON:
40.572910o North
-105.082799o West
Note the unit/format: “Degree.deg”
The conversion factors applicable in Fort Collins are:
For Latitude:
For Longitude:
1.85 meter per 0.001 min
1.41 meter per 0.001 min
IMPORTANT:
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I. Decimal figures: Please note that latitude and longitude coordinates are very sensitive figures. They
describe the position on our planet earth. A slight change in coordinate figure translates into a significant
figure in distance units.
For example:
In other words:
0.001 minute equals 1.85 meter
1-minute change in Latitude translates into 1850 meters in distance on earth in Fort
Collins area.
Likewise 1-minute change in Longitude translates into 1410 meters in distance in
Fort Collins area.
It is therefore advisable to work with 0.000000 six or more decimal places when working with Latitude
and Longitudes.
II. Conversion factors: Please note that conversion factors are handy only when the coordinates (lat/lon)
are in the appropriate unit format.
In the Example 1, above the benchmark coordinates are in Degree.Min.min format while the measured
GPS data is in Degree.deg format. You must convert either of the two so as to have both the figures in
the same format.
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Approach # 1. Let us convert the measured GPS data into Degree.Min.min format.
The mean of the measured GPS data is:
LAT:
40.572910o North
-105.082799o West
LON:
We need to convert only the fraction parts of the coordinates into “minutes”
0.572910 degree x 60 min/degree = 34.374600’
or the LATITUDE = 40o 34.3746’ (Degree.Min.min format)
Likewise for LONGITUDE:
0.082799 degree x 60 min/degree = 04.9679400’
or the LONGITUDE = -105o.04.96794’ (Degree.Min.min format)
Now, both the benchmark coordinates and the mean of measured GPS data are in the same format
(Degree.Min.min format). Take the difference between the two respective coordinates and convert the
difference into distance (meters).
LATITUDE: (40o 34.3796’) – (40o 34.3746’) = 0.0050’
The conversion factors applicable in Fort Collins for Latitude: 1.85 meter per 0.001 min
Therefore 0.0050 min x 1.85 meter/0.001min = 9.25 meters.
Likewise for LONGITUDE: (-105o 04.9663’) – (-105o.04.96794’) = 0.00164
The conversion factors applicable in Ft. Collins for Longitude: 1.41 meter per 0.001 min
Therefore 0.00164 min x 1.41 meter/0.001min =
Unit systems and conversions. Fall Semester 2015.
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2.31 meters.
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Approach # 2. Let us convert the benchmark data into Degree.deg format.
The benchmark data is:
LAT:
40o 34.3796’ North
LON:
-105o 04.9663’ West
We need to convert only the fraction parts of the benchmark coordinates into “.deg”
34.3796 minutes x 1 degree/60 minutes = 0.5729933o
or the LATITUDE = 40.5729933o (Degree.deg format)
Likewise for LONGITUDE:
04.9663 minutes x 1 degree/60 minutes = 0.0827717o
or the LONGITUDE = -105.0827717o (Degree.deg format)
Now, both the benchmark coordinates and the mean of measured GPS data are in the same format
(Degree.deg format). Let us take the difference between the respective coordinates to calculate the error
and convert the error into distance (meters).
LATITUDE: (40.5729933o) – (40.572910o) = 0.0000833o
The conversion factors applicable in Fort Collins for Latitude: 1.85 meter per 0.001 min, however before
we may use that we must convert the error from .deg to minutes by multiplying with 60
Therefore 0.0000833 degree x 60 min/degree x 1.85 meter/0.001min = 9.25 meters.
Likewise for LONGITUDE: (-105.0827717o) – (-105.082799o) = 0.0000273o
The conversion factors applicable in Ft. Collins for Longitude: 1.41 meter per 0.001 min, however before
we may use that we must convert the error from .deg to minutes by multiplying with 60
Therefore 0.0000273 degree x 60 min/degree x 1.41 meter/0.001min = 2.31 meters.
References: (Last updated / visited 08/27/2015)
Latitude and Longitude: http://itouchmap.com/latlong.html ; http://www.latlong.net/
Measuring latitude: http://www.open.edu/openlearn/society/politics-policy-people/geography/diy-measuringlatitude-and-longitude
Converting degrees, minutes, seconds: http://www.rapidtables.com/convert/number/degrees-to-degrees-minutesseconds.htm
Quick guide to using UTM Coordinates: http://www.maptools.com/UsingUTM/quickUTM.html
Universe Transverse Mercator Grid: http://earth-info.nga.mil/GandG/coordsys/grids/universal_grid_system.html
Unit systems and conversions. Fall Semester 2015.
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