Constants, Conversions, and Equivalence Factors
Calculating limits to growth requires many conversions between equivalent, or near equivalent quantities of land area, energy, emissions, and other quantities. This page assembles various quantities useful in these conversions. These have been gathered from a variety of sources (cited and listed at the bottom of this page.) Where reliable sources provide a range of values, this is often presented, and the preferred value, used for calculations in the course, is indicated. This course favors the International System of Units (SI).
Land Area
The following area equivalences are helpful in converting various area measures. These can be easily obtained from Wolfram|Alpha.
| Square Mile | Square Kilometer | Hectare | Acre |
|---|---|---|---|
| 1 | 2.59 | 259 | 640 |
| .3861 | 1 | 100 | 247.1 |
| .003861 | .01 | 1 | 2.471 |
| .001563 | .004047 | .4047 | 1 |
Time
| 1 year | 31,536,000 seconds | 525,600 minutes |
| 1 month | 2,628,000 seconds | 43,800 minutes |
| 1 week | 604,800 seconds | 10,080 minutes |
| 1 day | 86,400 seconds | 1,440 minutes |
| 1 hour | 3,600 seconds | 60 minutes |
| 1 minute | 60 seconds | 1 minute |
Mass
| Unit Name | Equals | Alternate Units |
|---|---|---|
| Kilogram | 2.205 | Pounds (weight on earth) |
| Metric Ton (Tonne) | 1,000 | Kilograms |
Volume
| Unit Name | Equals | Alternate Units |
|---|---|---|
| US Gallon | 3.785 | liters |
| Oil Barrel | 42 | US Gallons |
| Oil Barrel | 159 | liters |
| Bushel | 35.24 | liters |
| Acre foot | 1,233 | cubic meters |
| Acre foot | 325,851 | gallons |
Power and Energy
Energy is the ability to do work. Rolling a boulder up a hill represents a particular amount of energy. Power is the rate energy is applied. It takes more power to roll the boulder faster than slower, but the energy is the same if the boulder is moved the same distance, regardless of the speed. The equivalency between various units of power and energy are shown in this table. These can be readily verified at WolframAlpha or Google.
| Unit Name | Type | Equals | Alternate Units |
|---|---|---|---|
| Watt | Power | 1 | Joule Per second |
| Watt Hour | Energy | 3,600 | Joule |
| Kilowatt-hour | Energy | 3,600,000 | Joule |
| Megawatt-hour | Energy | 1,000,000 | Watt Hour |
| Kilowatt-hour / Day | Power | 41.67 | Watts |
| BTU | Energy | 1055 | Joule |
| BTU | Energy | .2931 | Watt Hours |
| Therm | Energy | 100,000 | BTU |
| Therm | Energy | 105,500,000 | Joule |
| Therm | Energy | 29.3 | Kilowatt-hour |
| Therm | Energy | 3.3454 | Watt Years |
| Calorie | Energy | 4.184 | Joule |
| Kcal (food) | Energy | 4184 | Joule |
| toe (ton of oil equivalent) | Energy | 41.868 | GJ |
| toe (ton of oil equivalent) | Energy | 11 630 | Kilowatt-hour |
| toe (ton of oil equivalent) | Energy | 10 million | Kilo-calories |
| toe (ton of oil equivalent) | Energy | 39.68 million | BTU |
| Horsepower | Power | 745.7 | Watts |
| Foot-pounds | Energy | 1.356 | Joule |
| Foot-pounds per second | Power | 1.356 | Watts |
Food and Nutrition
The United Nations Food and Agricultural Organization (FAO) uses the Minimum Dietary Energy Requirement, measured in kcal/person/day, to estimate the prevalence of undernourishment. Dietary energy requirements differ by gender and age, and for different levels of physical activity. Accordingly, minimum dietary energy requirements, the amount of energy needed for light activity and minimum acceptable weight for attained-height, vary by country, and from year to year depending on the gender and age structure of the population.
A listing of MDER by country is available as a spreadsheet from the FAO Food Security Statistics Division.
These have the following statistical characteristics for the years 2004-2006:
| Statistic | kcal/person/day |
|---|---|
| Maximum | 1990 |
| Minimum | 1680 |
| Median | 1820 |
| Mean | 1825 |
Because the MDER is expressed as a single aggregate number of kcal / person / day it does not directly account for variations in the distribution of food to individuals, nor the various requirements for fat, protein, and specific nutrients. Therefore the FAO follows a carefully developed statistical Methodology For The Measurement Of Food Deprivation when estimating the number of undernourished people.
Water for Food
Growing food requires significant quantities of fresh water. The amount of water required to grow each food type—"drops per crop"—varies significantly. The following table shows the average amount of water needed to produce 1 kilogram of food (2004 figures) along with the calorie equivalent of each.
| Food Type | Liters / kg [1] | Dietary calories / kilogram [2] | Liters / Calorie | Calories / 1,000 Liters |
|---|---|---|---|---|
| beef | 15,500 | 2,356 | 6.58 | 152 |
| cheese | 5,000 | 2,923 | 1.71 | 585 |
| millet | 5,000 | 1,190 | 4.20 | 238 |
| goat | 4,043 | 1,430 | 2.83 | 354 |
| poultry | 3,918 | 2,113 | 1.85 | 539 |
| rice (husked) | 2,975 | 1,274 | 2.34 | 428 |
| sorghum | 2,853 | 3,390 | 0.84 | 1,188 |
| wheat | 1,300 | 3,112 | 0.42 | 2,394 |
| potato | 625 | 1,265 | 0.49 | 2,024 |
If a person requires 2,000 calories / day to meet their minimum nutritional requirements, then the food they consume each day requires 840 liters of water to grow if they eat only wheat and 13,160 liters if they eat only beef.
Carbon Emissions
Burning fossil fuels emits carbon into the atmosphere in the form of carbon dioxide (CO2). This contributes to the overall concentration of Carbon dioxide in Earth's atmosphere. One gram of carbon is contained in 3.67 (44/12) grams of CO2.
Gasoline
Gasoline emits CO2 when it is burned, often as automobile fuel. The amount of carbon dioxide emitted per gallon of motor gasoline burned is 8.92×10-3 metric tons. This is equivalent to 8.92 Kg / Gallon. See: http://www.epa.gov/cleanenergy/energy-resources/refs.html
An automobile getting 20 miles per gallon (mpg) emits 8.93/20 = .4465 Kg CO2 / mile
In 2007, the weighted average combined fuel economy of cars and light trucks combined was 20.4 miles per gallon for the United States. The average vehicle miles traveled in 2007 was 11,720 miles per year.
Natural Gas
Natural Gas emits 0.005 metric tons CO2 / therm when burned. See: http://www.epa.gov/cleanenergy/energy-resources/refs.html
This is equivalent to:
- 5 Kg / therm and
- 170 g / Kwh
Note that emissions of unburned natural gas released to the atmosphere is 21 times higher.
Fuel Oil
Homes are often heated by burning heating fuel oil. According to the EPA Fuel oil emits 429.61 kg CO2 / barrel which is equivalent to 10.23 kg CO2 / Gallon or 2.70 kg CO2 / liter.
Crude Oil
Crude oil is the basis for petroleum products. When consumed, typically by burning, it emits 0.43 metric tons CO2 / barrel. See: http://www.epa.gov/cleanenergy/energy-resources/refs.html
This is equivalent to 2.7 kg CO2 / liter
Electric power
Electric power is generated in many ways, but primarily by burning fossil fuels. The quantity of CO2 emitted as electricity is generated is listed below. The amount depends on the fuel used and the efficiency of the generating equipment. Because different regions include various types of electric power generation systems, the emissions factors vary by region.
- 6.91 x 10-4 metric tons CO2 / kWh as an overall average for the US. See: http://www.epa.gov/cleanenergy/energy-resources/refs.html
- Equivalent to: .691 kg CO2 / kWh
- Equivalent to: 1.52 pounds CO2 / kWh
- Equivalent to: 1,520 pounds CO2 / MWh
- From Coal fired power plants: .96 kg CO2 / kWh See: http://www.wolframalpha.com/input/?i=carbon+footprint
- From Natural Gas fired power plants: .6 kg CO2 / kWh See: http://www.wolframalpha.com/input/?i=carbon+footprint
- From petroleum fired power plants: .9 kg CO2 / kWh See: http://www.wolframalpha.com/input/?i=carbon+footprint
These factors vary by location.
- See, for example: http://www.epa.gov/cleanenergy/documents/egridzips/eGRID2010V1_0_year07_SummaryTables.pdf
- and: http://www.inference.phy.cam.ac.uk/withouthotair/cI/page_335.shtml
- and: http://tonto.eia.doe.gov/FTPROOT/environment/e-supdoc-u.pdf
The book Our Choice, provides these somewhat different figures for the carbon footprints of electricity sources in Grams of CO2 per Kilowatt-Hour:
| Electricity Source | Grams CO2 Per Kilowatt-Hour |
|---|---|
| Solar Thermal | 13 |
| Wind | 15 |
| Geothermal | 38 |
| Photovoltaic Solar | 39 |
| Nuclear | 66 |
| Natural Gas | 469 |
| Coal | 974 |
Various Petroleum Products
| Fuel Type | kg CO2 per kWh (HHV) | kg CO2 per kWh (LHV) |
|---|---|---|
| Aviation Spirit | 0.23762 | 0.25012 |
| Aviation Turbine Fuel | 0.24555 | 0.25847 |
| Burning Oil | 0.24564 | 0.25857 |
| CNG | 0.18485 | 0.20515 |
| Coal (industrial) | 0.31659 | 0.33325 |
| Coal (electricity generation) | 0.31907 | 0.33587 |
| Coal (domestic) | 0.29582 | 0.31139 |
| Coking Coal | 0.32979 | 0.34715 |
| Diesel | 0.25011 | 0.26607 |
| Fuel Oil | 0.26475 | 0.28164 |
| Gas Oil | 0.25214 | 0.26823 |
| LNG | 0.18485 | 0.20515 |
| LPG | 0.21419 | 0.22999 |
| Lubricants | 0.26190 | 0.27862 |
| Naphtha | 0.23654 | 0.24899 |
| Natural Gas | 0.18485 | 0.20515 |
| Other Petroleum Gas | 0.20568 | 0.22357 |
| Petrol | 0.23965 | 0.25227 |
| Petroleum Coke | 0.32152 | 0.33845 |
| Refinery Miscellaneous | 0.24512 | 0.25802 |
Gross Calorific Value or higher heating value (HHV) is the Calorific Value under laboratory conditions. Net Calorific Value or lower heating value (LHV) is the useful calorific value in typical real world conditions (e.g. boiler plant). The difference is essentially the latent heat of the water vapor produced (which can be recovered in laboratory conditions).
Converting Kwh / Day to Tonne CO2 / Year
Many ecological footprint-oriented calculations are expressed in Tonnes CO2 / year. How can we convert from Kilowatt-hour / Day to this measure?
First consider Electric power generation, which is high in emissions per Kilowatt-hour.
0.691 kg CO2 / Kilowatt-hour × 365 days / year = 252.215 kg CO2 / Year = 0.252 Tonne CO2 / year
Then consider Natural Gas heating, which is relatively low in emissions per Kilowatt-hour.
0.17 kg CO2 / Kilowatt-hour × 365 days / year = 62.05 kg CO2 / Year = 0.062 Tonne CO2 / year
Blending these two calculations to represent a mix of usage gives the very approximate equivalence of 10 Kilowatt-hour / day ≈ 1 Tonne CO2 / year. Equivalently, 400 watts ≈ 1 Tonne CO2 / year.
Carbon Capture
Carbon can be removed from the atmosphere and stored by various biological systems. These are characterized below:
Forests and Crop Lands
The average carbon density of U.S. forests in 2008 was estimated by the EPA at 73 metric tons per hectare, or 29.55 metric tons per acre. This is equivalent to 108.35 metric tons CO2 per acre, or 267.73 metric tons CO2 per hectare.
The carbon content of cropland is calculated by the EPA to be 5.0 metric tons of carbon per hectare, or 2.02 metric tons per acre. This is equivalent to 7.40 metric tons CO2 per acre or 18.28 metric tons CO2 per hectare.
Reforesting by converting cropland to forest increases carbon capture capacity by (29.55 – 2.02) 27.53 metric tons per acre. This is 100.94 Metric Tons CO2 / acre, or 249.42 metric tons CO2 per hectare.
Deforestation, converting forest to cropland decreases carbon capture by (29.55 – 2.02) 27.53 metric tons per acre. This is 100.94 Metric Tons CO2 / acre, or 249.42 metric tons CO2 per hectare.
Deforestation, converting forest to unplanted land decreases carbon capture by 29.55 metric tons per acre. This is 108.35 Metric Tons CO2 / acre, or 249.42 metric tons CO2 per hectare.
Resources
- The US Government Environmental Protection Agency, Clean Energy Calculations and References
- Sustainable Energy - without the hot air Quick reference
- The quick-reference list of conversion factors used by the Bioenergy Feedstock Development Programs at Oak Ridge National Laboratory.
- U.S. energy Information Administration, Energy Kids Energy Calculators.
- NIST Guide to the SI, Factors for units listed by kind of quantity or field of science
- Höhne, Niklas; Dian Phylipsen; Sara Moltmann (2007). Factors underpinning future action, 2007 update (PDF).