Limits To Growth/conversions

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Constants, Conversions, and Equivalence Factors[edit]

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[edit]

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


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


Unit Name Equals Alternate Units
Kilogram 2.205 Pounds (weight on earth)
Metric Ton (Tonne) 1,000 Kilograms


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[edit]

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[edit]

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[edit]

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[edit]

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 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:

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[edit]

Natural Gas emits 0.005 metric tons CO2 / therm when burned. See:

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[edit]

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[edit]

Crude oil is the basis for petroleum products. When consumed, typically by burning, it emits 0.43 metric tons CO2 / barrel. See:

This is equivalent to 2.7 kg CO2 / liter

Electric power[edit]

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.

These factors vary by location.

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[edit]


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[edit]

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[edit]

Carbon can be removed from the atmosphere and stored by various biological systems. These are characterized below:

Forests and Crop Lands[edit]

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.



  1. Black, Maggie; Jannet King (2009). The Atlas of Water: Mapping the World's Most Critical Resource. University of California Press. pp. 128. ISBN 978-0520259348.  Page 57
  2. Wolfram|Alpha knowledgebase, 2011.