michaelminn.net / Energy

Energy Unit Conversions

Energy is "a fundamental entity of nature that is transferred between parts of a system in the production of physical change within the system" (Merriam Webster 2021).

Under Sir Issac Newton's definition, energy is the ability to do work, and work is the result of force moving something over a distance (Goldemberg and Lucon, 2010, 4). Energy is fundamental not only to physical processes but also to biological life itself.

Both academic and popular media present information about energy technologies and resources using variety of units that make it difficult to compare and contextualize values. Being able to convert values to common units and place values into context can enable you to evaluate the merits and limitations of different energy resources and technologies.

This tutorial will cover fundamentals of energy unit conversion. Statistical data and conversion factors are drawn from a variety of sources, most notably:

• bp Statistical Review of World Energy
• ORLN Transportation Energy Data Book
• EIA Monthly Energy Review

Measuring Energy

Energy comes in many forms: light, heat, movement, electricity, etc. and there are different units used for measuring power and energy depending on the form of energy being measured.

British Thermal Units

Measurements of energy in different forms and from different sources can be converted to common units for rough comparison.

The British thermal unit (BTU) is an energy unit commonly used in American energy literature which is equivalent to the amount of heat needed to raise the temperature of one pound of water at sea level by one degree Fahrenheit.

• Although various scales of Joules (MJ, EJ, etc.) are commonly used in scientific literature to conform to the International System of Units, BTUs are used in this document to eliminate unnecessary mental transformation when referencing source documents.
• Because the BTU is a fairly small unit, large-scale energy usage figures from government literature are commonly given in quadrillion BTU, or quads.
• Since American total energy use has hovered around 100 quads since the mid 2000s, use of quads also facilitates quick mental calculation to percents.
• Quads are also fairly close to exajoules (1 quad = 1.055 EJ), so there is a rough interchangeability with literature that uses exajoules.

The following are examples of the amount of energy in BTUs needed for some specific tasks:

Total Annual Energy Consumption

Depending on the source, the Americans use three to five times the amount of energy on a per capita basis than the global average.

Conversion Factors

The thermodynamic principle of conservation of energy recognizes the equivalence of heat and mechanical work (Fermi 1937). Conversion between forms of energy is a fundamental task performed by both machines and living organisms. While energy from different sources is often not interchangeable (e.g. solar-generated electricity cannot currently be used to power commercial jet airliners), technological and social adaptation can often permit significant levels of substitution (e.g. trains replace airliners).

Unit Cancellation

Calculations and analysis involving energy commonly involve conversions between units, and these conversions can become complex as they go through multiple steps.

One way of keeping track of these steps is unit cancellation, where units are written as sequences of fractions, and matching units on the tops and bottoms of these fractions cancel each other out to reach a desired end unit.

Given the 60-watt light-bulb example above, suppose we want to know the amount of energy used by the bulb in kilowatt-hours (which is the unit normally used to buy electricity) and the cost to run that bulb for that period of time.

Each kilowatt-hour represents 1,000 watts. First we set up the equation:

60 watts    8 hours    1 kilowatt-hour
-------- * --------- * ---------------
 1 bulb    1 workday   1000 watt-hours

Cancelling watts and hours, and multiplying through we get:

60 watts    8 hours    1 kilowatt-hour     480
-------- * --------- * --------------- = ------ = 0.48 kilowatt-hours
 1 bulb    1 workday   1000 watt-hours    1000

Tacking on a typical total cost of 25 cents per kilowatt-hour, cancelling, and multiplying through:

60 watts    8 hours    1 kilowatt-hour        $0.25
-------- * --------- * --------------- * ---------------
 1 bulb    1 workday   1000 watt-hours   1 kilowatt-hour

60 watts    8 hours    1 kilowatt-hour        $0.25         120
-------- * --------- * --------------- * --------------- = ---- = $0.12
 1 bulb    1 workday   1000 watt-hours   1 kilowatt-hour   1000

You can perform these calculations in R or Python using multiplication and division symbols and ignoring the multiplications or divisions by one.

watts_per_bulb = 60

hours_per_day = 8

watts_per_kwh = 1000

dollars_per_kwh = 0.25

total_cost = watts_per_bulb * hours_per_day / watts_per_kwh * dollars_per_kwh

print(total_cost)

[1] 0.12

Theoretical Conversion Factors

Listed below are some theoretical conversion factors between different energy measurement units, when losses in the real-life conversion processes are ignored.

Potential Energy Conversion Factors

Energy can be stored as potential energy. For example, photosynthesis is a biological process that stores solar energy in the carbohydrates that make up a plant. When that plant is burned, that stored energy is released as heat energy.

The table below summarizes conversions between units and typical heat values representing the potential energy in amounts of different fuels.

Electricity

Electricity is "a fundamental form of energy observable in positive and negative forms that occurs naturally (as in lightning) or is produced (as in a generator) and that is expressed in terms of the movement and interaction of electrons" (Merriam-Webster 2021).

Power

With energy, power is "the time rate at which work is done or energy emitted or transferred" (Merriam-Webster 2023).

Electrical energy is electrical power for a given amount of time.

Electricity generation and consumption is commonly specified in terms of the rate of energy use (power) rather than the amount of energy.

• Electrical power is commonly expressed in kilowatts (thousands of watts) or megawatts (millions of watts).
• Amounts of electrical energy are commonly expressed in kilowatt-hours (kWh) or megawatt-hours (mWh).
• One kilowatt of energy flow for one hour is a kilowatt-hour.
• When you pay your home electrical bill, the amount of electricity you use is usually given in kilowatt-hours.

For example, suppose you use a 45-watt laptop, eight hours a day, 360 days per year.

45 watts   8 hours   360 days      1 kW      129.6 kWh
-------- * ------- * -------- * ---------- = ---------
1 laptop    1 day     1 year    1000 watts   per year

If electricity costs on average $0.25 per kWh:

45 watts   8 hours   360 days      1 kW      $0.25    $32.40
-------- * ------- * -------- * ---------- * ----- = --------
1 laptop    1 day     1 year    1000 watts   1 kWh   per year

Heat Rate

Assuming 100% efficiency, there are 3,412 BTU in each kWh of electricity.

However, because fossil-fueled plants generally only convert about one-third of the heat energy in fuel to electrical energy, EIA uses a heat rate to convert electrical energy numbers to heat equivalents (EIA 2023, appendix A6).

• This average heat rate varies over time and generating technology.
• Even though renewables (solar and wind) do not generate electricity in the same manner as fossil-fueled plants, this same heat rate is commonly used with renewables to keep the numbers comparable across generating sources.

Given the 45 watt laptop example above:

45 watts   8 hours   360 days      1 kW      8843 BTU   1,146,053 BTU
-------- * ------- * -------- * ---------- * -------- = -------------
1 laptop    1 day     1 year    1000 watts    1 kWh        per year

Efficiency

Although conversion between measurement units is generally trivial, converting energy between different forms usually involves the loss of energy, usually as wasted heat that cannot be completely recovered for any useful purpose.

For example, most fossil fuels are burned with useful kinetic energy released as a by-product of generated heat. As such, with current technologies, much of the potential energy in fossil fuels and biomass is lost as waste heat sent up cooling towers or vented in radiators.

Efficiency is the amount of the input energy that actually comes out in some useful form. Efficiency of power converters covers a wide range:

• 15% for spark ignition (Otto cycle) gasoline engines (DOE 2011)
• 43% for advanced commercial truck diesel engines (Lutsey 2015)
• 58% for combined-cycle natural gas power plants (Franco and Russo 2002)
• 80% co-generating power plants where waste heat is used for building heating (Rosen, Le and Dincer, 2005)

There are two heating values that can be given for fuel combustion.

• A high (gross) heating value considers the energy that vaporizes the water resulting from combustion. High values are used by the US Energy Information Administration and this document follows that convention in using high heating values (EIA 2015).
• A low (net) heating value ignores that energy. Low values are commonly used in reports from Europe.

In considering efficiency, a conventional 60-watt incandescent light bulb is rated at emitting 800 lumens. Leaving that light on for an hour:

 800 lumens     0.005 BTU     4 BTU light energy
------------ * ------------ = ------------------
1 light bulb   1 lumen-hour   1 light bulb hour


  60 watts      3.412 BTU    205 BTU electricity
------------ * ----------- = -------------------
1 light bulb   1 watt-hour    1 light bulb hour


4 BTU light energy
------------------------- = 0.02 = 2% efficiency
205 BTU electrical energy


The other 98% of the energy is lost as unused heat.

An equivalent compact florescent bulb emitting the same amount of light would use around 15 watts:

 800 lumens     0.005 BTU     4 BTU light energy
------------ * ------------ = ------------------
1 light bulb   1 lumen-hour   1 light bulb hour

  
  15 watts      3.412 BTU    51 BTU electricity
------------ * ----------- = ------------------
1 light bulb   1 watt-hour    1 light bulb hour


   4 BTU light
------------------ = 0.08 = 8% efficiency
51 BTU electricity


Compact florescent bulb is 4x as efficient as comparable incandescent

Capacity Factor

All energy sources (especially renewables) have some level of intermittency. Coal-fired generators must be taken off-line occasionally for maintenance, solar power is not generated at night, and wind power is unavailable when the wind slows or stops blowing.

Capacity factor is the percentage of the rated maximum potential power that a system creates over time under real-world conditions. Capacity is an especially important consideration with renewable energy generators, with US hydroelectric dams having average capacity factors of 30% to 40% and commercial US wind farms having average capacity factors between 21% to 52% (EIA 2017; USDOE 2022, 34)

For example: Contemporary wind turbines are commonly rated at two to three megawatts apiece (National Wind Watch 2023). Given an average capacity factor of 32%:

Therefore, for one turbine over a year:

2 MW to 3 MW   32% capacity factor   365 days   24 hours    5,600 to 8,400 MWh
------------ * ------------------- * -------- * -------- = ---------------------
 1 turbine     average over a year    1 year     1 day     1 turbine over a year

Using the BTU common unit, it is possible to compare the amount of energy used or produced in different forms. For example, in 2021 in the US, fossil-fueled power plants required an average of 8,843 BTU to generate one kW of electricity (EIA 2023, appendix A6). Given that heat rate, each wind turbine can generate the equivalent of:

 5,600 to 8,400 MWh     1000 kW    8,843 BTU heat rate   50 B to 74 B BTU
--------------------- * ------- * -------------------- = ----------------
1 turbine over a year    1 MW       1 kW electricity       over a year

In 2022, the US used around 98 quads of primary energy for all activities (BP 2022). So to estimate the number of wind turbines needed to convert the US entirely to wind power:

98 quads total    1,000,000 billion BTU   1 turbine over a year   1.3 to 2.0 million turbines
--------------- * --------------------- * --------------------- = ---------------------------
1 year total US          1 quad            50 B to  74 B BTU            Total US demand

Provided you could find windy locations to install all those turbines, and given a cost of $3 to $4 million to install each turbine:

1.2 to 1.8 million turbines   $3,000,000 to $4,000,000     $3.6 T to $7.2 T
--------------------------- * ------------------------- = ------------------
     Total US demand          installation cost/turbine   Total capital cost

In 2022, the US gross domestic product (total economic activity) was around $26.15 trillion (BEA 2023). While all those turbines would not be installed in one year, anyone proposing a major conversion of US energy to wind needs to also indicate what will need to be foregone in order to devote the labor and materials to build and install all those turbines.

Load Factor

Load factor which represents how effectively a system's capacity is utilized by customer demand. Capacity factor focuses primarily on supply while load factor represents the level of harmony between supply and demand.

Load factor is commonly used in transportation to measure the percent of maximum capacity used on an average basis, such as the average percentage of seats occupied on an airplane). A car with four seats but carrying only a solo driver has a load factor of 25%. Transportation system operators strive to increase their load factor to increase profits.

The variability in load factors across time of day and day of the year can dramatically affect the comparative efficiency of transportation modes. Because transit agencies must run buses around the clock to make their systems useful to the community, they rarely fill all seats (100% load factor), and are often circulating large, nearly empty vehicles around the community.

For example, in 2019, the Champaign-Urbana Mass Transit District (CUMTD) carried 21.1 million passenger miles (one passenger for one mile), in buses that drove around 3.4 million vehicle miles, meaning on average over the year, each bus was carrying 6.21 passengers (USDOT 2020b).

21.1 MM passenger miles   6.21 passengers
----------------------- = ---------------
 3.4 MM vehicle miles       1 vehicle

Given a capacity of 38 seats per bus (CUMTD 2022), on average over the year, this gives a load factor of 16.3%.

6.21 passengers   
--------------- = 16.3% load factor
   38 seats

Miles per Gallon

Energy efficiency for vehicles is commonly expressed in miles per gallon (MPG).

Continuing the CUMTD example given above, in 2019 the CUMTD used 710 thousand gallons of diesel fuel for 3.4 million vehicle miles (USDOT 2020a; USDOT 2020b). Given a capacity of 38 seats per bus and compensating for the higher energy content of diesel vs. a gallon of gasoline:

3.4 MM bus miles   38 seats         1 year         138111 BTU / gal diesel      201 seat miles
---------------- * -------- * ------------------ * ------------------------- = -----------------
   1 year            1 bus    0.71 MM gal diesel   125000 BTU / gal gasoline   1 gallon gasoline

However, when we consider the load factor and the average number of passengers on each bus, the energy efficiency of the CUMTD system as a whole is about the same as driving alone in a 32 MPG Toyota Corolla or a little less than two people in a large 20 MPG (40 passenger MPG) Ford Explorer. While mass transit allows denser development that reduces the total distance that passengers need to travel, the low efficiencies of mass transit systems should be considered in assessing the broader environmental value of those systems.

3.4 MM bus miles   6.21 passengers          1 year         138111 BTU / gal diesel      33 passenger miles
---------------- * ---------------  * ------------------ * ------------------------- = --------------------
   1 year              1 bus          0.71 MM gal diesel   125000 BTU / gal gasoline     1 gallon gasoline

Miles per Gallon Equivalent

When comparing electrified transportation systems to fossil-fueled transportation systems, you will need to add additional factors to convert the electricity used into a comparable amount of fossil-fuel.

MPGe (miles per gallon equivalent) is a measurement of efficiency for electrified transportation that considers the heat energy needed to generate electricity (the heat rate) and the equivalent amount of heat in gasoline.

For example, in 2019, the New York Metropolitan Transit Authority (MTA) subways carried 10,462 million passenger miles using 1,773 million kWh of electricity.

10462 MM pass-mi     1 year        1 kWh      125000 BTU        83.4 passenger-miles
---------------- * ----------- * -------- * -------------- = ----------------------------
    1 year         1773 MM kWh   8843 BTU   1 gal gasoline   1 gallon gasoline equivalent

Resources vs. Reserves

In looking at estimates for the amount of a resource that is available, it is important to distinguish between three different ways of looking at a resource.

• Resource or in-place figures give the estimate of the total amount of resource that is in the ground. Because these resources can only be measured indirectly, there is always some uncertainty about the accuracy of such figures.
• Potential or technically feasible figures give the amount of a resource that might be extractable with current technology or potential future technology. These figures are always lower than the in-place figures since it is generally impossible to extract every last drop of a resource.
• Reserves are the actual amount of a resource that can be extracted with existing technology at a profit. This figure is lower than the potential figure both due to technical limitations and the portion of the potential resource that would require so much expense to extract that it would not be profitable.

These figures can change due to improvements in technology, changes in accounting standards, or increases in resource prices that make previously inaccessible resources economically viable. Adding to the uncertainty of these figures are commercial or political considerations that provide incentives to overstate or understate reserves. For example, OPEC production quotas are based on a country's reserves, which provides an incentive for countries to overstate their reserves.

Reserves / Consumption Ratio

The volume of reserves can be placed in context by evaluating them in terms of current consumption rates.

For example, various estimates put the amount of technically recoverable oil resources in the environmentally-sensitive (and politically-controversial) Arctic National Wildlife Refuge (ANWR) at around 10 billion barrels (USGS 1999, USGS 2013).

For context, the US Energy Information Administration (2023) reported that the United States consumed an average 20.28 million barrels per day in 2022. Oil production and consumption is commonly reported in barrels per day rather than by year.

19.4 million barrels   365 days   7.1 billion barrels
-------------------- * -------- = -------------------
      1 day             1 year		1 year


10 B barrels             1 year		         1.4 years
------------ * ------------------------- = --------------------
  resource     7.1 B barrels consumption   US total consumption

So, you can make the case that placing that area at environmental risk in exchange 17 months of US consumption is a dubious proposition. And since US oil consumption will likely increase, and not all of that 10 billion barrels can be assured to be economically feasable to extract, the number is likely lower.

Reserves / Production Ratio

Energy resources cannot be produced all at once, and the rate of production can be used to estimate how long a resource will last as the the reserves-to-production ratio.

For example, if production could be ramped up to two million barrels per day:

10 B barrels    1000 million          1 day         1 year       13.7 years
------------- * ------------ * ----------------- * -------- = ---------------
ANWR resource    1 billion     2 MM barrels prod   365 days   ANWR production

And, given a price for oil of $54/barrel (on 1/6/2017):

10 B barrels      $54      $540 B revenue
------------ * -------- = ----------------
  resource     1 barrel      resource

While a significant amount of that revenue would be involved in paying the costs of exploring and extracting that oil, half a trillion dollars is indeed alot of revenue for an oil producer, and is a significant incentive for the development of this resource.

Human Energy

Putting energy consumption values in the context of what a human can do can be useful for contextualizing the tremendous gift that fossil fuels have been for modern life, as well as the nature of lifestyle changes that may be needed to adapt to the post fossil-fuel world.

While high-performance athletes can work at levels up to 2.5 horsepower for brief spurts, over extended periods, humans can only generate the equivalent of 0.1 to 0.3 horsepower over extended periods:

0.1 to 0.3 horsepower    2,500 BTU      250 to 750 BTU
-------------------- * ------------ = ------------------
     1 human day       1 horsepower      1 human day


 250 to 750 BTU        8 hours     2,000 to 6,000 BTU
------------------- * ---------- = ------------------
1 farm worker hour    1 work day   1 farm worker day


    125,000 BTU        1 farm worker day    21 to 63 days human labor
-------------------- * ------------------ = -------------------------
1 gallon of gasoline   2,000 to 6,000 BTU    per gallon of gasoline!

Going in the other direction, A drive from Spokane, WA to Missoula, MT in a 30 MPG compact sedan is around 200 miles:

     200 miles        1 gallon gasoline       6.7 gallons
------------------- * ----------------- = -------------------
Spokane to Missoula       30 miles        Spokane to Missoula


6.7 gallons gasoline   21 to 63 days human labor   140 to 420 days human labor
-------------------- * ------------------------- = ---------------------------
Spokane to Missoula      1 gallon gasoline             Spokane to Missoula

This does not consider the embedded energy used in the manufacture of the car, construction or maintenance of the highway, etc.

Time-Space Compression

A further consideration should be given to the difference between conversion efficiency and use efficiency. Modern jet airplanes use a tremendous amount of fuel, but they are actually quite efficient in terms of the amount of energy needed to transport a single person for a single mile (passenger-mile).

For example: On a 2011 vacation to Israel, I flew a Boeing 777 between Atlanta and Tel Aviv. On disembarking at both ends, I asked the pilots how much fuel we had used in pounds:

  ATL -> TLV = 240,000 pounds of Jet A fuel
+ TLV -> ATL = 465,000 pounds of Jet A fuel
----------------------------------------------
= 465,000 lbs of fuel


 465,000 lbs fuel    1 ton       233 tons fuel
------------------ * -------- = ------------------
Round trip ATL/TLV   2000 lbs   Round trip ATL/TLV


465,000 lbs-fuel     20,260 BTU   9.42 trillion BTU
------------------ * ---------- = ------------------
Round trip ATL/TLV   1 lb fuel    Round trip ATL/TLV


9.42 trillion BTU        125,000 BTU        75,400 gal gasoline equivalent
------------------ * -------------------- = ------------------------------
Round trip ATL/TLV   1 gallon of gasoline        Round trip ATL/TLV

The trip was a total of around 12,800 statute miles:

12,800 miles 
÷ 75,400 gallons 
----------------------------------------------
0.17 miles-per-gallon-equivalent for a B777

The B777 holds around 300 passengers and both of my flights were full:

300 passengers      12,800 miles      Round trip ATL/TLV     51 passenger-miles
-------------- * ------------------ * ------------------ = ----------------------
  1 Aircraft     Round trip ATL/TLV   75,400 gal gas eq.   1 gallon gas eqivalent

Since the typical compact sedan gets around 30 MPG, taking a B777 is more energy efficient than driving alone in a typical compact sedan.

Time-Space Compression is an alteration of the relationship between space and time asssociated with technological change under capitalism (Harvey 1990, 240 - 307).

Humans generally perceive the length of travel in terms of time (or financial expense) rather than in terms of distance. Technology has permitted humans to harness fossil energy and move very quickly (both on land and in the air), so the perceived distance of my Israel trip was actually quite short. The equivalent trip 300 years ago by sailing ship would have taken weeks and would have been a complex, expensive and dangerous endeavor.

One significant implication of time-space compression is that although developed countries often use energy efficiently in thermodynamic terms, they tend to use more energy in total than developing countries. The flip side of that is the use value of a gallon of diesel to a farmer in the developing world (such as to get crops to a local market) is greater than the use value of that same gallon to an American (who would use that same gallon only to move a truck of lettuce six miles on its way from California). This is referred to as marginal value.