How should we measure energy (and power)?

The recent consultation on so-called “calories” on menus, together with the launch of more new models of electric cars has prompted these thoughts on the dysfunctional way in which we measure energy and power. This muddle reflects a lack of understanding of basic science and prevents people from making useful comparisons. We should standardise on the joule (J) and the watt (W).

Consider some of the different units that are or have been used for measuring energy and power (not an exhaustive list):

Energy

  • British Thermal Units (BTU), typically for domestic boilers (although they usually mean BTU/h) – see below
  • kilowatt hours (kWh), for electricity (and sometimes gas) bills
  • joules (J) – the SI unit – used for food energy (nutrition) on package labels
  • calories (cal) (often confused with kilocalories – kcal) also for food energy
  • ergs – an obsolete unit from a previous version of the modern metric system
  • electronvolts (eV) – used by physicists to measure very tiny quantities of energy

Power

  • horsepower (HP) – still sometimes used to describe car engine output
  • brake horsepower (BHP) – now rarely used
  • tax horsepower – formerly used to calculate tax on cars (e.g. Austin 7)
  • Pferdestärke (PS) – a German version of HP for car engines
  • chevaux fiscaux (CV) – similarly, a French version of “tax horsepower” (e.g. Citroën 2CV)
  • watt (W) – the SI unit, defined as a joule per second (J/s)
  • British Thermal Units per hour (BTU/h) – used for heating systems

How – if at all – do all these units relate to each other? To explain this we need to revise a little basic science.

What are energy and power – and how do they relate?

There are various forms of energy (which may be why different measurement units have evolved), but they have one thing in common: energy is what makes things move, or heat, or light up, or make a sound. So it can be thermal (i.e. heat), or electro-magnetic, gravitational, or mechanical etc. But it is all energy. Energy cannot be created or destroyed, but one form of energy can be transformed into another form of energy – e.g. when a turbine generates electricity, which in turn heats a kettle or drives a motor: or when chemical energy stored in a battery is transformed into sound waves from your radio. As it is all basically the same “stuff” – energy – it is helpful if it can be measured in the same way.

Power is the rate at which energy is transformed – e.g. a 60 watt incandescent light bulb converts 60 joules of electrical energy every second into light and heat (mainly the latter by the way). Similarly, it is the rate at which chemical energy stored in petrol is transformed into mechanical energy to drive the car and generate electrical energy to charge its battery. Again, although it can take many forms, it is useful if it can be measured in the same way.

Making comparisons

So if we were to measure energy and power using a single, common unit for each, which units should we choose, and what sort of comparisons would be possible?

For energy, the obvious choice has to be the SI unit, the joule. It has the merit that it is defined in terms of other SI units and does not have to be established experimentally. Energy is in fact “mass × acceleration × distance”, so a joule is defined as the quantity of energy needed to accelerate a mass of one kilogram at a rate of one metre per second squared over a distance of one metre.

All the other possible units listed above have disadvantages. The calorie is the amount of energy required to raise the temperature of 1 g of pure water from 14.5 °C to 15.5 °C at atmospheric pressure of 100 kPa. However, these conditions can only be reproduced in a controlled laboratory situation, and are not generally applicable. Similar objections apply to the British Thermal Unit, which is the amount of energy required to heat one pound of water by one degree Fahrenheit, which also makes it completely incompatible with other SI units. The electronvolt is appropriate for nuclear physics (albeit its value must also be determined experimentally) but it is far too small for normal use.

The “kilowatt hour” (kWh), as seen on electricity and gas bills, is an especially unsatisfactory unit.  As we have seen, a watt is a joule per second. So a kWh is a kilojoule divided by a second multiplied by an hour. There are 3600 seconds in an hour, so a “kilowatt-hour” is in fact 3600 kJ – that is 3.6 MJ.  So wouldn’t it be more sensible to measure the energy contained in electricity or gas in joules – or in this case, megajoules?

Since, as shown above, power is the rate of conversion of energy, the choice of unit for measuring power follows from the choice of unit of energy. “Horsepower”, with all its variants, is not a serious candidate since very few people could actually define it – except to say that an engine with a big number is more powerful than an engine with a small number. “British thermal units per hour” (BTU/h) are unsatisfactory for the same reason as the BTU is unsatisfactory. So it has to be the watt.

Not rocket science

The above relationships are not rocket science, and anybody within the normal intelligence range can easily understand them. So why aren’t they better known and used? I suspect a combination of reasons, such as:

  • inertia – people are comfortable with what they are familiar with – so people carry on using different units to measure the same thing.
  • the media dumb down to the lowest common denominator of understanding.
  • ignorance of basic science (like not being good at maths) is tolerated and even considered fashionable by people who would not admit to ignorance of, say, Charles Dickens or the Battle of Trafalgar.
  • mistaken beliefs that traditional “British” units (such as Fahrenheit!) have cultural value.
  • fear of incomprehension or even ridicule from their peer group if units are used in an unfamiliar context – e.g. kW for measuring a car’s engine power, or metres in cricket or football.

How can these barriers to understanding be overcome? Basically, by increasing familiarity. Much depends on setting a good example – and this will depend on schoolteachers (especially outside the maths or science lesson), politicians (Tony Blair, to his discredit, did great harm by feigning ignorance of kilometres in 2006), broadcasters and journalists, role models in sport and show business. A lead from the Government would also help.

Reverting to the issue of “calories” on menus (which is where this article started from), it is quite deplorable that a Government agency – the Food Standards Agency – should have encouraged extended use of the unsatisfactory unit, the “calorie” (or did they mean “kilocalorie” or indeed “Calorie”?) instead of the proper SI unit, the joule. They even used the word “calorie” as a synonym for “energy”. In doing so, they are promoting ignorance and misunderstanding, and they are failing even to try to educate people to relate the energy they absorb in food and expend in their physical activity to the energy that is so wastefully used in transport, electricity generation and in domestic heating systems – to the detriment of our planet.

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18 Responses to How should we measure energy (and power)?

  1. David Brown says:

    Comparison of different forms of energy is fraught with difficulties. You can’t put sugar in a lightbulb, for example, or eat natural gas. So first you have to consider what comparison you are making – is it the raw energy content, or would you convert to a common form – e.g. electricity – before you do the comparison. It depends on your context. One thing is certain, however: whatever your basis for comparison, using different units only muddies the water. Consistent units are as crucial as context if you’re going to understand the results. For example, an incandescent lightbulb uses about 60 W of electrical energy, so in one 24 hour period it consumes just over 5 MJ. A male human consumes about 10 MJ of chemical energy over a 24 hour period – about the same as 2 lightbulbs. The comparison may be academic (I find it fascinating), but if you work with kWh and calories, you simply can’t make any comparison at all.

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  2. Martin Clutterbuck says:

    Power output for cars in the UK is almost always specified in terms of bhp and torque in ft lb. Could you imagine Jeremy Clarkson saying anything else?
    The latest Volvo S60 petrol engine, however, according to recent advertising, "places a thrilling 304 PS at your command".
    The diesel engine, by the way, delivers "a massive 420 Nm of torque".
    Well if the diesel can be specified in correct SI terminology, why not the petrol version?
    Also... On Volvo's website, for example the V70 1.6D DRIVe (109 PS) has its 'Max Output ECE' shown as '80 kw'.
    Yes they cannot get kW correct but at least power is in kilowatts in the small print specifications. So why not elsewhere?

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  3. A says:

    I think the automotive industry will be the last to adopt SI units and the hardest to convince to use SI units. Non-SI are abundant, frequently used and "understood". People still have trouble relating MPG to their vehicles, some don't even bother and just say how much they pay gets them how far (ie - £10 gets me 90 mi) and I don't think people can really relate to the units either. They are just things that follow numbers and thus they are used to reading, hearing and speaking them.

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  4. philh says:

    If someone said to me "£10 gets me 90 miles" I'd have to ask where from?

    It's no good using price as a measure of economy or consumption because it varies from one petrol station to another.

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  5. Jeremiah says:

    The whole logic behind a plethora of non-related units is precisely so the consumer can not make a comparison. The energy suppliers, such as electric and gas don't want you to know which is more cost effective. If people who use electric heating devices found it was cheaper to use gas devices by a simple comparison, then the electrical industry would lose a large customer base.

    As far as I know, the auto industry world wide is completely metric and has been so since the '70s. Even in the US cars are designed, manufactured and serviced in metric. Unless you have an historical vehicle, all the tools required to service your vehicle will be metric as are all the information on the service specification manuals. Of course, these are mostly hidden from the public.

    The marketing departments of auto companies and dealerships are the ones who dumb-down the metric used behind the scenes for public consumption. Yet, even with that some metric gets through. I haven't heard an engine described in cubic inches in decades. It is always litres now and has been for some time.

    The use of non-metric in marketing most likely only exists in the US and possibly the UK, but nowhere else.

    It seems that energy consumption in US electric vehicles and hybrids are also avoiding the joule. The unit is being adopted is a mix of metric and imperial. The unit is the watt-hour per 100 miles. Watt is a metric unit, hour is a unit common to both metric and imperial and mile is imperial. Of course in metric countries the 100 miles will be replaced by 100 km, thus creating an inability in comparing data between US sources and the rest of the world.

    http://www.pfindexer.org/index.php/Energy_Efficiency:_Mini-e_vs._Aptera_2e

    Energy Efficiency: Mini-e vs. Aptera 2e

    From Pfarner Family Wiki
    Energy Efficiency

    I saw this review [http://kenkuhl.com/mini-e-review.html] of the new electric Mini-e, and wondered how the energy efficiency related to the Aptera 2e.

    Energy efficiency is measured in odd units of kilowatt-hours per 100 miles. It multiplies a power unit (Watt) by a time (hour) without reducing them to an energy unit (some number of Joules), and it mixes metric with imperial units (miles). I might expect MJ/km, but that’s typically going to be less than 1, so maybe kJ/km … but that might as well be J/m. Whatever, it’s what the US is using, and at least the metric units outnumber the imperials. I’ll work in kWhr/100mi below.

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  6. John Steele says:

    A,

    Having worked for one of the US Big Three, let me say that we and all other international auto manufacturers are internally metric, and we would be glad to make cars "all metric." (I don't know about any uniquely British manufacturers, if any are left).

    In general, essentially the same model is offered in inch-pound and metric versions from the POV of the customer (mostly instrument cluster and trip computer). The US requires a miles cluster (by law), Canada requires a kilometers cluster, the UK and the rest of the EU have a similar situation, made more complex by left/right drive.

    In both our US operations (some of which are Canadian) and European operations we made both models in the same plant.

    The drawings that show where to put the marks on the MPH speedo are dimensioned in millimeters, just as on the km/h speedo.

    However, we are NOT going to go out of our way to fight with customers on units. We will design in metric and do graphics and instructions in what they want. First we have to obey local law, second we consider customer preference. For what they pay, we can calculate all the conversions they need. On US cars, the owners manual normally does dimensions and specs in dual. Customers will read the one they like.

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  7. John Steele says:

    Getting back to the original question of kilojoules or nutritional calories for food energy, two points:
    *Food calories are ALWAYS kilocalories or Calories, whether proper notation is used or not, gram-calories are too tiny to be meaningful
    *You may be interested in the following link
    http://www.fao.org/docrep/meeting/009/ae906e/ae906e17.htm

    The organizations responsible for this position paper are the Food and Agriculture Operation and World Health Organization of the UN. The paper is from 1971, so they are doing a great job of meeting their goal of "gradual change." 🙂

    The most interesting point is about half way down the paper. The process of calorimetry and calibration of it is such that the caloric values of food are really determined in joules and converted to calories. The proper inverse conversion factor is the reciprocal of the conversion that screwed up the data originally. If only the unnecessary conversion to Calories could have been avoided in the first place.

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  8. Pat Naughtin says:

    Dear All,

    The metric system unit for measuring energy is the joule.

    Prior to the selection of the unit, joule, by the British Association for the Advancement of Science (BAAS) in 1889 there were many varied, randomly generated and poorly defined words associated with measuring energy.

    For example, there were multiple British Thermal Units and multiple calories that arose because of the many definitions used for these words. These definitions vary wildly according to the whimsy of the definition creators. For example 1 Calorie is 1000 times larger than 1 calorie according to whether the initial letter is an upper C or a lower case c. British Thermal Units and calories also vary with temperature – a calorie at 20 °C is not the same as a calorie at 37 °C for example.

    Many of the old energy words are still in use. I made a collection from news media over a 12 month period. Previous words used in the context of energy measurement included:

    Atomic energy unit, barrel oil equivalent, bboe, billion electron volts, Board of Trade unit, BOE, BOT, brake horsepower-hour, British thermal unit, British thermal unit (16 °C), British thermal unit (4 °C), British thermal unit (international), British thermal unit (ISO), British thermal unit (IT), British thermal unit (mean), British thermal unit (thermal), British thermal unit (thermochemical), British thermal unit-39, British thermal unit-59, British thermal unit-60, British thermal unit-IT, British thermal unit-mean, British thermal unit-th, BThU, BThU-39, BThU-59, BThU-60, BThUIT, BThU-mean, BThU-th, Btu, Btu-39, Btu-59, Btu-60, Btu-IT, Btu-mean, Btu-th, cal, cal-15, cal-20, cal-mean, calorie,Calorie, calorie (16 °C), calorie (20 °C), calorie (4 °C), calorie (diet kilocalorie), calorie (int.), calorie (IT) (International Steam Table), calorie (mean), calorie (thermochemical), calorie-15, Calorie-15, calorie-20, Calorie-20, calorie-IT, Calorie-IT, calorie-mean, Calorie-mean,
    calorie-th, Calorie-th, cal-th, Celsius heat unit, Celsius heat unit (int.), Celsius heat unit-IT, Celsius heat unit-mean, Celsius heat unit-th, centigrade heat unit, centigrade heat unit-mean, centigrade heat unit-th, Chu, Chu-IT, Chu-mean, Chu-th, coulomb volt, cubic centimetre atmospheres, cubic foot atmospheres, cubic metre atmospheres, double Rydberg, duty, dutys, dyne centimetres, E-h, electron mass energy equivalent, electron volt, equivalent volt, erg, eV, foot grains, foot pound, foot pound force, foot poundal, ft-lb, ft-lbf, ft-pdl, gigaelectronvolt, gram calorie, gram calorie-15, gram calorie-20, gram calorie-IT, gram calorie-mean, gram calories (mean), gram calorie-th, grand calorie, grand calorie-15, grand calorie-20, grand calorie-IT, grand calorie mean, grand calorie-th, hartree, Hartree energy, horsepower hours, horsepower hours (metric), inch pound force, Kayser, kcal, kcal-15, kcal-20, kcal-mean, kcal-th, kgfm, kilocalorie, kilocalorie (16 °C), kilocalorie (4 °C), kilocalorie (int.), kilocalorie-15, kilocalorie-20, kilocalorie-IT, kilocalorie-mean, kilocalorie-th, kiloelectronvolt, kilogram calorie, kilogram calorie-15, kilogram calorie-20, kilogram calorie-IT, kilogram calorie-mean, kilogram calories (int.), kilogram calorie-th, kilogram force metre, kiloton TNT equivalent, kilowatt hour, kilowatt minute, kilowatt second, kWh, large calorie, large calorie-15, large calorie-20, large calorie-IT, large calorie (mean), large calorie-th, Latm, latm, litre atmosphere, major calorie, major calorie-15, major calorie-20, major calorie-IT, major calorie-mean, major calorie-th, megaelectronvolt, megaton TNT equivalent, megawatt hours, metric ton oil, metric ton TNT, metric ton coal, micri-erg, natural unit of energy, newton metre, petit calorie, petit calorie-15, petit calorie-20, petit calorie-IT, petit calorie-mean, petit calorieth, Q unit, quad, quadrillion, Rydberg, small calorie, small calorie-15, small calorie-20, small calorie-IT, small caloriemean, small calorie-th, therm, therm (EC), therm (EU), therm (UK), therm (US), thermie (16 °C), ton coal equivalent, ton oil equivalent, ton TNT equivalent, tonne coal equivalent, tonne oil equivalent, tonne TNT equivalent, watt hour, watt minute, and watt second.

    Note that for a journalist or a politician to comprehend all of these 199 old energy words 39 402 conversion factors are needed.

    Cheers,

    Pat Naughtin

    Geelong, Australia

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  9. George Carty says:

    If kilowatt-hours for energy are unsatisfactory, are not kilometres per hour for speed (as opposed to metres per second) also unsatisfactory?

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  10. John Steele says:

    Depends on what calculation is being carried out. If you wish to utilize the coherent properties of the SI, km/h and kWh are poor unit choices. For many engineering calculations, they will need to be converted to meters per second and joules.

    However, for estimating how long it will take to drive somewhere, kilometers per hour is quite useful. For estimating impact on your electric bill, watts times hours makes a certain amount of sense too. The kilowatt hour is deeply seated in the electric industry; we may have to settle for it there and strive to prevent its expansion.

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  11. philh says:

    Kilowatt-hours are a roundabout way of measuring energy. It's like measuring distance as metres per second-seconds.
    Kilometres per hour is at least a direct measurement of speed even if not based on pure SI units.

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  12. Incandescent light bulbs will soon be phased out because they waste a lot of energy.

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  13. Philip says:

    The “kilowatt hour” (kWh) is used on electricity and gas bills in the UK, what unit is used in European Countries? And what is used in Australia, and New Zealand?
    Which countries measure domestic electricity or gas use in SI units in this case, megajoules?

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  14. Henry says:

    Full marks to the Wellcome Trust; in their publication 'Big Picture' issue 14, deals with food and diet. On page 3:
    DAILY ENERGY REQUIREMENTS in megajoules (MJ)
    Baby girl 2.2
    Baby boy 2.4
    Teenage girl 9.9
    Teenage boy 11.7
    Woman 8.8
    Man 11.0
    Expectant mother 9.6
    Breast-feeding mother 10.3
    Olympic swimmer 48
    ============
    and on page 5, in terms of approximate energy content:
    One burger = Six times one Iceberg lettuce

    The publication is available free from the Wellcome Trust
    see: www.wellcome.ac.uk/bigpicture/order and freepost address in the UK
    Big Picture series,
    Wellcome Trust, FREEPOST RSHU-ZJKL-LCZK, Feltham, TW14 0RN

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  15. Mary says:

    1. Andrew Landsley MP (Secretary of State for Heath), should look at this Wellcome Trust publication.
    He is the UK Cabinet Minister who wants restaurants and food outlets to include 'Calories' on menus. It's time he 'shed calories' and used proper energy units!
    2. Anne Milton MP should do the same - she is the Parliamentary Under Secretary of State for Public Health, in her portfolio is 'Food, diet and nutrition'.

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  16. BrianAC says:

    The kWh is used for electricity in France certainly and I believe that to be universal globally, except in UK they perversely continue to use the totally meaningless 'unit' which is 1 kWh. In France (EU?) gas appliances are also rated in kW enabling a simple and direct comparison between gas and electric usage. Likewise engine power is also in kW. What I am finding hard to take (in UK) is the media usage of 'homes' for electrical power. It sames to me '1 home equals 1.3 kW'. Anyone care to explain that irrational 'logic'?

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  17. John Steele says:

    @BrianAC

    The American media also loves the "homes" analogy for what a power plant can power.

    Obviously it is possible to calculate a home's avergae usage in kilowatts (take kilowatt-hours for any period, divide by the hours in the period).

    Our media particularly loves to use it in misleading ways. They take the nameplate capacity of a wind turbine or solar system (which is max rated power, not average), disregard the capacity factor (sometimes there is little or no wind, or it is dark or cloudy), and assume the plant always outputs max. power and powers a representative number of homes. Typically, these issues will limit "renewables" plants to about 20-30% of their nameplate capacity, which is fine if the implications are correctly thought out.

    Also ignored is the home's load factor. You don't use "average" 24/7. Household usage has peaks and valleys. Some average out, but typically everybody has a peak around dinnertime (just as the sun goes down and the wind calms). Much more serious analysis is required to assess what the plant can really power.

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  18. philh says:

    Interesting to note the use of kilojoules on the Weight Watchers web site for Australia and New Zealand:

    http://www.weightwatchers.com.au/util/art/index_art.aspx?tabnum=1&art_id=30991

    Slightly concerned though that they fall into the same trap as users of the calorie, i.e. use it as a synonym for energy and describe it as though it originated in food science:

    "The common term for this used to be 'calorie'. By definition, a calorie (technically called a kilocalorie or kcal) is the amount of heat required to raise 1 gram of water 1 degree Centigrade. One calorie has the same energy value as 4.186 kilojoules which is now the term accepted internationally. Kilojoules quantify the fuel energy that is available from food and measure the heat output that comes from metabolism, which is the number of kilojoules the body burns. "

    It really should have been made clear that the joule is a measure of energy regardless of the form it takes. For example the following paragraph ...

    "Resting metabolism is the kilojoules used to keep all systems going day in and day out; it is the kilojoules burned by the brain, heart, kidneys and all organs and cells in the body. About two-thirds to three-quarters of the kilojoules we burn every day are accounted for in resting metabolism. "

    ... would better describe the concept if the word 'energy' were used in place of 'kilojoules' as follows:

    Resting metabolism is the energy used to keep all systems going day in and day out; it is the energy burned by the brain, heart, kidneys and all organs and cells in the body. About two-thirds to three-quarters of the energy we burn every day are accounted for in resting metabolism.

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