Conversion from 3 Decajoules to Calories

Information about the Decajoule (daJ)

The decajoule is a unit of energy equal to ten joules. Its symbol is daJ, and the spelling dekajoule with a k is also accepted. It is the least written of all the joule multiples, not because the quantity is obscure but because deca is the least used prefix in the entire metric system, and understanding that is more useful than memorising the unit itself.

The quantity is one of the easiest in physics to picture. Lifting a one-kilogram bag of sugar by one metre takes 9.81 joules, so almost exactly one decajoule. A heart beats about a joule per stroke, so ten beats. A rifle pellet from an unlicensed air rifle in Britain carries up to 16 joules, or a little over 1.6 decajoules. These are quantities the body understands directly as effort.

Deca survives in ordinary life in only a handful of places, and almost all of them involve mass. In Austria, Poland, Hungary and the Czech lands, delicatessen counters still sell by the dekagram, so a customer asks for twenty deka of ham rather than two hundred grams. The decanewton is used for rope and cable ratings and, in France, for towing capacities, because it happens to be close to the weight of a kilogram.

Elsewhere the prefix simply lost. Engineering standardised on steps of a thousand, which places kilo directly above the base unit and leaves nothing for deca to do that a two-digit number does not already do better. Writing 40 joules is shorter than writing 4 decajoules, and it sorts correctly in a table alongside 400 joules and 4 kilojoules without any mental arithmetic.

The scale itself is worth knowing even under another name, because it is the scale of single human actions. Throwing a ball, closing a heavy door, lifting a full kettle onto a hob, drawing a bow: each of these costs a few tens of joules. Impact tests on packaging and protective equipment are specified here too, and so are the energy limits written into rules for airguns and industrial fastening tools.

When a decajoule appears in a document, converting it takes one step in either direction. Multiply by ten for joules, divide by a hundred for kilojoules. Both forms are exact, and the joule form is the one that will match every other figure in a modern specification.

One decajoule equals 10 joules, about 2.39 calories, or about 0.00278 watt-hours.

Information about the Calorie (cal)

The calorie is a unit of energy equal to 4.184 joules. Its symbol is cal. It was originally defined as the heat needed to raise the temperature of one gram of water by one degree Celsius, and it is not an SI unit, though it survives almost everywhere that food and heat are discussed.

The original definition was awkward because the answer depends on the starting temperature. Water takes slightly more heat to warm from 14.5 to 15.5 degrees than from 19.5 to 20.5, so several competing calories existed: the fifteen-degree calorie, the mean calorie and the International Steam Table calorie among them. The thermochemical calorie now used is simply defined as exactly 4.184 joules, cutting the link to water entirely and ending the ambiguity.

The greater confusion is one of scale. The calorie printed on food packaging in the United States is not this unit at all but the kilocalorie, a thousand times larger, sometimes distinguished by a capital C. A biscuit described as containing sixty calories in fact contains sixty thousand of the unit described here. The convention is entrenched and unlikely to change, so nutritional figures and physical ones must be read in different registers.

Chemistry retained the calorie long after physics moved on. Enthalpies of reaction, bond energies and heats of formation were tabulated in kilocalories per mole for most of the twentieth century, and older literature and some current American textbooks still are. The equivalent SI figure in kilojoules per mole is larger by a factor of 4.184, and misreading which is meant produces errors that look plausible.

Nutrition science uses it because human energy balance happens to sit at a convenient scale in kilocalories, with a daily requirement of around two thousand. In joules the same figure is roughly eight and a half million, which is accurate but harder to reason with.

Air conditioning and refrigeration in some countries still rate capacity in kilocalories per hour, and heating values of fuels appear in calories per gram in older engineering tables.

One calorie equals exactly 4.184 joules, 0.001 kilocalories, or about 0.00116 watt-hours.