Conversion from Decajoules to Kilocalories

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 Kilocalorie (kcal)

The kilocalorie is a unit of energy equal to 1000 calories, or exactly 4184 joules. Its symbol is kcal. It is the unit in which food energy is counted almost everywhere in the world, whether or not the label actually says so.

The naming is a mess that nobody has been willing to fix. In the United States and much of the English-speaking world, food labels print the word calorie when they mean kilocalorie, sometimes capitalising it as Calorie to mark the difference, a distinction that survives no spoken conversation and few printed ones. Most of Europe avoids the trap by printing kcal explicitly, usually alongside kilojoules.

The figures on a label are not measured by burning the food. They come from the Atwater system, devised in the late nineteenth century, which assigns fixed energy values to the macronutrients: four kilocalories per gram of protein and carbohydrate, nine per gram of fat, and seven per gram of alcohol. The values are averages that ignore how much energy the body actually extracts, which varies with cooking, processing and the individual.

Human requirements sit at a convenient scale. An adult needs roughly 2000 to 2500 kilocalories a day depending on size and activity, a walk of an hour costs around 250, and a kilogram of body fat stores about 7700. That last figure is where the common advice to run a deficit of 500 kilocalories a day to lose half a kilogram a week comes from, though the body adjusts its expenditure and real weight loss is slower than the arithmetic suggests.

Sports science and clinical nutrition use the unit precisely, in indirect calorimetry and in the calculation of basal metabolic rate. Animal feed, hospital nutrition and food manufacturing all specify energy density in kilocalories per hundred grams.

Older chemistry and engineering literature uses the kilocalorie for reaction enthalpies and fuel heating values, where it competes with the kilojoule and requires care in reading.

Exercise figures in the unit are routinely overstated, and the reason is arithmetic rather than dishonesty. A machine that reports 300 kilocalories for half an hour usually counts gross energy expenditure, including the amount the body would have burned sitting still, so the extra attributable to the exercise is smaller. The three macronutrients themselves differ sharply: fat supplies about 9 kilocalories per gram against 4 for protein and carbohydrate, and alcohol falls between at 7, which is why a small change in the fat content of a food moves its figure so much. Understanding those two points explains most of the confusion the unit causes in everyday life.

One kilocalorie equals 1000 calories, 4184 joules, or about 1.162 watt-hours.