| Reference | Joules (J) | Decajoules (daJ) |
|---|---|---|
| One food calorie (kcal) | 4184 J | 418.4 daJ |
| An AA alkaline battery | 10000 J | 1000 daJ |
| Daily adult food intake | 8368000 J | 836800 daJ |
| One unit on an electricity bill | 3600000 J | 360000 daJ |
| A lightning strike | 1 × 109 J | 100000000 daJ |
The joule is the SI unit of energy, work and heat. Its symbol is J. One joule is the work done when a force of one newton moves its point of application through one metre, and equally the energy dissipated when one watt of power flows for one second.
That equivalence is the reason the unit exists. Before the nineteenth century, heat and mechanical work were treated as different things measured in different units, heat in calories and work in foot-pounds. James Prescott Joule spent years demonstrating that a fixed amount of mechanical work always produces the same amount of heat, most famously by stirring water with a paddle wheel driven by falling weights and measuring the temperature rise. Establishing that exchange rate, the mechanical equivalent of heat, unified mechanics and thermodynamics into one subject.
Because it is defined through the base units, the joule connects everything. It is a newton metre, a watt second, a coulomb volt and a kilogram metre squared per second squared, and every one of those forms appears in ordinary use depending on which branch of physics is speaking. Electrical, mechanical, thermal and chemical energy are all counted in the same unit, which is what makes energy accounting across a system possible at all.
The scale is human-sized in a useful way. Lifting an apple one metre takes about one joule. A heartbeat uses roughly one joule. Dropping a textbook from a desk releases about ten. Below that, joules become clumsy and the prefixed units take over; above it, kilojoules and megajoules do the same.
Food energy is properly measured in joules, and labels in Australia, New Zealand and the European Union give kilojoules alongside or instead of calories. The calorie survives in general use mainly through habit, and the conversion, one calorie equal to 4.184 joules, is fixed by definition rather than measured.
Nutrition, ballistics, battery capacity, laser output, explosive yield and the energy released by an earthquake are all quoted in joules or its multiples, which allows quantities from completely different domains to be compared directly.
One joule equals one newton metre, one watt second, about 0.239 calories, or about 0.000278 watt-hours.
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.