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non-si · exactly 4.184 j
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cal SYMBOL PLATE 4.184 J 1 g H₂O 14.5 → 15.5 °C ISO 80000-5
What the plate shows

In a vessel of water stands a sealed steel bomb, and inside it, from time to time, a sample flares up: an orange halo spreads around it, and bubbles of different sizes rise through the water from the bottom, each at its own pace. The surface of the water breathes, the thermometer column on the right climbs after the flash and reaches the yellow mark, and along the scale below the reading marker runs from edge to edge.

Unit passport
Non-SI · kept for nutrition sheet 1/1 · rev. 2026-09

Calorie cal · kcal

Non-SI unit · quantity: energy · exactly 4.184 joules

The unit we eat

The number on a packet of biscuits looks like the result of a measurement, but no measurement took place. Nobody burned those biscuits in a calorimeter: someone took the protein, fat and carbohydrate content, multiplied by four, nine and four, added it up — and printed it. The factors were chosen by the American chemist Wilbur Atwater at the end of the nineteenth century, by comparing how much energy in food is released by fire and how much is left to a person once digestion and the kidneys have taken their share.

The difference between these two numbers is no trifle. Dry egg white in a steel bomb gives about five point seven kilocalories per gram, whereas the body receives roughly four, because nitrogen leaves with urea without burning completely. Fibre burns in the bomb as well as sugar does, yet in the gut it is barely half absorbed, and even that by other hands — the work of bacteria — which is why European rules assign it only two kilocalories per gram.

The unit itself comes from an age when heat was thought to be a substance: the calorie meant the amount of 'caloric' needed to warm a gram of water by one degree. The substance was never found, the theory collapsed, but the unit survived because it proved a convenient measure in experiments with water, and in the end it was defined simply as a number of joules — four point one eight four, with no mention of water at all.

Notationcal · kcal (Cal)
Valueexactly 4.184 J · 1 kcal = 4.184 kJ
Originwarming a gram of water by one degree
On the label4 · 9 · 4 kcal/g — protein, fat, carbohydrate
SourceISO 80000-5 · Codex Alimentarius · EU Regulation 1169/2011
Translations ready36 / 36
To the conversion To the historical section
Register

Lowercase cal is the small calorie, while the capitalised Cal in American books on nutrition means the kilocalorie, exactly a thousand times more, so that the same letter differs by three orders of magnitude from one edition to another. In technical writing it is safest to write kcal, without a full stop, and to keep 'calorie content' for a property of the food rather than the name of the unit.

Do not confuse

There is more than one calorie, and they are not equal: the thermochemical calorie is exactly four point one eight four joules, the international one four point one eight six eight, and the fifteen-degree calorie is defined through an actual experiment with water. Besides, the number on a label is obtained not in a calorimeter but by calculation, and the unit itself has long been displaced by the joule everywhere except the kitchen.

01 · Definition
a gram of water per degree · the bomb · Atwater's corrections

Historically the calorie is the quantity of heat that warms a gram of water by one degree Celsius, and the definition proved shaky, because the heat capacity of water itself depends on temperature. Hence several calories at once: the fifteen-degree one, counted from the interval between fourteen and a half and fifteen and a half degrees, the international steam-table calorie, and the thermochemical one, which in the end was simply set equal to four point one eight four joules.

That definition is final, and the water experiment remains only a reminder of where the unit came from. It is convenient, though, because the simple relation survived: one kilocalorie still warms a kilogram of water by about a degree, so any food figure is easy to turn into a picture — a can of sugary soda poured into a kettle would bring a litre of water almost to the boil.

Food is harder, because a person is not a furnace. In a steel bomb under thirty atmospheres of oxygen everything burns without residue, whereas in the body part of the energy leaves undigested, part is spent on absorption itself and part leaves with nitrogen compounds. Atwater measured these losses on people in a respiration chamber and derived factors that have hardly changed since: four kilocalories per gram of protein, nine per gram of fat, four per gram of carbohydrate, seven per gram of ethanol.

Later it turned out that even these numbers are averaged too far. Almonds counted by the label give about six kilocalories per gram, but measured on people roughly four point six, because the fat is locked inside cell walls and part of it passes straight through; for whole nuts and pulses the gap reaches a quarter. The unit is not to blame — it counts joules honestly — but the way it is applied to food remains an approximation that the packet does not mention.

4.184 J
in one calorie — exactly, by definition
4 · 9 · 4
kcal per gram of protein, fat and carbohydrate
1 kcal
warms a litre of water by one degree
Calorimeter ·
what the fire released what the body will get rise in water temperature bubbles in the jacket
left: bomb in water, thermometer to the right of the vessel right: two energy columns, kcal
released in the bomb
credited to the body by Atwater
the water warms this much
gap between fire and digestion

Interactive · fire counts more generously than the gut

Why the bomb always overstates

On the left the sample lies in a steel bomb lowered into water: at the flash a flame spreads around it, the water bubbles at the walls, and the thermometer column creeps up exactly as far as the released heat allows for the amount of water poured into the jacket. On the right the same thing is laid out in two columns: the full heat of combustion and the part of it that the Atwater factors credit to a person, and for protein and nuts the gap is visible at once. Change the sample mass and the amount of water: the energy does not depend on the water, but the temperature rise very much does, and that is the whole trick of the measurement.

Q — heat · m — mass · c — specific heat capacity · ΔT — temperature rise · C — calorimeter constant · P, F, C — grams of protein, fat and carbohydrate
Definition
1 cal = 4.184 J exactly
The water experiment
Q = c · m · ΔT, heat capacity of water ≈ 1 cal/(g·K)
Heat from the calorimeter
Q = C of the calorimeter · ΔT
The label by Atwater
E in kcal = 4·P + 9·F + 4·C + 2·fibre
Kilocalories to kilojoules
E in kJ = 4.184 · E in kcal
A tonne of TNT
1 t TNT = 10⁹ cal = 4.184 GJ
The first line is the definition in joules, the second is the very water experiment the unit came from. The third shows how heat is counted in a real calorimeter, where not only the water warms but also the steel vessel and the stirrer, so the instrument constant is found beforehand with reference benzoic acid. The fourth is the label calculation, the fifth converts kilocalories to kilojoules, which Europe prints alongside, and the sixth is a reminder that the tonne of TNT is defined through that same calorie.
02 · Conversion
energy · plate · movement

One energy in three conversations

The first tab spreads the number you enter across units of energy. The second turns it into food: how many grams of fat, sugar or protein that is and what share of the daily ration. The third answers the question asked more often than any other — how much you have to move to use it up.

A rule to remember: a kilocalorie is a little over four kilojoules, and a kilojoule is about a quarter of a kilocalorie.

Careful

The movement lines are calculated for a person weighing seventy kilograms and are good only for the order of magnitude: expenditure depends on body mass, fitness and pace, and part of what is eaten the body spends on digestion itself. The precision here is illusory, and rounding such numbers to tenths is pointless.

Conversion table
QuantityValueNote
03 · Orders of magnitude · what is measured in calories

04 · Measuring instruments
ice calorimeter · bomb · chamber · mask

Four ways to catch heat

LAVOISIER AND LAPLACE'S ICE CALORIMETER
the meltwater is collected in a beaker and weighed

An instrument that measured with ice

Lavoisier and Laplace placed a source of heat in a cavity surrounded by ice and, instead of a thermometer, weighed the water that ran off the melting shell, since melting each gram of ice takes a strictly fixed amount of heat. In this machine, in the winter of seventeen eighty-two, they kept a guinea pig to find out how much heat living respiration gives off, and obtained a value close to the heat of burning charcoal — the origin of the view of respiration as slow combustion.

they measured not degrees but the weight of meltwater
BOMB CALORIMETER · 30 ATMOSPHERES OF OXYGEN the instrument constant is found with benzoic acid, 26.43 kJ/g

A steel bomb in a bucket of water

A sample of a fraction of a gram is ignited by a wire inside a thick-walled vessel filled with pure oxygen, and all the heat released goes into the surrounding water, whose temperature is read to thousandths of a degree. The instrument does not know what exactly was burned — a biscuit, coal or paper — and so gives the full heat of combustion, the one a person never receives in full. The calorimeter constant is determined beforehand with benzoic acid, whose heat of combustion is taken as the reference.

an honest number, but not about a person
RESPIRATION CHAMBER · A PERSON UNDER OBSERVATION oxygen in carbon dioxide out

A room that measures a person

Atwater built an airtight chamber in which a volunteer lived for days, and measured everything: what was eaten, breathed out, excreted, and the heat given off. It was from these experiments that the factors four, nine and four came, and with them the first reliable confirmation that the law of conservation of energy holds in a human being too. Today's chambers do the same, but count energy not from heat but from gas exchange, because the ratio of oxygen taken in to carbon dioxide breathed out reveals what exactly the body is burning at that minute.

energy counted from breathing
WEARABLE SENSOR · AN ESTIMATE FROM PULSE AND STEPS the expenditure curve is built from a model, not from a measurement of heat

A bracelet that measures nothing

A fitness tracker sees neither oxygen nor heat; it reads pulse and accelerations and feeds them into a regression built on other people, so its number is not a measurement but an estimate with a spread of tens of percent. Comparisons with a respiration chamber show that such devices catch heart rate reasonably well and energy expenditure poorly, and the error grows exactly where the user is most interested: in strength work and at rest. They are best used like scales that show a trend, not like an instrument.

an estimate instead of a measurement
05 · Writing rules
cal and Cal · kcal · kJ side by side

One letter worth a thousand

Almost all the mistakes here come from confusing the small calorie with the kilocalorie, and in writing about nutrition such a slip costs three orders of magnitude.

Correct
250 kcal (1046 kJ)
1 cal = 4.184 J
energy value per 100 g
daily intake 2000 kcal
fat 9 kcal/g, protein and carbohydrate 4 each
1 t TNT = 10⁹ cal
Incorrect
an apple has 52 cal
250 Cal — a thousand or one?
1 kcal = 4.2 kJ in a calculation
burned 300 cal on a run
KCal · CAL · kcal.
energy value 500 cal per 100 g

The first and fourth lines confuse the small calorie with the kilocalorie, and so promise that an apple will warm fifty-two grams of water by a degree, when in fact it will warm fifty-two litres. The second is ambiguous by its very notation, so in scientific writing the capitalised Cal is best not used at all. The third saves on the factor where it shows: rounding to four point two adds a third of a percent, and in the balance of a large study such a trifle surfaces. The fifth mangles a symbol that is written in lower case and without a full stop, and the sixth combines both troubles at once, promising the food the calorific value of wet paper.

06 · Neighbouring units
joule · kilowatt-hour · British thermal unit

All the calorie's neighbours are the same energy, only measured out for different purposes: the joule came from mechanics, the kilowatt-hour from the electricity meter, the British thermal unit from heating, and the calorie from the water experiment. There is nothing between them but factors, and only the habits of an industry tell them apart.

J 0.239 cal
Joule

The unit of the system through which the calorie is now defined: the work of a force of one newton over a path of one metre, which is also heat, which is also the energy of an electron in a field.

kWh 860 kcal
Kilowatt-hour

The unit of the meter: it holds as much energy as three hearty dinners, and the comparison sobers anyone who makes it for the first time.

BTU 0.252 kcal
British thermal unit

Exactly the same idea as the calorie, but with a pound of water and a degree Fahrenheit; it lives in the specifications of air conditioners and boilers.

Calorie in joules
1 cal = 4.184 J
Kilowatt-hour in kilocalories
1 kW·h = 860.42 kcal
British thermal unit
1 BTU = 0.252 kcal

Among the Simetrium data sheets, standing nearby are kilowatt-hour and horsepower: both arose not from theory but from trade — one for the electricity bill, the other to explain the gain of the steam engine — and both, like the calorie, outlived the system that was meant to replace them.

07 · Historical section
archive · from caloric to the label

How a vanished substance stayed on the packet

KCAL PER GRAM · SCALE FROM ZERO FatProteinCarbohydrateFibre 9.49.0 5.654.0 4.14.0 4.12.0 upper bar — fire in the bomb lower — credited to a person 18 px per kilocalorie, common zero on the axis
where fire is more generous than digestion

For fat the gap is small, for protein it reaches a third, and fibre is credited under European rules with exactly half of what it gives to the fire.

Metrological note

A unit without a standard and without a claim to precision

ENERGY 1046 kJ 250 kcal fat 12 g protein 6 g LABEL UNDER THE EU REGULATION
the number was calculated

The calorie has no standard and cannot have one, because from the start it is not an independent quantity but the joule on another scale, and all that can be verified are the instruments that measure heat. The bomb calorimeter is verified with benzoic acid, the respiration chamber by burning a known quantity of alcohol right inside it, but the number on the packet is verified by nobody, because it is calculated, not measured.

Hence the unit's strange status. In physics it has been displaced for good: thermal calculations are done in joules, and the calorie survives only in old tables and in the definition of the tonne of TNT, which by convention equals exactly a billion calories. In nutrition, though, it holds as firmly as can be, because numbers in the four-kilojoule range feel unfamiliar, while the scale of 'two thousand a day' has taken root in everyday life as firmly as the degree Celsius.

One need only remember that the precision of these numbers is not what it seems. The law allows the energy value to differ from the declared one by a fifth, the composition of a food varies from batch to batch, the Atwater factors are averaged over all foods at once, and absorption depends also on whether the food is ground and what is eaten with it. The unit is not to blame: it counts joules honestly, but the arithmetic that applies it remains an approximation, and expecting a third significant figure from it is like measuring height by a shadow.

4.184 J THE HEAT GOES INTO THE WATER
the instrument is verified, not the unit
Catalogue of quantities
energy, heat and metabolism

SI base units

kilogram, metre and second are highlighted — the joule is built from them

What is on the plate and what it costs in movement

all columns are calculated from composition, not typed in
ServingkcalkJShare WalkingRunning

The last two columns explain why the 'eat it and work it off' calculation almost never adds up: you can eat a thousand kilocalories in ten minutes, but using them up by movement takes several hours, so eating and physical work are incomparable in speed, even though they are measured in one unit. Besides, the body at rest spends most of its daily energy by itself, on breathing, circulation and keeping warm, so movement adds less to that than people tend to think.

08 · Your language
every link is a real page in that locale

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