Specific Heat Calculator - Q = m x c x dT in kJ and BTU

The one number that decides how long anything takes to heat

Boiling 1.5 kg of water from 20 to 100 °C takes 502.32 kJ, and a 1.5 kW kettle, which is as much as a 120 V outlet will give you, gets there in 5.58 minutes. Put the same energy into 1.5 kg of copper and it would rise by more than 800 degrees. Same mass, same energy, a different substance, and the whole difference sits in one coefficient called specific heat.

This calculator solves Q = m x c x dT in whichever direction you need it: the heat required, the mass you can heat with the energy you have, the temperature rise a given amount of energy buys, or the coefficient itself from a measurement you made. It takes joules, kilojoules, watt-hours, kilowatt-hours, kilocalories or BTU, kilograms or pounds, Celsius or Fahrenheit, and it will optionally turn the answer into a time if you tell it how powerful your heater is.

Work it in five steps, whichever quantity is missing

Name the quantity you do not have. Heat, mass, temperature change or the specific heat itself. Everything else on the form is the three quantities you do have, and the form hides the field for the one being solved.
Enter the substance. Eighteen of them carry a published figure, from water at 4,186 J/(kg K) down to lead at 128. If yours is not there, take the last entry and type the number off the datasheet, in SI or in BTU/(lb °F).
Enter the mass, in the unit you actually weighed in. Kilograms, grams, metric tons, pounds or ounces. This is the mass of the thing changing temperature, not the pan it sits in and not the tank around it. For water, one liter is one kilogram closely enough for anything this equation is used for.
Enter both temperatures. Celsius or Fahrenheit, both readings on the same scale. Only the span matters, and the calculator converts the span, not the reading: a rise of 90 °F is a rise of 50 K.
Optionally, add the power of your heater. Watts, kilowatts or BTU per hour. The answer then also arrives as a time, computed with nothing lost to the room, so treat it as the floor rather than the estimate.

The same 2 kW into six different jobs

Every row below went through the calculator itself. Two kilowatts is a 240 V appliance: a water heater element, a baseboard heater, a large hotplate. On a 120 V outlet the ceiling is closer to 1.5 kW, which stretches the first row from 4.19 to 5.58 minutes. The times also assume a perfect transfer, which nothing is, so a real kettle takes longer than the figure in the last column and a real room takes much longer.

What is being heated	Mass	Temperature change	Heat	Time at 2 kW
Kettle of water	1.5 kg	20 to 100 °C	502.32 kJ	4.19 min
Cast iron pan	2 kg	20 to 200 °C	161.64 kJ	80.8 s
Air in a small room	60 kg	15 to 22 °C	422.1 kJ	3.52 min
Water heater tank	200 kg	10 to 60 °C	11.63 kWh	5.81 h
Concrete floor slab	500 kg	20 to 60 °C	4.89 kWh	2.44 h
Aluminum block	40 lb	70 to 300 °F	1,971 BTU	17.3 min

The room is the one worth staring at. Warming the air itself takes about three and a half minutes of a 2 kW heater, and yet no 2 kW heater warms a cold room in three and a half minutes. The reason is in the next row down: the floor, the walls and the furniture are hundreds of kilograms of concrete, plaster and wood, and they are what the heat actually has to go into before the air stops giving it away again.

Three problems, worked from the first field to the answer

Solving for the heat. A water heater tank holding 200 kg of water, which is 52.8 US gallons, goes from 10 to 60 °C.
Q = m x c x dT = 200 kg x 4,186 x 50 K = 41,860,000 J, which is 11.63 kWh.
At a 240 V heating element's 3 kW that is 3.88 hours of continuous running, which is why a tank is heated on a schedule rather than on demand, and why tankless units are rated in tens of kilowatts.

Solving for the mass. You have exactly 1 kWh and you want water 40 K warmer. How much water?
m = Q / (c x dT) = 3,600,000 J / (4,186 x 40 K) = 21.5 kg.
One unit of electricity moves about a bucketful of water from the cold faucet to a hot bath temperature. Everything you know about the cost of hot water follows from that one figure.

Solving for the temperature change. The same 100 kJ goes into 2 kg of water and into 2 kg of copper.
Water: dT = 100,000 / (2 x 4,186) = +11.9 K. Copper: dT = 100,000 / (2 x 385) = +129.9 K.
A factor of 10.87, which is the ratio of the two coefficients and nothing else. This is the whole reason a copper pan responds to the burner in seconds and the water in it does not.

Five ways this goes wrong by a whole factor

Using it through a phase change. Q = m c dT describes a substance getting warmer, not one melting or boiling. Turning 1 kg of water at 100 °C into steam at 100 °C takes about 2,260 kJ at constant temperature, which is about four and a half times the 502 kJ that got it from room temperature to boiling in the first place. Ice at 0 °C needs about 334 kJ/kg before it is water at 0 °C. Neither figure is in this equation.

Weighing the container along with the contents. A 2 kg cast iron pan holding 1 kg of water is two separate calculations, not one. The pan takes 161.64 kJ to reach 200 °C, the water takes 335 kJ to reach boiling, and lumping the masses together with either coefficient gives an answer that is wrong in both directions at once.

Converting a Fahrenheit reading instead of a Fahrenheit span. Going from 68 to 212 °F is a span of 144 °F, which is 80 K. Subtracting 32 and multiplying by five ninths on each reading first gives the same answer; doing it to the difference gives 62, and everything downstream is 22 percent low. The calculator converts the span, so type the readings as they are.

Mixing up the calorie and the kilocalorie. The calorie on a nutrition label is a kilocalorie, 4,184 J. The physicist's calorie is a thousandth of that. A figure quoted in "calories" without a capital and without context is worth checking before it goes anywhere near a heat balance.

Treating the answer as a time without allowing for losses. The power line here divides the heat by the power and stops. A kettle is close to that because it is insulated, immersed and quick. A room heater is nowhere near it, because the room leaks heat to the outside the entire time it is warming up.

Specific heat of eighteen substances, in both unit systems

The third column is the share of water's figure, which is the fastest way to see why water is the outlier of the whole table. The fourth is the same coefficient in the unit American equipment is rated in, and it is a straight division by 4,186.8, exact by definition.

Substance	J/(kg K)	Share of water	BTU/(lb °F)
Water	4,186	100.0 %	0.99981
Ethanol	2,440	58.3 %	0.5828
Ice at -10 °C	2,090	49.9 %	0.4992
Steam	2,010	48.0 %	0.4801
Engine oil	2,000	47.8 %	0.4777
Wood	1,700	40.6 %	0.4061
Air	1,005	24.0 %	0.2401
Aluminum	897	21.4 %	0.2142
Concrete	880	21.0 %	0.2102
Glass	840	20.1 %	0.2006
Dry sand	835	19.9 %	0.1994
Soil	800	19.1 %	0.1911
Carbon steel	490	11.7 %	0.1170
Iron	449	10.7 %	0.1072
Copper	385	9.2 %	0.0920
Silver	235	5.6 %	0.0561
Gold	129	3.1 %	0.0308
Lead	128	3.1 %	0.0306

Water reads 0.99981 in the last column and that is not a coincidence. The BTU was defined as the heat that raises one pound of water by one degree Fahrenheit, so water comes out at one by construction, and the last four decimal places are just the modern joule-based definition disagreeing politely with the old one.

Seven questions where the answer turns on the mass

Why does the sand at the beach burn my feet while the sea is freezing?

Sand carries 835 J/(kg K) against water's 4,186, a ratio of 5.01. The same sunshine falling on both raises the temperature of the sand five times as fast, and the water has the further advantage that it circulates, spreading the heat through a depth the sand never mixes into.

How much water will one kilowatt-hour actually heat?

About 21.5 kg through 40 K, which is cold faucet to a comfortable bath. Halve the temperature rise and you double the water: the same unit takes 43 kg up by 20 K. Every argument about the cost of hot water reduces to that one line.

Does specific heat tell me how fast something heats up?

It tells you how much energy the job needs, not how fast the energy gets there. Speed also depends on how well the material conducts heat and how much surface it presents. Copper and aluminum feel fast for both reasons at once: a small c and a very high conductivity. A thick concrete slab has a modest c and terrible conductivity, so it takes hours whichever way you look at it.

Why is the room still cold when the calculator says the air needed four minutes?

Because the air is the smallest part of the room. Sixty kilograms of it takes 422 kJ to go up 7 K, but the plaster, floor and furniture are several hundred kilograms of material at a similar coefficient, and they pull the air back down until they have warmed too. Heat one and you heat all of it, which is also why a warm house stays warm for hours after the heating stops.

Can I use this to work out what an unknown sample is made of?

Roughly, and that is what the fourth mode is for. Put in the heat, the mass and the temperature change and it returns c, then names the closest substance in the table and states the percentage match. Treat a match below ninety percent as a hint rather than an identification: heat lost to the container or the air always pushes the measured coefficient upward, and a phase change ruins the reading entirely.

Is c a constant?

Not exactly. It drifts with temperature, and for water it dips slightly around 35 °C before climbing again toward boiling, a variation of well under one percent across the whole liquid range. Solids vary more over a wide span. For anything you would do in a kitchen, a workshop or a heating system, one figure is good to a couple of percent and the mass you weighed is a bigger source of error.

What about heat capacity per volume rather than per mass?

That is the version storage engineers use, and it changes the ranking. Water at 4,186 J/(kg K) and one metric ton per cubic meter stores about 4.19 MJ per cubic meter per kelvin. Concrete at 880 but 2.4 metric tons per cubic meter stores about 2.11 MJ, closer than the per-kilogram figures suggest. Multiply this calculator's answer by your material's density when the constraint is space rather than weight.

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