Heat Capacity Calculator

What the heat capacity calculator does

This calculator works out the heat capacity of an object, the energy it takes to raise that whole object's temperature by one degree, from its mass and the specific heat of what it is made of. A substance picker can fill in the specific heat for you from a built-in list of materials.

Below is what heat capacity is, how it differs from specific heat, the equation behind it, and a worked example.

How to use it

1. Enter the mass of the object, with its unit.
2. Enter the specific heat of the material, or pick a substance from the list to fill it in automatically.
3. Press Calculate for the heat capacity, or Reset to clear it.

What heat capacity is

Heat capacity is the amount of energy needed to raise the temperature of a particular object by one degree. Unlike specific heat, which is a property of a material, heat capacity belongs to a specific thing, with a specific size. It answers the practical question: for this actual object, how much heat does one degree of warming cost?

The bigger the object, the more heat it takes, which is why heat capacity depends on how much material is present. A teaspoon of water and a full bathtub of water are the same substance with the same specific heat, but the bathtub has an enormous heat capacity and the teaspoon a tiny one. Heating the bathtub by a degree takes vastly more energy simply because there is so much more of it. Heat capacity captures that total.

Heat capacity versus specific heat

These two ideas are closely related and easy to confuse, so it helps to pin down the difference. Specific heat is per kilogram: it describes the material and is the same whether you have a gram or a tonne of it. Heat capacity is the total for the object in front of you, and it grows with the amount of material.

Think of specific heat as a rate and heat capacity as a bill. The specific heat of water is fixed, the cost per kilogram per degree, but the heat capacity of your particular kettle of water depends on how full the kettle is. To get from one to the other, you multiply the per-kilogram rate by how many kilograms you actually have. That is exactly what this calculator does, turning a material property into a number for a real object.

The equation it uses

Heat capacity, often written C, is the mass m multiplied by the specific heat c of the material:

C = m × c

The more mass you have, or the higher the material's specific heat, the larger the heat capacity. Once you know it, the heat capacity gives you the energy for a temperature change directly: the energy needed is simply the heat capacity times the number of degrees, since the per-degree cost has already been worked out for the whole object. The calculator computes C from the mass and specific heat, taking the latter from your entry or from the substance you select.

Why it is the number that matters in practice

For real objects, heat capacity is often the more useful figure, because it already accounts for how much material there is. If you want to know how long a storage heater will stay warm, how much energy it takes to heat a tank of water, or how well a heavy stone floor will hold the day's warmth into the evening, heat capacity is what you reach for.

It explains why massive things make good thermal stores. A thick masonry wall or a large body of water has a high heat capacity, so it absorbs a lot of heat without its temperature shooting up, then releases that heat slowly as its surroundings cool. This is the principle behind night-storage heating, behind the thermal mass that keeps old stone buildings cool by day and warm by night, and behind using water tanks to bank heat from a boiler. The specific heat sets the material's character; the heat capacity tells you what a given lump of it will actually do.

Units and precision

The calculator works in SI units underneath, with mass in kilograms and specific heat in joules per kilogram per kelvin, giving the heat capacity in joules per kelvin, while the menus offer other mass and energy units including calorie-based and British thermal unit forms. As with specific heat, a degree Celsius and a kelvin are the same size for these purposes. The relationship is exact. Results carry several significant figures.

A worked example

Take 2 kilograms of water, whose specific heat is about 4,184 joules per kilogram per kelvin.

The heat capacity is C = m × c = 2 × 4,184 = 8,368 joules per kelvin. That means every degree of warming for this two-kilogram lot of water costs 8,368 joules. Double the amount of water and the heat capacity doubles too, because there is twice as much to heat, even though the specific heat stays the same.

Questions people ask

How do you calculate heat capacity?

Multiply the object's mass by the specific heat of its material, C = mc. The result is the energy needed to raise that whole object's temperature by one degree.

What is the difference between heat capacity and specific heat?

Specific heat is per kilogram and describes the material; heat capacity is the total for a particular object and grows with its mass. Multiply specific heat by mass to get heat capacity.

Does heat capacity depend on how much material there is?

Yes. More material means more heat capacity. A bathtub of water has a far larger heat capacity than a teaspoon of it, though both share the same specific heat.

Why do heavy objects make good thermal stores?

Because they have a high heat capacity, absorbing a lot of heat without a large temperature rise and releasing it slowly. This is the basis of thermal mass in buildings and storage heaters.

References

A quick note on where the physics comes from. Heat capacity and its relationship to specific heat are standard thermodynamics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The SI units follow the US National Institute of Standards and Technology. The HyperPhysics link is worth a quick click to confirm it lands where you expect.

1. OpenStax, University Physics Volume 2, Section 1.4, Heat Transfer, Specific Heat, and Calorimetry. https://openstax.org/books/university-physics-volume-2/pages/1-4-heat-transfer-specific-heat-and-calorimetry
2. HyperPhysics, Specific Heat and Heat Capacity. http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/spht.html
3. National Institute of Standards and Technology (NIST), Special Publication 811, Guide for the Use of the International System of Units (SI). https://www.nist.gov/pml/special-publication-811