Specific Heat Converter — J/(kg·K), BTU, cal and molar

The specific heat converter above handles heat capacity on all three bases that appear in real work: per unit mass, per mole and per unit volume. They describe the same physical property of a material but answer different questions, and moving between them requires the molar mass or the density, which this tool asks for rather than assuming.

Arb Digital publishes this converter as part of a free technical reference library. The BTU and calorie factors are computed from their exact defined values rather than copied from a rounded table, which is why several of them come out as exact whole numbers here where other tools show a trailing rounding error.

What This Specific Heat Converter Does

Specific heat capacity mode covers joules and kilojoules per kilogram kelvin, joules per gram degree Celsius, both calorie flavours per gram degree Celsius, kilocalories per kilogram degree Celsius, both BTU flavours per pound degree Fahrenheit, kilowatt-hours per kilogram kelvin and the foot pound-force form used in some older aerospace work.

Molar mode covers joules and kilojoules per mole kelvin, calories per mole degree Celsius, and BTU per pound-mole degree Fahrenheit. Volumetric mode covers joules, kilojoules and megajoules per cubic metre kelvin, joules per cubic centimetre kelvin, BTU per cubic foot degree Fahrenheit and kilocalories per cubic metre degree Celsius. The fourth supporting panel always shows the value on one of the other bases, computed from the molar mass or density you enter.

How to Use It

1. Choose the basis. A materials datasheet usually quotes per kilogram. A thermodynamics table usually quotes per mole. Building and HVAC work often quotes per cubic metre or per cubic foot.
2. Enter the value and pick the from and to units. The list is filtered to the basis you selected.
3. Set the molar mass in grams per mole if you want to cross between the mass and molar bases. Water is 18.015, iron is 55.845, air is about 28.97.
4. Set the density in kilograms per cubic metre if you want the volumetric basis. This is where the largest surprises live, because gases and solids differ enormously here.
5. Use Swap to reverse the conversion and confirm the factor has been applied in the right direction.

The Formula and How It Is Calculated

Within a basis, conversion is a multiplier chain through the SI unit: result = value × factor(from) ÷ factor(to). Crossing bases uses two simple relationships. Molar heat capacity is specific heat capacity multiplied by the molar mass in kilograms per mole: C_m = c_p × M. Volumetric heat capacity is specific heat capacity multiplied by density: C_v,vol = c_p × ρ.

The defined values that generate the imperial factors are worth stating. The International Table BTU is exactly 1055.05585262 joules, the pound is exactly 0.45359237 kilograms, and a Fahrenheit interval is exactly five ninths of a kelvin. Those three together give one BTU per pound degree Fahrenheit as exactly 4186.8 J/(kg·K). The International Table calorie is exactly 4.1868 joules and a gram is a thousandth of a kilogram, so one calorie per gram degree Celsius is also exactly 4186.8. The two systems land on the same number by design. These definitions come from NIST Special Publication 811, with the underlying units defined in the BIPM SI Brochure.

Two Calories, Two BTUs, and Why It Matters

Both the calorie and the BTU exist in more than one flavour, and the difference is small enough to be invisible in a spot check and large enough to matter in a precise calculation. The thermochemical calorie is exactly 4.184 joules. The International Table calorie is exactly 4.1868 joules. They differ by about 0.07%.

The same split runs through the BTU: the thermochemical BTU is 1054.35026444 joules while the International Table BTU is 1055.05585262 joules. Consequently, one thermochemical calorie per gram degree Celsius is 4184 J/(kg·K) while the International Table version is 4186.8. Chemistry literature generally uses the thermochemical calorie; steam tables and mechanical engineering data generally use the International Table version. This converter offers both explicitly, because silently picking one is how a 0.07% bias enters a calculation and never gets found. Energy units in general are handled by the energy converter.

Mass, Molar and Volumetric: The Same Property, Three Answers

Consider water and iron. Water has a specific heat capacity of about 4187 J/(kg·K) and iron about 449, so per kilogram water stores roughly nine times more heat per degree. On a molar basis the picture reverses: water is about 75.4 J/(mol·K) while iron is about 25.1, a factor of only three, because a mole of water weighs far less than a mole of iron.

The volumetric basis tells a third story that matters most in engineering practice. Water at 998 kg/m³ has a volumetric heat capacity of about 4.18 MJ/(m³·K); iron at 7870 kg/m³ reaches about 3.53. They are nearly equal, which is why iron and water are comparably effective thermal masses per unit space even though their per-kilogram figures differ ninefold. Air, by contrast, has a respectable 1005 J/(kg·K) but a density of only 1.2, giving barely 1.2 kJ/(m³·K), roughly three thousand times worse than water per unit volume. That single ratio explains why water is the working fluid in heating systems and air is not. Densities convert in the density converter.

The Dulong-Petit Pattern in Molar Heat Capacity

One of the most useful sanity checks in thermal work is that most solid elements have a molar heat capacity close to 25 J/(mol·K) at room temperature. Iron is 25.1, copper 24.4, aluminium 24.2, lead 26.4, silver 25.4. The pattern is not a coincidence: classical statistical mechanics predicts three times the gas constant, which is 24.94 J/(mol·K), for a simple crystalline solid.

This gives you a fast plausibility test. Convert a published specific heat to the molar basis with this tool, and if a metallic element comes out far from 25, either the value or the molar mass is wrong. The exceptions are informative too: light, stiffly bonded elements such as carbon as diamond fall well below the rule at room temperature because their vibrational modes are not fully excited until much higher temperatures, and all solids approach zero heat capacity near absolute zero. Molar masses can be calculated from a formula with the molar mass converter.

Constant Pressure Versus Constant Volume

Heat capacity depends on what is held fixed while the material is heated. At constant pressure the substance is allowed to expand and does work against its surroundings, so more heat is needed for the same temperature rise. At constant volume no expansion work is done. The two values are written c_p and c_v.

For solids and liquids the difference is usually under a few percent and is often ignored. For gases it is large and cannot be ignored: for dry air c_p is about 1005 J/(kg·K) and c_v about 718, a ratio of 1.4 that is the familiar heat capacity ratio appearing throughout compressible flow and thermodynamic cycle analysis. Using the wrong one in a gas calculation introduces a 40% error immediately. A unit conversion cannot detect this mistake, so establish which quantity a source is quoting before converting it. Temperature intervals convert in the temperature converter.

Full Heat Capacity Conversion Table

Specific heat capacity, one unit expressed in J/(kg·K):

Molar heat capacity, one unit expressed in J/(mol·K):

Volumetric heat capacity, one unit expressed in J/(m³·K):

Common Mistakes to Avoid

• Mixing thermochemical and International Table calories — they differ by 0.07%, which is invisible in a spot check and real in a precise energy balance.
• Comparing specific heats across materials without checking density — per kilogram water beats iron ninefold, but per cubic metre they are almost equal.
• Using constant-pressure heat capacity in a constant-volume gas calculation — for air that single substitution introduces a 40% error.
• Forgetting that molar heat capacity needs the molar mass — there is no fixed factor between the mass and molar bases.
• Treating a room-temperature value as valid at all temperatures — heat capacity rises with temperature in most materials and falls toward zero near absolute zero.

Related Free Tools From Arb Digital

Thermal calculations use several unit families together. Convert heat quantities in the energy converter, heating rates in the power converter, temperature scales in the temperature converter, sample mass in the weight converter, and material density in the density converter. Conduction is handled by the thermal conductivity converter, formula masses by the molar mass converter, and everything else by the general unit converter.

Frequently Asked Questions

This converter handles units only. Thermal design, energy balances, and safety-related calculations should use property data measured at the relevant temperature and pressure for your specific material.