Enthalpy is defined as internal energy plus the product of pressure and volume: H = U + pV. It is a bookkeeping device, invented because most chemistry and most engineering happens in vessels open to the atmosphere, where a reacting system that expands has to push the surrounding air out of the way. That pushing costs energy which never appears as heat, and enthalpy is the quantity that accounts for it automatically so nobody has to track expansion work by hand.
This calculator works the definition in three directions: absolute enthalpy from internal energy, pressure and volume; enthalpy change from a change in internal energy plus expansion work; and enthalpy change from heat measured at constant pressure. Arb Digital publishes it as the missing input step for thermochemistry, because most of the tools that need an enthalpy value expect you to already have one.
What This Enthalpy Calculator Does
The first mode applies H = U + pV directly. Give it an internal energy in kilojoules, a pressure in kilopascals and a volume in cubic metres, and it returns the enthalpy of the state along with the size of the pV term on its own, which is usually more revealing than the total.
The second mode computes ΔH = ΔU + pΔV for a process at constant pressure. This is the one that makes the sign conventions bite: a system that expands does work on its surroundings, so ΔV is positive and the enthalpy change exceeds the internal energy change; a compression reverses it.
The third mode uses the central practical result of the whole subject — that heat exchanged at constant pressure is the enthalpy change, qp = ΔH. It takes a mass, a specific heat capacity and a temperature change, computes the heat, and reports it as an enthalpy change. Every mode also divides by the amount of substance to give a molar figure, because that is the form in which enthalpies are tabulated and the form the rest of thermochemistry expects.
How to Use It
- Choose the mode that matches what you actually measured. If you have a calorimeter reading, use the third mode. If you have state variables from a table, use the first. If you are tracking a process, use the second.
- Watch the units on pressure and volume. The tool takes kilopascals and cubic metres, which multiply to kilojoules directly — a pascal times a cubic metre is a joule, so the kilo prefixes carry through cleanly.
- Keep the sign on ΔV and ΔT. A compression has a negative volume change and a cooling has a negative temperature change. Entering magnitudes only will give you the right size and the wrong direction.
- Enter the amount of substance if you want a molar value. Two moles of a reaction releasing 200 kJ is −100 kJ/mol, and it is the molar figure that can be compared against a data table.
- Read the thermal character before anything else. Exothermic means the system released energy and carries a negative enthalpy change. Getting the sign right matters more than getting the third decimal place right.
The Formula: Why pV Is There at All
Start with the first law: ΔU = q + w, where w is work done on the system. For a system expanding against a constant external pressure, that work is −pΔV. Rearranging gives qp = ΔU + pΔV, and the right-hand side is precisely the change in the quantity U + pV. Define H = U + pV and you have qp = ΔH. The whole construction exists so that one measurable — heat in an open vessel — maps onto one state function.
Work the defaults. Internal energy 100 kJ, pressure 101.325 kPa, volume 0.500 m³. The pV term is 101.325 kPa × 0.500 m³ = 50.66 kJ, so H = 100 + 50.66 = 150.66 kJ. At two moles that is 75.33 kJ/mol. Expressed in the thermochemical kilocalorie, defined as exactly 4.184 kJ in the conversion tables of NIST Special Publication 811, it is 36.01 kcal.
For an ideal gas the pV term has a simpler form still, since pV = nRT with R the molar gas constant, exactly 8.314462618 J mol−1 K−1 in the 2022 CODATA set. That is why gas-phase reactions have ΔH = ΔU + ΔngasRT: only the change in the number of gas molecules matters, and a reaction with no change in gas moles has an enthalpy change equal to its internal energy change.
Where This Sits Next to Our Gibbs and Calorimetry Tools
Arb Digital publishes two neighbouring thermodynamics tools and the boundaries are clean. The Gibbs free energy calculator solves ΔG = ΔH − TΔS, and it treats ΔH as something you already have — typically looked up from a table. This page is where that ΔH comes from. If you are trying to decide whether a reaction is spontaneous, you need both pages in sequence: this one to get the enthalpy change, that one to weigh it against the entropy term.
The calorimetry calculator solves a different problem: two substances at different temperatures reaching thermal equilibrium, where the unknown is the final temperature. It balances heat between bodies. This page takes a known temperature change and converts the heat into an enthalpy change with a molar value attached. One finds the temperature; the other interprets the energy thermodynamically.
For the heat side alone, without any enthalpy interpretation, the specific heat calculator handles q = mcΔT on its own terms.
Constant Pressure Versus Constant Volume: Why Two Numbers Exist
Burn a fuel in a sealed steel bomb and the volume cannot change. No expansion work is done, so all the released energy appears as heat and what you measure is ΔU, the internal energy change. Burn the same fuel in an open dish and the hot gases expand against the atmosphere, spending some energy on pushing air aside, so the heat you measure is smaller in magnitude. That measurement is ΔH.
This is why combustion data sometimes appears with two slightly different values for the same fuel, and why the difference is nearly always small. For a typical hydrocarbon the gap is a fraction of a per cent, because chemical bond energies are enormous compared with the work of shoving some air out of the way. Small does not mean zero, and precise thermochemistry always states which condition applies.
The gap becomes significant only when the number of gas molecules changes a lot. A reaction that consumes several moles of gas and produces none has a substantial ΔngasRT term, and confusing ΔU with ΔH there produces a real error rather than a rounding one.
Absolute Enthalpy Is Not Measurable — Only Changes Are
The first mode returns a number for H, and it is worth being honest about what that number is. Internal energy has no natural zero: there is no experiment that reads out the absolute internal energy of a substance, because that would require accounting for every form of energy down to nuclear binding. Since H is built on U, absolute enthalpy inherits the same problem.
Chemistry works around this by declaring a convention: the standard enthalpy of formation of any element in its most stable form at 298.15 K and 1 bar is defined to be zero. Every tabulated enthalpy of formation, including the extensive thermochemical data in the NIST Chemistry WebBook, is a change measured relative to that reference, not an absolute quantity.
The practical upshot is that the first mode is most useful for seeing the relative size of the pV contribution against U, and the second and third modes are the ones that produce numbers you can compare with published data. Enthalpy changes are real and measurable; absolute enthalpy is a bookkeeping entry whose zero someone chose.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Calling enthalpy "heat content" — heat is energy in transit, not something a system stores. Enthalpy equals heat only under the constant-pressure condition, and calling it heat content hides that requirement.
- Dropping the sign — a negative enthalpy change means energy left the system. An exothermic reaction quoted as positive reverses the physical meaning entirely.
- Mixing pressure and volume units — kilopascals with cubic metres give kilojoules. Bars with litres do not, and the resulting pV term can be out by orders of magnitude.
- Using a bomb calorimeter value as an enthalpy change — a sealed vessel measures internal energy change. Converting to enthalpy requires adding the gas-mole term.
- Forgetting to divide by moles before comparing to a table — tabulated values are per mole. A total in kilojoules cannot be checked against them until it is scaled by the amount of substance.
Related Free Tools From Arb Digital
To take an enthalpy change through to spontaneity, use the Gibbs free energy calculator. For equilibrium temperatures when two substances are mixed, use the calorimetry calculator, and for the underlying heat equation the specific heat calculator. Gas-state relationships behind the pV term are covered by the ideal gas law calculator and the pressure calculator. To move between joules, calories and kilowatt-hours, use the energy converter. Everything Arb Digital publishes is listed on the free online tools hub.
Frequently Asked Questions
Enthalpy is defined as H = U + pV, where U is internal energy, p is pressure and V is volume. For a process at constant pressure the change is the change in internal energy plus the pressure multiplied by the volume change.
No. Heat is energy in transit and enthalpy is a state function of the system. They happen to be numerically equal for a process at constant pressure, which is why chemists use enthalpy, but the equality fails at constant volume where heat measures the internal energy change instead.
Because the sign is taken from the system's point of view. An exothermic reaction releases energy to its surroundings, so the system's enthalpy falls and the change is negative. Endothermic reactions absorb energy and have a positive enthalpy change.
Delta U is the internal energy change, measured at constant volume where no expansion work is done. Delta H adds the pressure-volume work of expanding against the surroundings. For gas reactions the difference is the change in the number of gas moles multiplied by R and the temperature.
No. Internal energy has no natural zero, so neither does enthalpy. Chemistry uses a convention instead, defining the standard enthalpy of formation of every element in its most stable state as zero, and all tabulated values are changes relative to that reference.
The Gibbs calculator takes an enthalpy change as an input and combines it with entropy and temperature to judge spontaneity. This page produces the enthalpy change in the first place, from state variables or from heat measured at constant pressure.
Kilopascals and cubic metres, which is what this tool expects. A pascal multiplied by a cubic metre is exactly one joule, so kilopascals times cubic metres gives kilojoules with no conversion factor needed anywhere in the calculation.
This tool is provided for educational and study use. It applies idealised constant-pressure thermodynamics, assumes specific heat is constant over the temperature range entered, and ignores phase changes, which absorb or release energy without any temperature change at all.
