Find the overall enthalpy change ΔH of a reaction from a set of step reactions using Hess's law, or directly from standard enthalpies of formation — since enthalpy is a state function, both paths agree.
Enter each step reaction's ΔH (kJ). Reverse a step to flip its sign, or scale it with a multiplier, so the steps add up to your target reaction — Hess's law guarantees the sum is the same regardless of path.
Reaction (optional)ΔH (kJ)×Reverse
Default example: forming CO(g) from C(s) + ½O₂(g), built from two combustion steps with the second one reversed — a classic Hess's law problem.
Enter every species in the balanced target reaction with its coefficient and standard enthalpy of formation ΔHf (kJ/mol). ΔH = ΣΔHf(products) − ΣΔHf(reactants).
Some reactions are impossible or impractical to measure directly in a calorimeter — carbon burned in a limited oxygen supply won't stop cleanly at carbon monoxide, for instance, it keeps going to carbon dioxide.
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Walk-through
How to Use This Calculator
4 steps▸
1
Choose a method
Pick the Step Reactions tab if you have a set of known reactions whose ΔH values you want to combine into a target reaction. Pick the Formation Enthalpies tab if you instead have standard enthalpies of formation (ΔHf) for every species in a balanced equation.
2
Fill in step ΔH values, with reverse/multiplier as needed
On the Step Reactions tab, enter each given reaction's ΔH in kJ. If a step needs to run backward to combine into your target reaction, check its Reverse box — that flips the sign of its ΔH. If a step needs to be scaled (for example, doubled to match a coefficient in the target), set its multiplier.
3
Or fill in formation enthalpies for products and reactants
On the Formation Enthalpies tab, list every species on the product side and the reactant side of your balanced target equation with its coefficient and ΔHf (kJ/mol). The calculator subtracts the reactant total from the product total automatically.
4
Read the overall ΔH and its reading
The Result card and the Result tab show the overall ΔH for the reaction along with whether it's exothermic (releases energy, ΔH < 0) or endothermic (absorbs energy, ΔH > 0).
Because enthalpy is a state function, the overall ΔH of a reaction is the same no matter which path of intermediate steps you take to get from reactants to products. So you can add up the ΔH values of any set of reactions that combine — after reversing and/or scaling some of them — into your target reaction. Reversing a step (running it backward) flips the sign of its ΔH; scaling a step by a coefficient scales its ΔH by that same amount.
Formation-enthalpy difference
ΔH = ΣΔHf(products) − ΣΔHf(reactants)
For a balanced equation, the overall enthalpy change equals the sum of the standard enthalpies of formation of the products (each multiplied by its coefficient) minus the same sum for the reactants. Elements in their standard states (like O₂(g) or C(s), graphite) have ΔHf = 0 by definition, since forming an element from itself releases or absorbs no energy.
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Glossary
Key Terms Explained
7 terms▸
Hess's law ↗The principle that the total enthalpy change of a reaction is independent of the path taken — it only depends on the initial and final states. This lets chemists calculate ΔH for reactions that are difficult or dangerous to measure directly, by combining the ΔH values of reactions that are easy to measure.
Enthalpy (H) ↗A thermodynamic quantity representing the total heat content of a system at constant pressure. Enthalpy itself can't be measured directly, but changes in enthalpy (ΔH) during a reaction can be measured calorimetrically.
ΔH (enthalpy change) ↗The heat absorbed or released by a reaction at constant pressure. A negative ΔH means the reaction releases heat (exothermic); a positive ΔH means it absorbs heat (endothermic). Units are typically kJ or kJ/mol.
Formation enthalpy (ΔHf) ↗The enthalpy change when one mole of a compound forms from its elements in their standard states. Tabulated ΔHf values (often written ΔH°f, the standard enthalpy of formation) are the building blocks for the formation-enthalpy method.
Exothermic ↗A reaction with ΔH < 0 — it releases energy (usually as heat) to its surroundings. Combustion reactions are a common example.
Endothermic ↗A reaction with ΔH > 0 — it absorbs energy from its surroundings. Photosynthesis and many dissolution reactions are endothermic.
State function ↗A property that depends only on a system's current state (its composition, temperature, and pressure), not on the path used to reach that state. Enthalpy, along with internal energy and entropy, is a state function — which is exactly why Hess's law works.
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Scenarios
Real-World Examples
3 worked examples▸
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Chemistry student
Finding ΔH for CO formation via two combustion steps
The target reaction C(s) + ½O₂(g) → CO(g) can't be measured directly (carbon tends to burn all the way to CO₂), but it equals Step 1 plus the reverse of Step 2. Reversing Step 2 flips its sign to +283.0 kJ. Sum: −393.5 + 283.0 = −110.5 kJ, which matches the tabulated formation enthalpy of CO — a real, checkable answer.
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Lab technician
Combustion of methane via the formation-enthalpy method
For CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l), ΔH = −965.1 − (−74.8) = −890.3 kJ, the well-known heat of combustion of methane. Because O₂(g) is an element in its standard state, its ΔHf is 0 and drops out of the sum.
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Instructor explaining the reverse rule
Why reversing a step flips its sign
Given: A → B ΔH = −50 kJ (releases 50 kJ)Needed: B → A ΔH = +50 kJ (must absorb the same 50 kJ back)
If forming B from A releases 50 kJ, then converting B back to A must absorb exactly that 50 kJ — energy is conserved along the reverse path. That's why the calculator's Reverse toggle simply multiplies a step's ΔH by −1 rather than recomputing anything.
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Reference
Cite This Calculator
APA & MLA▸
Use either format to cite this calculator in a paper, report, or resource list.
Some reactions are impossible or impractical to measure directly in a calorimeter — carbon burned in a limited oxygen supply won't stop cleanly at carbon monoxide, for instance, it keeps going to carbon dioxide. Hess's law is the tool chemists use to get the ΔH of such reactions anyway, by building them out of reactions that can be measured.
Enthalpy is a state function
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Hess's law follows directly from a single fact: enthalpy depends only on a system's current state — its composition, temperature, and pressure — not on how it got there. That means the total ΔH for going from a set of reactants to a set of products is fixed, regardless of whether the reaction happens in one step or is built out of several intermediate steps. Add up the ΔH of any path between the same start and end points, and you get the same total every time.
Combining steps: reversing and scaling
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To use the step-summation method, you find a set of reactions (usually ones with well-known, measured ΔH values) that can be added together — after some manipulation — to produce your target reaction. Two manipulations are allowed: reversing a step (running it backward), which flips the sign of its ΔH, and scaling a step by a coefficient (to match the stoichiometry of the target), which scales its ΔH by that same coefficient. Once the manipulated steps sum to the target reaction, their manipulated ΔH values sum to the target's ΔH.
The formation-enthalpy shortcut
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Rather than hunting for a chain of measurable reactions every time, chemists have tabulated the standard enthalpy of formation (ΔHf) for thousands of compounds — the ΔH of forming one mole of that compound from its elements in their standard states. Because forming any reaction's reactants and products from elements is itself a valid Hess's law path, ΔH for the overall reaction is simply the sum of the products' ΔHf values (weighted by their coefficients) minus the same sum for the reactants. This is usually the faster method when formation data is available for every species involved.
Where this shows up in practice
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Hess's law underlies how energy content is calculated for fuels, how reaction feasibility is estimated before running an experiment, and how textbooks derive the ΔH of reactions that would be dangerous or slow to measure directly (like partial combustion, or reactions of unstable intermediates). It's one of the first tools students meet for reasoning about thermochemistry without needing a calorimeter for every single reaction.
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Questions
Frequently Asked Questions
6 questions▸
What is Hess's law?+
Hess's law states that the total enthalpy change of a reaction is the same regardless of the path taken, because enthalpy is a state function — it depends only on the initial and final states, not on the intermediate steps. This lets you calculate ΔH for a reaction by summing the ΔH values of a set of steps that combine to the same overall reaction.
How do I reverse a step in the calculator?+
Check the Reverse box on that step's row. Reversing a reaction (running it backward) flips the sign of its ΔH — if the forward reaction releases 50 kJ, the reverse reaction absorbs 50 kJ. The calculator applies this automatically when you toggle Reverse.
What does the multiplier field do?+
It scales that step's ΔH by the given factor, matching how you'd multiply an entire reaction equation (all coefficients and its ΔH) by a constant to line up stoichiometry with your target reaction. For example, doubling a step to supply two moles of a needed intermediate also doubles its ΔH contribution.
How does the formation-enthalpy method work?+
ΔH = ΣΔHf(products) − ΣΔHf(reactants), using each species' standard enthalpy of formation (kJ/mol) multiplied by its coefficient in the balanced equation. Elements in their standard states (like O₂(g) or graphite) have ΔHf = 0 by definition, so they contribute nothing to the sum.
What units does this calculator use?+
ΔH and ΔHf values are entered and reported in kilojoules (kJ) — or kJ/mol for formation enthalpies, which the calculator multiplies by each species' coefficient to get its total contribution in kJ. Make sure any values you look up are consistent (not mixed with kcal or J) before entering them.
What makes a reaction exothermic versus endothermic?+
A reaction is exothermic when its overall ΔH is negative — it releases energy (usually as heat) to its surroundings. It's endothermic when ΔH is positive, meaning it absorbs energy. The calculator labels the result with whichever applies based on the computed overall ΔH.
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