Turnover number & frequency calculator.

The Turnover Number (TON) is the total number of moles of product formed per mole of catalyst over the full course of a reaction. It is the definitive measure of how much work a catalyst does before it is deactivated or consumed: a catalyst with a TON of 10,000 converts ten thousand times its own molar quantity into product. The Turnover Frequency (TOF) normalises TON by reaction time, giving the rate of catalytic turnover in units of h⁻¹, and is used to compare the intrinsic activity of different catalyst systems under comparable conditions.

The formulae

TON uses the actual moles of product isolated, not the theoretical maximum. If catalyst loading is reported as a mol% of substrate, convert: \(n_{\text{catalyst}} = \text{mol\%} \times n_{\text{limiting reagent}} / 100\). TOF is meaningful only when measured at a defined conversion, ideally under initial-rate conditions; the value reported here is an average TOF over the full reaction time.

Report conditions alongside TON and TOF

TON, and especially TOF, are strongly condition-dependent. The same catalyst can give very different numbers depending on how and under what conditions it was measured. Reported values can shift substantially with temperature, the concentrations of substrate, catalyst, and additives, solvent, pressure (for gas-phase reactants), the level of conversion at which the measurement is taken, whether the value is an initial rate or an average over the whole reaction, the physical form of the catalyst (homogeneous complex, nanoparticle, supported, or enzyme), and the presence of inhibitors, poisons, or deactivation pathways. A TON or TOF quoted without this context is close to meaningless for comparison, so always report the conditions alongside the number.

Strengths and limitations

Academic discourse: is TOF even a well-defined quantity?

The definitions above are not as settled as textbooks make them sound. Kozuch and Martin (2012) proposed standardised versions, TOF° and TON°, measured at a hypothetical 1 M concentration and 273.15 K, arguing by analogy with thermodynamic standard states (ΔG°, K°) that catalysts cannot be fairly compared unless the reaction conditions are normalised away.

Lente (2013) pushed back on some of the proposals made in a published comment. Borrowing the concept of a standard state from thermodynamics is, in Lente's view, is a category error, since kinetics deals with concentrations and rate constants, not state functions, and no single number, however standardised, can substitute for the full rate law of a catalytic cycle. He also questioned the authors' use of the Eyring equation to describe a combination of several rate constants rather than a single elementary step.

Kozuch's reply (2013), mounted a targeted defence of the "energetic span approximation", arguing that once rate constants are translated into energies via transition state theory, an Eyring-shaped expression is legitimate wherever a single rate-determining intermediate and rate-determining transition state can be identified (a condition satisfied by most simple catalytic cycles). More broadly, he defended the practical case for a standardised TOF, since catalysis can be described at many levels of detail, from reactor engineering down to the quantum dynamics of a single transition state, and a full rate law or mechanism is not always available or necessary just to compare two catalysts. Quoting the proverb "were I to await perfection, my book would never be finished," Kozuch argued that a standardised, if imperfect, benchmark is more useful to the field than no benchmark at all.

A Viewpoint, a Comment, and a Reply, all in the same journal within twelve months, is a genuinely enjoyable example of academic discourse at work, revealing how much conceptual nuance is required to define even seemingly simple concepts.

TON in context: complementary green metrics

References are sorted alphabetically by first author.

1. P. T. Anastas and J. C. Warner, Green Chemistry: Theory and Practice, Oxford University Press, 1998. ISBN 978-0-19-850698-0. Original statement of the 12 Principles; Principle 9 on catalysis frames TON as a key measure of catalyst efficiency.
2. A. Behr and L. Johnen, ChemSusChem, 2009, 2, 1072–1095. DOI. Myrcene as a natural base chemical in sustainable chemistry; discusses TON in the context of renewable feedstocks.
3. D. J. C. Constable et al., Green Chem., 2002, 4, 521–527. DOI. Green chemistry metrics for the pharmaceutical industry; discusses catalyst turnover as a key green metric.
4. S. Kozuch and J. M. L. Martin, ACS Catal., 2012, 2, 2787–2794. DOI. "Turning Over" Definitions in Catalytic Cycles: the authoritative discussion of TON/TOF definitions, common pitfalls, and the distinction between average and instantaneous values.
5. S. Kozuch, ACS Catal., 2013, 3, 380. DOI. Reply to the comment by Lente, defending the energetic-span approximation and the practical case for a standardised TOF/TON.
6. G. Lente, ACS Catal., 2013, 3, 381–382. DOI. Comment arguing that a standardised TOF/TON misapplies thermodynamic concepts to kinetics and cannot substitute for the full rate law.
7. C. Ortega, "TOF and TON Calculations," LinkedIn, 27 July 2020. Link. Practitioner-oriented explainer distinguishing TOF (catalytic activity) from TON (catalyst stability), with practical guidance on measurement and reporting.
8. S. K. Ritter, "The Turnover Fallacy," Chem. Eng. News, 2013, 91 (9). Link. Magazine feature on the Kozuch and Martin versus Lente exchange for a broader chemistry audience, including caution from catalysis researchers against confusing TOF with a rate constant.
9. R. A. Sheldon, Green Chem., 2007, 9, 1273–1283. DOI. The E-factor fifteen years on; discusses TON/TOF in context of catalysis and waste prevention.
10. R. A. Sheldon, Green Chem., 2017, 19, 18–43. DOI. The E-factor 25 years on; comprehensive metrics landscape including TON and catalyst efficiency.
11. D. Sinou, Top. Curr. Chem., 1999, 206, 41–59. DOI. Metal Catalysis in Water; foundational context for interpreting TON in organic synthesis.
12. B. M. Trost, Science, 1991, 254, 1471–1477. DOI. Atom economy, a search for synthetic efficiency; introduces atom economy and discusses catalyst role in step economy.

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