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Scientific Converter

Type a value in one unit and read it in every other unit of the same quantity, from hartrees and wavenumbers to debye and bar, on the 2018 CODATA constants.

Energy

Type a value in any field and the others fill in. Use a point for decimals; exponents work too, as in 1.5e-3.

Factors are computed from the exact SI (2019) constants and the 2018 CODATA recommended values. Each unit’s button gives its definition and source, and the method and references give the rest.

How-to guide

How to convert a value

Every unit of the chosen quantity is on screen at once, so one entry gives you all of its equivalents, each computed from a single reference constant.

1

Pick a quantity

Energy, length, time, force, pressure, dipole moment, charge, polarizability, spectroscopy, temperature, or heat capacity and entropy.

2

Type into any field

Every other field updates as you type. Standard and exponential notation both work (1.5e-3). Decimals take a point; commas are read only as thousands separators, and only where they can be nothing else (1,234,567 or 1,234.5), so 1,5 is refused rather than guessed. In Spectroscopy, wavelength is the reciprocal of the others, so raising it lowers them.

3

Copy what you need

Each field has a copy button. Results switch to exponential notation above 107 and below 10-4, and otherwise keep up to eight decimal places.

Method and references

How the factors are defined, and where they come from

Every conversion in this tool reduces to a single reference constant per category. The numbers are not rounded conveniences, they are the 2018 CODATA recommended values and the exact SI (2019) definitions. Pick a domain below for the exact relations and the primary source of each constant.

Energy: the Hartree as the anchor

All energy units are expressed relative to the Hartree, Eh, the atomic unit of energy. Its SI value is fixed by the Rydberg constant through Eh = 2R∞hc.

The defining chain:

E_\mathrm{h} = 4.359\,744\,722\,2071\times10^{-18}\ \mathrm{J} = 27.211\,386\,246\ \mathrm{eV} = 2\ \mathrm{Ry}1\ E_\mathrm{h} \equiv 2625.4996\ \mathrm{kJ/mol} = 627.5095\ \mathrm{kcal/mol} = 219474.63\ \mathrm{cm^{-1}}

Molar units (kcal/mol, kJ/mol) multiply the per-particle energy by the Avogadro constant NA = 6.022 140 76×1023 mol-1, which is exact since the 2019 SI redefinition. The thermochemical calorie (1 cal = 4.184 J, exact by definition) links kcal/mol to kJ/mol, this is the calorie used by AMBER and CHARMM, not the 15°C or IT calorie. The wavenumber relation E = hcν̃ makes cm-1 an energy unit in spectroscopy.

Unit1 Eh equalsBasis
eV27.211386246CODATA 2018 (exact eV since 2019)
kJ/mol2625.499639CODATA 2018 × NA
kcal/mol627.509474+ thermochemical calorie (4.184 J)
cm-1219474.6314CODATA 2018 hartree–inverse-metre
K (E/kB)315775.02CODATA 2018 hartree–kelvin

Atomic units: length, force, dipole, charge, polarizability

Quantum-chemistry codes (Gaussian, ORCA, Psi4, Quantum ESPRESSO) work internally in atomic units, where ℏ = me = e = 1 and 4πε0 = 1. Converting their output to lab units needs the CODATA values below.

The atomic units used here:

\begin{aligned} a_0 &= 5.291\,772\,109\,03\times10^{-11}\ \mathrm{m} && \text{length} \\ e\,a_0 &= 8.478\,353\,6255\times10^{-30}\ \mathrm{C\,m} = 2.541746\ \mathrm{D} && \text{dipole} \\ e &= 1.602\,176\,634\times10^{-19}\ \mathrm{C}\ \text{(exact)} && \text{charge} \\ E_\mathrm{h}/a_0 &= 8.238\,723\,4983\times10^{-8}\ \mathrm{N} && \text{force} \\ E_\mathrm{h}/a_0^3 &= 2.942\,101\,5697\times10^{13}\ \mathrm{Pa} && \text{pressure} \\ e^2a_0^2/E_\mathrm{h} &= 1.648\,777\,274\,36\times10^{-41}\ \mathrm{C^2\,m^2\,J^{-1}} && \text{polarizability} \end{aligned}

The debye is fixed exactly by 1 D = 10-21/c C·m = 3.335 641×10-30 C·m (c is exact), giving 1 e·a0 = 2.541746 D. Force-field partial charges are always in units of e, so the charge tab lets you cross-check RESP/CHELPG output against C or statC. Volume polarizability (Å3, the number usually tabulated) follows the Gaussian-CGS convention α[Å3] = α[a.u.] × 0.148185.

Spectroscopy: one photon, four ways to write it

Wavenumber, frequency, photon energy and wavelength all describe the same excitation. Three of them scale linearly; wavelength is the reciprocal.

The relations (h and c are exact SI constants):

E = h\nu = hc\tilde{\nu} \qquad \lambda = 1/\tilde{\nu} = c/\nu1\ \mathrm{cm^{-1}} \equiv 29.9792458\ \mathrm{GHz} \equiv 0.1239842\ \mathrm{meV} \equiv 1/\lambda\,[\mathrm{cm}]

Because wavelength is inversely proportional to the others, the tool normalises to a base wavenumber and takes the reciprocal for λ, whichever field you type into. Constants used: c = 299 792 458 m/s and h = 6.626 070 15×10-34 J·s, both exact since 2019. The cm-1↔eV factor, 1.239842×10-4, is the reciprocal of 8065.54 cm-1/eV.

Temperature, kBT, and molar entropy

Temperature conversions include the two offset scales (Celsius, Fahrenheit) and the thermal-energy equivalents kBT that appear constantly in statistical mechanics and free-energy work.

Offset scales are affine, not multiplicative:

T[^\circ\mathrm{C}] = T[\mathrm{K}] - 273.15 \qquad T[^\circ\mathrm{F}] = (T[\mathrm{K}] - 273.15)\times 9/5 + 32k_\mathrm{B}T\ \text{at}\ 300\ \mathrm{K} = 2.4943\ \mathrm{kJ/mol} = 0.5961\ \mathrm{kcal/mol} = 25.85\ \mathrm{meV}

The tool converts temperature through kelvin with explicit affine maps, so °C and °F are handled correctly (a plain ratio would be wrong). The kBT rows use kB = 1.380 649×10-23 J/K (exact) and, for molar values, the gas constant R = NAkB = 8.314 462 618… J mol-1 K-1. In the Heat Capacity tab, the entropy unit (e.u., “gibbs”) is 1 cal mol-1 K-1, and quantities are also given as dimensionless multiples of R (or kB per particle).

References & data sources

  1. Tiesinga, E., Mohr, P. J., Newell, D. B., & Taylor, B. N. (2021). CODATA recommended values of the fundamental physical constants: 2018. Rev. Mod. Phys. 93, 025010. doi:10.1103/RevModPhys.93.025010.
  2. NIST. Fundamental Physical Constants (2018 CODATA adjustment), Hartree energy, Bohr radius, atomic units of time, force, pressure, electric dipole moment and polarizability, elementary charge. physics.nist.gov/cuu/Constants.
  3. NIST. Non-SI units accepted for use with the SI, and units based on fundamental constants (2018 CODATA). nonsi_2018.pdf (a.u. of electric dipole moment = 8.4783536255×10-30 C·m; a.u. of polarizability = 1.64877727436×10-41 C2m2J-1).
  4. BIPM. The International System of Units (SI Brochure), 9th edition (2019). Exact defined values of c, h, e, kB and NA. bipm.org/en/publications/si-brochure.
  5. Thompson, A., & Taylor, B. N. (2008). Guide for the Use of the International System of Units (SI), NIST Special Publication 811. Definitions of the atmosphere, torr, psi, calorie and other non-SI units. nist.gov/pml/special-publication-811.
  6. Abraham, M. J., et al. (2015). GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers. SoftwareX 1–2, 19–25. See also the GROMACS Reference Manual, Definitions and Units. manual.gromacs.org.
  7. Case, D. A., et al. AMBER Reference Manual (unit system: kcal·mol-1, Å, thermochemical calorie). ambermd.org.
  8. Debye unit definition: 1 D = 10-18 statC·cm = (10-21/c) C·m ≈ 3.335641×10-30 C·m. See NIST Molecular Spectroscopy special-units notes. physics.nist.gov.
NIST CODATA constants SI Brochure GROMACS units

Conversion factors are the 2018 CODATA / exact SI (2019) values. All computation runs entirely in your browser, nothing you type leaves your device.

Frequently asked questions

Which calorie does the kcal/mol use?
The thermochemical calorie, 1 cal = 4.184 J exactly. This is the definition used by the AMBER and CHARMM force fields, so energies convert consistently with those programs. It is not the 15°C calorie (4.1855 J) or the international-table calorie (4.1868 J).
Why is the Hartree the base unit for energy?
Because it is the natural unit that quantum-chemistry codes report, and its SI value is one of the most precisely known conversions (fixed through the Rydberg constant, Eh = 2R∞hc). Anchoring on it keeps the whole energy matrix internally consistent to the full CODATA precision.
Why does the wavelength field behave differently in Spectroscopy?
Wavenumber, frequency and photon energy are all directly proportional to each other, but wavelength is their reciprocal (λ = 1/ν̃). The tool normalises everything to a base wavenumber and inverts for wavelength, so typing a longer wavelength gives a smaller wavenumber, frequency and energy, and typing into any of those gives the wavelength back. A wavelength of zero has no wavenumber, so the other fields stay empty.
Why can't temperature use a single multiplication factor?
Celsius and Fahrenheit are offset (affine) scales, not ratio scales, 0 °C is not zero energy. The converter therefore routes temperature through kelvin with explicit T = K − 273.15 and T = (K−273.15)×9/5+32 formulas. The kBT rows convert the thermal energy at that temperature.
How precise are these numbers?
Each factor is computed in double precision from the exact SI (2019) constants and the 2018 CODATA recommended values of the Bohr radius and the Hartree energy; none is typed in rounded, so the tables agree with each other to the last digit shown. Since the 2019 redefinition, c, h, e, kB and NA are exact, so any conversion depending only on those (e.g. eV↔J, charge, bar↔Pa) is exact; those depending on measured constants (Bohr radius, Hartree) inherit CODATA's relative uncertainty of order 10-10.
Is a.u. of polarizability the same as the Å3 I see in tables?
Not numerically. Molecular polarizabilities are usually tabulated as a volume in Å3 (Gaussian-CGS convention), whereas QM codes print the atomic-unit value. The conversion is α[Å3] = α[a.u.]×0.148185. Both are provided so you can move between a calculation and a reference table.
Is my data sent anywhere?
No. Every calculation runs locally in your browser using JavaScript. Nothing you enter is transmitted or stored.

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