Electronvolts to Calories Converter
Common Conversions
| eV | cal |
|---|---|
| 1 | 3.829e-20 |
| 10 | 3.829e-19 |
| 100 | 3.829e-18 |
| 1000 | 3.829e-17 |
| 10000000000 | 3.829e-10 |
| 1000000000000000 | 0.00003829 |
| 1000000000000000000 | 0.03829 |
| 10000000000000000000 | 0.3829 |
| 26110000000000000000 | 1 |
| 100000000000000000000 | 3.829 |
| 1e+22 | 382.9 |
Why this conversion matters in chemistry
NIST Atomic Spectra Database lists ionization energies in electronvolts — 13.598 eV for hydrogen, 11.260 eV for carbon. Older thermochemistry references list the same quantities as 313.6 kcal/mol for H, with a per-atom value in calories that is dividing by Avogadro's number. Hydrogen's 13.598 eV ionization equals 5.21 × 10⁻¹⁹ cal per atom, the exact same energy in different units. The constant of 3.8293 × 10⁻²⁰ cal per eV comes from 1 eV = 1.602 × 10⁻¹⁹ J and 1 cal = 4.184 J. The setting is straightforward — when atomic-physics spectroscopy meets per-particle thermochemistry.
Formula
Where the factor comes from
Two definitions meet here and neither one was measured. The electronvolt is fixed to the joule through the elementary charge, exactly 1.602176634 × 10⁻¹⁹ C since 2019, and the thermochemical calorie is fixed to the joule at exactly 4.184 J. Divide one by the other and the joules cancel: 1.602176634 × 10⁻¹⁹ ÷ 4.184 = 3.829294058317… × 10⁻²⁰ cal per electronvolt. The result is exact in the sense that it is a ratio of two defined numbers, yet it does not terminate — 4.184 hides a factor of 523, which divides nothing in the numerator — so the decimal runs on and every written form of it is a rounding. That is a weaker sort of exactness than either parent definition enjoys.
Precision and significant figures
Because the decimal never closes, the number you carry is a choice rather than a given. Six figures, 3.82929 × 10⁻²⁰, exceeds anything a measured eV value will need and is worth reaching for only when the factor sits inside a longer chain. The larger hazard is assembling it from rounded parts: dividing 1.602 × 10⁻¹⁹ by 4.184 returns 3.8289 × 10⁻²⁰, already off in the fourth figure before your data has been touched. On the calorie side, remember that per-particle calories are a bookkeeping construct — no calorimeter resolves 10⁻²⁰ cal, and the quantity only becomes measurable after multiplication by Avogadro's number.
Worked Examples
The conversion anchor — one electronvolt as a per-particle calorie.
The reverse anchor — about how many eV make a calorie.
Hydrogen ionization energy per atom, in thermochemistry units.
A typical C–C bond energy per particle, expressed in calories.
Common mistakes
Which calorie the source meant
The 3.8293 × 10⁻²⁰ factor assumes the thermochemical calorie at 4.184 J. Against the IT calorie of exactly 4.1868 J it becomes 3.8267 × 10⁻²⁰, a shift of 0.067 percent. Negligible beside most spectroscopic input, and not negligible at all when the whole point of the exercise is reconciling two historical compilations that already disagree by under a percent.
cal and cal/mol share an abbreviation
Legacy thermochemistry prints cal or kcal where it means per mole, leaving the mole to context a modern reader no longer has. Feeding a per-mole figure into a per-particle factor produces an answer wrong by Avogadro's number in whichever direction the confusion ran. Settle whether the source quantity describes one atom or one mole first; the printed magnitude usually gives it away.
A tiny calorie is not a small energy
Hydrogen's 13.6 eV ionization comes out as 5.208 × 10⁻¹⁹ cal, an exponent that invites the reader to dismiss it. Per-particle calories are always minute, so their size carries no information about whether a process matters. Judge against thermal energy in the same units — kT at 298 K is about 9.8 × 10⁻²² cal per particle — and that ionization is suddenly 530 times larger.