Calorie (nutritional) to Electron Volt

In the late 19th century, nutritionists adopted the kilocalorie as the practical unit for food energy but dropped the "kilo" prefix in everyday speech. A banana labelled "90 calories" actually contains 90 kilocalories (90,000 small calories). Some labels use a capital "C" (Calorie) to distinguish it from the small calorie, but this convention is inconsistently applied and remains a source of confusion worldwide.

One kcal (kilocalorie) equals 1,000 cal (calories). European and Australian labels typically show energy in both kJ and kcal explicitly. US labels use "Calories" (capital C), which actually means kcal. If a label says 200 Calories, it means 200 kcal = 200,000 small calories = 836.8 kJ. The small calorie (4.1868 J) is rarely seen outside laboratory contexts.

Adults typically need 1,600–2,500 kcal per day depending on sex, age, weight, and activity level. Sedentary women average about 1,800 kcal; active men about 2,500 kcal. Endurance athletes during competition can burn 4,000–8,000 kcal/day. These figures are based on the International Table calorie (4.1868 J), though the thermochemical calorie gives near-identical results in practice.

Australia, New Zealand, and EU member states mandate SI-based labeling, so they use kilojoules (kJ) as the primary energy unit. The US and Canada use kilocalories (labelled as "Calories"). To convert, multiply kcal by 4.1868 to get kJ, or divide kJ by 4.1868 for kcal. A 2,000 kcal daily diet equals 8,374 kJ.

Wilbur Atwater and colleagues in the 1890s used bomb calorimeters to burn food samples and measure heat released. They established that carbohydrates yield ~4 kcal/g, protein ~4 kcal/g, and fat ~9 kcal/g — the Atwater factors still printed on food labels today. Modern methods use chemical analysis and Atwater factors rather than direct calorimetry for every product.

Because subatomic energies in joules have absurdly small exponents — a visible-light photon carries about 3 × 10⁻¹⁹ J, but a convenient 1.9 eV. The electron volt is scaled to the quantum world, making numbers human-readable. It also doubles as a mass unit (via E = mc²): a proton is 938.3 MeV/c², far easier to work with than 1.673 × 10⁻²⁷ kg.

Visible light photons range from about 1.65 eV (deep red, 750 nm) to 3.1 eV (violet, 400 nm). Green light, where the human eye is most sensitive, sits around 2.3 eV. Ultraviolet photons start at 3.1 eV and can exceed 100 eV in the extreme UV. These energies are why UV can damage DNA (breaking molecular bonds of 3–5 eV) while visible light cannot.

A semiconductor's bandgap — the minimum energy to free an electron from its bond — is expressed in eV. Silicon has a bandgap of 1.12 eV, gallium arsenide 1.42 eV, and gallium nitride 3.4 eV. The bandgap determines which wavelengths of light a solar cell can absorb and what color an LED emits. Lower bandgap means longer-wavelength (redder) light.

The LHC accelerates protons to 6.5 TeV (6.5 × 10¹² eV) per beam, giving collisions a center-of-mass energy of 13 TeV. That sounds enormous, but 13 TeV is only about 2 microjoules — the kinetic energy of a flying mosquito. The power of the LHC lies in concentrating that energy into a space a million times smaller than an atom.

Multiply by 1.602 176 634 × 10⁻¹⁹. So 1 eV = 1.602 × 10⁻¹⁹ J, 1 keV = 1.602 × 10⁻¹⁶ J, and 1 MeV = 1.602 × 10⁻¹³ J. This conversion factor is exactly the elementary charge in coulombs, because an electron volt is defined as the energy gained by one electron charge crossing one volt of potential.