Erg to Watt Hour

Astrophysics literature built decades of reference data in CGS units before SI became dominant. Key constants like solar luminosity (3.828 × 10³³ erg/s) and supernova energy (10⁵¹ erg, called a "foe") are baked into textbooks and databases. Switching to SI would require rewriting thousands of reference values, so the field maintains CGS by convention.

A core-collapse supernova releases roughly 3 × 10⁵³ ergs total, of which about 99% escapes as neutrinos. The visible light and kinetic energy of the ejected shell account for about 10⁵¹ ergs — a unit so common in astrophysics it has its own name: one "foe" (ten to the Fifty-One Ergs). In joules, that is 10⁴⁴ J, or the Sun's total output over 10 billion years.

An erg per second is the CGS unit of power, equivalent to 10⁻⁷ watts. Astronomers quote stellar luminosities in ergs per second because the numbers align well with astrophysical scales: the Sun emits 3.846 × 10³³ erg/s, and supernovae peak at ~10⁴³ erg/s. Using watts would give the same exponents minus seven — less tidy for a field that already juggles 40-digit numbers daily.

CGS (centimeter-gram-second) is a metric system that predates SI, formalised in the 1870s. It derives mechanical units from cm, g, and s: force in dynes (g·cm/s²) and energy in ergs (dyne·cm). CGS was standard in physics until the mid-20th century, and its Gaussian variant remains preferred in electromagnetism and astrophysics because Maxwell's equations take a simpler form.

One erg is 10⁻⁷ joules — roughly the kinetic energy of a mosquito in flight or the energy of a single grain of sand falling one centimeter. You would need about 10 million ergs to equal one joule, or 42 billion ergs to match the energy in a single dietary Calorie. The erg is useful precisely because atomic and astronomical quantities span so many orders of magnitude.

Watt-hours account for both current and voltage, giving the true energy stored. A 10,000 mAh power bank at 3.7 V holds 37 Wh, but at 5 V output it delivers only about 7,400 mAh due to voltage conversion losses. Airlines use the Wh rating (max 100 Wh carry-on) because it reflects actual energy — and therefore actual fire risk — regardless of battery voltage.

Most smartphones have batteries rated at 10–18 Wh. An iPhone 15 Pro holds about 12.7 Wh; a Samsung Galaxy S24 Ultra about 18.4 Wh. For context, fully charging an 18 Wh phone from a wall outlet costs less than 0.01 kWh — roughly one-tenth of a cent on a typical electricity bill.

Most airlines allow lithium-ion batteries up to 100 Wh in carry-on luggage without approval. Batteries between 100 and 160 Wh (e.g., large camera or drone batteries) require airline permission, and batteries above 160 Wh are banned from passenger flights. A standard laptop battery is 50–100 Wh; a large power tool battery can exceed 160 Wh.

Watt-hours map directly to how consumers think about devices: a 50 Wh battery powering a 10 W laptop lasts about 5 hours — simple division. Expressing the same battery as 180,000 joules gives no intuitive sense of runtime. Airlines also adopted Wh for lithium battery safety limits (100 Wh carry-on threshold) because it communicates energy density risk in a unit engineers and passengers can both grasp.

A typical laptop battery holds 50–100 Wh, so a full charge from empty uses 50–100 Wh of energy (plus about 10–15% lost as heat in the charger). At average US electricity rates, that is roughly 1–2 cents per charge. Over a year of daily charging, a laptop costs about $4–$7 in electricity — far less than most people assume.