Core answer: AWG runs backward — smaller numbers are thicker wires, and every −6 steps doubles the diameter (12AWG≈2.05mm carries ~20A); for hardness, use HRC for hardened steel, HB for annealed/soft metals, and HV as the near-universal scale; energy units chain as 1kWh = 3.6MJ = 860kcal = 3412BTU.

Wire gauge: AWG to mm²

AWGDiameterCross-sectionTypical copper ampacity
181.02 mm0.82 mm²~7A
161.29 mm1.31 mm²~10A
141.63 mm2.08 mm²~15A
122.05 mm3.31 mm²~20A
102.59 mm5.26 mm²~30A
83.26 mm8.37 mm²~40A

Ampacity varies with insulation rating and bundling — derate 20–30% in conduit or hot environments.

AWG current-capacity table

Rule of thumb: every −6 AWG doubles the diameter (quadruples the cross-section); every −3 AWG doubles the cross-section. Metric equivalents: 12AWG≈3.3mm², 14AWG≈2.1mm², 16AWG≈1.3mm².

Aluminum wire needs about two AWG steps thicker (or ×1.6 cross-section) for the same current as copper.

Hardness scales compared

ScaleIndenterBest forTypical reading
HRC (Rockwell C)diamond conehardened steel, bladesfiles 62–65, knives 56–60
HB (Brinell)steel/tungsten ballannealed steel, aluminum, cast ironstructural steel 120–180
HV (Vickers)diamond pyramidthin layers, coatings, universalpure copper ~50, nitrided layer 1000+

Rough conversions: HRC 60 ≈ HB 601 ≈ HV 697; HRC 30 ≈ HB 283. Conversions are empirical — measure in the native scale when precision matters.

Energy unit conversions

UnitEqualsEveryday anchor
1 kWh3.6 MJone hour of a 1kW appliance
1 kWh860 kcal~1.5 hamburgers of energy
1 kcal4.184 kJfood labels use kcal
1 BTU1.055 kJair conditioners and furnaces
1 Wh3.6 kJbattery specs (mAh × V = mWh)

Example: wire for a 30A EV charger

A Level-2 charger draws 30A continuous. NEC-style continuous-load derating (×1.25) means sizing for 37.5A:

  • 10AWG copper ≈ 30A — not enough for a continuous load
  • 8AWG copper ≈ 40A — correct choice

Voltage drop on a 15m run at 30A through 8AWG (3.3Ω/km): 2×15m×0.0033×30 ≈ 3V — acceptable. Skipping the derating logic and matching “30A wire to a 30A load” is the classic overheating scenario.

Example: which hardness scale to specify

Ordering a machined shaft, quenched and tempered:

  • Hardened to ~HRC 40? Specify HRC — the diamond cone handles hard surfaces with a small indentation
  • Annealed aluminum bracket? HB — HRC’s sharp cone sinks too deep in soft metal and reads unreliable values
  • Nitrided surface layer 0.3mm deep? HV with low load — HB’s ball would punch through the layer

Writing “hardness 40” with no scale is meaningless — always attach HRC/HB/HV.

Common mistakes

  • “Bigger AWG = thicker wire”: it is the opposite — 8AWG dwarfs 18AWG. The number counts historical drawing dies.
  • Matching ampacity exactly to load: continuous loads (chargers, heaters) need ×1.25 headroom; exact matches run hot for hours.
  • Mixing hardness scales without conversion: “HRC 60” and “HB 600” describe similar hardness, but “HRC 60” vs “HV 60” are worlds apart (HV 60 is soft copper).
  • kW vs kWh: kW is power (rate), kWh is energy (amount). A 2kW heater running 3h uses 6kWh — bills charge kWh.