Current density units — A/cm², A/mm² and A/in²
Current density sets the temperature rise. Miss the unit and copper melts.
Current density (A per unit area) is what actually heats a conductor. Different disciplines use different area units, and the factors are not friendly numbers.
The exact factors
1 A/mm² = 100 A/cm² = 10⁶ A/m² = 645.16 A/in² > 1 A/cm² = 6.452 A/in² > 1 A/in² = 0.00155 A/mm²
Typical safe values
Copper wire in still air (residential): 3–5 A/mm². Copper wire in cable trays: 2–3 A/mm². Motor windings (Class F, continuous): 4–6 A/mm². PCB internal trace: 20 A/mm² for short lengths. Electroplating cathodes: 0.01–0.1 A/cm².
Worked example — motor rewind
A rewind spec says 5 A/mm² for continuous duty. A 100 A motor needs 20 mm² of copper — 4 mm × 5 mm strap, or 26 turns of AWG 6 magnet wire. Miscopy the spec as 5 A/cm² and you install 2000 mm² of copper — 100× oversized, physically impossible.
Recap
A/mm² and A/cm² differ by 100. Match the unit on the datasheet.
Try the converters mentioned in this article
FAQ
What determines safe current density?+
Temperature rise. Insulation class, cooling, and duty cycle all shift the limit.
Is bus-bar current density different?+
Yes — solid bar dissipates heat over larger surface area. Typical values 1.5–3 A/mm² for continuous.
This article was written by The Turbo Unit Converter engineering desk (Applied metrology & engineering units) and last reviewed on 2026-07-07 against NIST SP 811 and the BIPM SI Brochure. Read our full editorial policy.