Get precise current density for any conductor. Choose geometry, convert units, and compute instantly safely. Compare materials and keep electrical designs within limits always.
Select a method, choose what to solve for, then enter known values. Results appear above this form after you press Calculate.
| Case | Current (A) | Area (mm²) | Current Density (A/m²) |
|---|---|---|---|
| Small wire | 2.0 | 0.50 | 4.0×106 |
| Bus bar | 120 | 50 | 2.4×106 |
| Lab lead | 0.25 | 1.00 | 2.5×105 |
Current density describes how electric current is distributed across a conductor cross‑section. For a uniform current through area A, the magnitude is:
Here, I is current (A), A is cross‑sectional area (m²), n is carrier density (1/m³), q is carrier charge (C), and vd is drift velocity (m/s).
Current Density in Real Systems
Current density J is current per cross‑sectional area. In practice it connects electrical loading to temperature rise and long‑term reliability. Because J scales inversely with area, small geometry changes can produce large heating changes.
In power wiring, steady copper conductors often run around 106 to 107 A/m² depending on insulation, airflow, and duty cycle. On circuit boards, limits vary with copper thickness and allowed temperature rise; designers often aim for a few 106 A/m².
Joule heating depends on current density through p = J²ρ, where p is volumetric heat generation (W/m³) and ρ is resistivity (Ω·m). For copper near room temperature, ρ is about 1.68×10‑8 Ω·m, so increasing J quickly raises heat generation. Doubling J quadruples heating, so margin is not linear.
For a round conductor, area comes from radius or diameter, A = πr². A 10% diameter increase raises area by about 21%, reducing J similarly. For rectangular conductors, A = width × height, typical for bus bars and shunts. This calculator also reports an equivalent circular diameter for quick comparisons.
The drift relation J = n q vd links macroscopic current to carrier motion. Metals have very large n (often near 1028 1/m³), so drift velocities can be tiny, commonly 10‑4 to 10‑3 m/s.
At very high current densities, interconnects can suffer electromigration. In microelectronics, sustained 1010 A/m² level current densities can accelerate material transport, forming voids or hillocks. For connectors and weld points, high J can also concentrate heating at small contact areas.
This tool reports J in A/m² and also converts to A/mm² and mA/mm² for quick comparisons. Remember 1 A/mm² = 106 A/m², so small A/mm² values may still be large in SI units. Always record both current and area in your notes for traceability.
Enter the maximum expected current, select a geometry mode, and input dimensions. If you have an allowable current density from standards or internal rules, switch to solving for area to estimate the minimum cross‑section. Export CSV or PDF to document assumptions and results.
The SI unit is ampere per square meter (A/m²). Many engineers also use A/mm² for compact conductors; 1 A/mm² equals 106 A/m².
Use J = I/A for conductor sizing and geometry problems. Use J = n q vd when you want drift velocity insight or carrier‑density based analysis.
Yes. Choose circular area from radius or diameter for wires, or select rectangular width × height for bus bars, shunts, and flat conductors.
Resistive heating per volume scales as J²ρ. Higher current density increases temperature rise rapidly, especially in small cross‑sections or poor airflow.
The magnitude of electron charge is about 1.602×10‑19 C. Use the magnitude unless you are tracking direction with an explicit sign convention.
Select the current‑and‑area method, choose “Area (A)” as the unknown, then enter current and a target current density. The tool returns area and an equivalent circular diameter.
It is the diameter of a round conductor that has the same area as your computed cross‑section. It helps compare a rectangular area to a comparable wire size.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.