Compute area in mm² for 5 shapes, round-wire cross-section, and AWG ↔ mm² conversion.
Standard IEC wire sizes and indicative current
| Cross-section | Typical use | Indicative current* |
|---|---|---|
| 1.0 mm² | Lighting circuits | ≈ 10 A |
| 1.5 mm² | Domestic lighting, small loads | ≈ 15 A |
| 2.5 mm² | Socket outlets | ≈ 20 A |
| 4 mm² | Cooker / oven circuits | ≈ 25 A |
| 6 mm² | Electric shower | ≈ 32 A |
| 10 mm² | Sub-main, heavy appliance | ≈ 40 A |
| 16 mm² | Service entrance | ≈ 63 A |
| 25 mm² | Main service / sub-distribution | ≈ 80 A |
| 35 mm² | Distribution | ≈ 100 A |
| 50 mm² | Distribution | ≈ 125 A |
Common AWG to mm² reference
| AWG | Diameter (mm) | Area (mm²) | Closest IEC |
|---|
How the calculations work
Shape area formulas
Rectangle / Square: A = w × h
Circle: A = π × r² = π × (d / 2)²
Triangle (base × height): A = ½ × b × h
Trapezoid: A = ½ × (a + b) × h, where a and b are the parallel sides
Annulus (ring): A = π × (D² − d²) / 4 — used for washers and pipe cross-sections
Every input is converted to millimetres first, so you can mix units per field (mm, cm, m, μm, inches).
Round-wire cross-section
For a solid round conductor the cross-section is a circle, so A = π × (d / 2)². Example: a 2.5 mm diameter wire gives π × (1.25)² ≈ 4.91 mm². Note the subtle but important difference between wire diameter (physical thickness) and nominal cross-section (the catalogue mm² figure such as 1.5 or 2.5), which is the value used for ampacity tables.
AWG formula
The American Wire Gauge scale is logarithmic. For sizes 36 to 0000, the diameter in inches is:
din = 0.005 × 92(36 − n) / 39
Equivalently, n = −39 × log10(din / 0.005) + 36 for the inverse. Each 6-gauge step roughly doubles the cross-section, and each 3-gauge step roughly doubles the diameter.
Frequently asked questions
What is 1 mm² in cm² and m²?
1 mm² = 0.01 cm² = 0.000001 m² = 10⁻⁶ m². One square centimetre contains 100 square millimetres, and one square metre contains one million square millimetres. The confusion comes from squaring the linear factor: 1 cm = 10 mm, so 1 cm² = 10² = 100 mm².
What is the difference between wire gauge and mm²?
Wire gauge (AWG or SWG) is a numbered scale derived from the conductor diameter, while mm² is the true geometric cross-sectional area. IEC and most non-US electrical codes specify cables by mm² (1.5, 2.5, 4, 6, 10, 16 mm² …). North American wiring is usually specified by AWG, and you need the cross-section in mm² to map to European ampacity tables or to check voltage drop calculations.
How do I convert AWG to mm²?
Compute the AWG diameter using dmm = 0.127 × 92(36 − n) / 39, then square it and multiply by π/4. The AWG ↔ mm² tab does this automatically. Examples: AWG 14 ≈ 2.08 mm², AWG 12 ≈ 3.31 mm², AWG 10 ≈ 5.26 mm², AWG 8 ≈ 8.37 mm².
How do I calculate the cross-section of a round wire?
Measure the bare conductor diameter with a calliper (in mm), halve it to get the radius, and apply A = π × r². A 2.05 mm wire yields π × (1.025)² ≈ 3.30 mm², which matches AWG 12. For stranded cable the sum of the areas of the individual strands gives the conductor cross-section; the overall bundle diameter is larger because of air gaps between strands.
What are the standard IEC wire sizes?
The IEC 60228 nominal cross-sections used in power and installation cables are 0.5, 0.75, 1, 1.5, 2.5, 4, 6, 10, 16, 25, 35, 50, 70, 95, 120, 150, 185, 240, 300, 400 mm² and larger. For domestic wiring the most common values are 1.5 mm² (lighting, ≈ 15 A), 2.5 mm² (socket outlets, ≈ 20 A), 4 mm² (cooker, ≈ 25 A), 6 mm² (shower, ≈ 32 A), 10 mm² and 16 mm² for sub-mains.
Work out area in square millimetres for five shapes — rectangle, circle, triangle, trapezoid and annulus (ring) — with a per-field unit picker for μm, mm, cm, m and inches, plus secondary results in cm², m² and in². The wire tab gives the cross-section of a round conductor from diameter or AWG using A = π(d/2)², and flags the closest IEC size (1.5, 2.5, 4, 6, 10, 16, 25 mm²…) and closest AWG gauge. A 2.5 mm diameter wire comes out at 4.91 mm², close to the 4 mm² IEC rung. A 16 mm² service cable sits around 63 A domestic ampacity. The AWG ↔ mm² tab converts in both directions for drafting, PCB layout and electrical design.