Fusing Current Formulas: Wire Fuse Estimate
Fusing current of a bare wire from Preece’s rule: current that melts a copper or aluminium wire in free air, wire diameter for a chosen current, with a table.
The formulas
| To find | Formula |
|---|---|
| Fusing current (diameter in inches) | I = K × d^1.5 |
| Fusing current (diameter in mm) | I = K × (d / 25.4)^1.5, so K′ = K / 25.4^1.5 |
| Diameter for a fusing current | d = (I / K′)^(2/3) |
Preece’s constant K is about 10,244 for copper and 7,585 for aluminium with d in inches. In millimetres that is about 80 for copper and 59 for aluminium. The current is the value that melts a bare, straight wire in free air at room temperature, and it is only an estimate. A fuse must carry its rated current indefinitely, so a real fuse rating is far lower than the fusing current. Use a manufactured fuse for protection, not a piece of wire.
Worked example: 0.5 mm copper wire
- d = 0.5 / 25.4 = 0.01969 in
- I = 10,244 × 0.01969^1.5 = 28.29 A
- For aluminium, I = 7,585 × 0.01969^1.5 = 20.95 A
Worked example: diameter for a 20 A fusing current in copper
- d = (20 / 80.02)^(2/3) = 0.3968 mm
Fusing current by wire diameter
| Diameter | Copper | Aluminium |
|---|---|---|
| 0.1 mm | 2.531 A | 1.874 A |
| 0.2 mm | 7.158 A | 5.3 A |
| 0.5 mm | 28.29 A | 20.95 A |
| 1 mm | 80.02 A | 59.25 A |
| 2 mm | 226.3 A | 167.6 A |
Frequently asked questions
Is the fusing current the same as the safe current?
No. It is the current at which the wire melts, usually after a time. The safe continuous current is many times lower and comes from the cable ratings.
Why does it depend on d to the power 1.5?
The heat generated depends on the cross-section, which goes with d², and the heat lost depends on the surface, which goes with d, so the balance gives a power near 1.5.
Can I make a fuse from a piece of wire?
It is not advised. The time to melt, the arc and the temperature are not controlled. Use a fuse with a tested time-current curve.
Does it work for a short-circuit time of a fraction of a second?
No. For short faults the heat does not escape, and the adiabatic formula in the short-circuit cable calculator is the right tool.
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