This calculator determines the minimum required cross-sectional area for protective earthing (grounding) conductors based on fault current, fault duration, and conductor material properties. It applies the adiabatic equation as per international standards like IEC 60364-5-54 and principles from IEEE Std 80.
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Properly sizing a Protective Earth (PE) conductor, or "earthing cable," is one of the most critical aspects of electrical safety design. Its sole purpose is to provide a low-impedance path for fault current to flow back to the source, allowing a protective device (like a circuit breaker or fuse) to operate almost instantly, de-energizing the circuit and preventing electric shock or fire. An undersized earthing conductor can act like a fuse itself—vaporizing during a fault and leaving the system dangerously live and ungrounded.
This calculator uses the adiabatic equation, the internationally accepted method described in standards like IEC 60364-5-54 and IEEE Std 80, to determine the minimum required size. This guide explains the principles behind the calculation.
The term "adiabatic" assumes that during the very short duration of a fault (e.g., 0.1 to 1 second), all the heat generated by the fault current (I²R losses) is absorbed by the conductor itself, with no time to dissipate into the surrounding environment. This is a worst-case scenario calculation.
The formula is:
The '$k$' factor is not just a simple constant; it is calculated from the fundamental thermal and electrical properties of the conductor material. The calculator derives this value for you using the full formula:
This formula precisely calculates how much current a conductor can withstand before its temperature rises from $T_i$ to $T_f$ in one second.
While the calculator computes the exact '$k$' value, standards provide tables for common scenarios. These values are what you would use for a quick manual calculation.
| Material | Insulation / Condition | Initial Temp ($T_i$) | Final Temp ($T_f$) | '$k$' Factor |
|---|---|---|---|---|
| Copper | PVC Insulation | 30°C | 160°C | 143 |
| Copper | XLPE/EPR Insulation | 30°C | 250°C | 176 |
| Copper | Bare (Bolted joints, limit 300°C) | 30°C | 300°C | 192 |
| Aluminum | PVC Insulation | 30°C | 160°C | 95 |
| Aluminum | XLPE/EPR Insulation | 30°C | 250°C | 116 |
| Steel | Bare (Bolted joints, limit 300°C) | 30°C | 300°C | ~58 |
This is the maximum root mean square (RMS) current that would flow in the event of a "bolted" short circuit (a solid, zero-impedance connection) at the point of installation. This value is critical and must be accurate. It is typically determined by:
This is the total clearing time of the upstream protective device (circuit breaker or fuse). A common misconception is to use the device's instantaneous trip time (e.g., 0.02s). However, many breakers have a "short-time" delay to ensure coordination, so a time of 0.1s, 0.2s, or even 0.5s is often more realistic and conservative. As you can see from the $\sqrt{t}$ in the formula, a longer duration significantly increases the required cable size.
The formula gives a minimum size based on thermal withstand. Codes often add further requirements:
Many standards (like IEC 60364) mandate a minimum size for mechanical robustness, regardless of the calculation. For example, a PE conductor may be required to be at least 2.5 mm² (if mechanically protected) or 4 mm² (if unprotected) simply so it doesn't break easily, even if the formula calculates a smaller size.
An earthing conductor buried in soil must resist corrosion for decades. This influences material choice. Bare copper is excellent but expensive. Galvanized steel is common for earth grids (like in substations) but is less conductive. Copper-clad steel offers a balance of conductivity and corrosion resistance.
Choosing between a round cable and a flat bar (busbar) depends on the application:
While this calculator uses the same fundamental adiabatic equation found in both standards, it's important to know their primary focus:
For sizing a PE conductor for a motor, panel, or transformer within a commercial or industrial building, the IEC 60364 approach (as used by this tool) is the standard method.