Adiabatic Equation Calculator
Under BS 7671 Regulation 543.1.3, the circuit protective conductor (CPC) must withstand the thermal energy let-through (I²t) of the protective device during a fault without exceeding the insulation's maximum temperature limit. Rather than acting as a black box, this tool evaluates the adiabatic equation from first principles, shows the intermediate energy let-through, and verifies existing CPC suitability.
Calculation Summary
Note on fast-acting devices (t < 0.1 s): The formula S = √(I²t) / k assumes symmetrical current over duration t. For current-limiting devices operating in under 0.1s (such as BS EN 60898 MCBs or BS 88 fuses), use the manufacturer's published energy let-through (I²t) characteristic per Reg 543.1.3 Note 2.
Full 6-Step Adiabatic Design Working
Fault Current & Duration Parameters
I = 1,000 A, t = 0.10 s
Prospective fault current flowing through the protective device under short-circuit or earth fault conditions, with the corresponding device operating time.
Conductor Thermal Coefficient (k Factor)
k = 115
Factor derived from Table 54.2 for copper conductors with 70°C PVC insulation incorporated in a cable (initial temperature 70°C, final limiting temperature 160°C).
Energy Let-Through Calculation (I²t)
I²t = I × I × t
I²t = 1,000² × 0.10 = 100,000 A²s
Thermal energy developed in the conductor during the fault duration.
Theoretical Minimum Conductor Area (S)
S = √(I²t) / k
S = √(100,000) / 115 = 316.23 / 115 = 2.75 mm²
Minimum cross-sectional area required to prevent conductor insulation damage or melting.
Standard Metric Conductor Size Selection
Selected Standard Size = 4.0 mm²
Rounded up to the next commercially manufactured standard metric conductor size (1.0, 1.5, 2.5, 4.0, 6.0, 10.0, 16.0, 25.0, 35.0, 50.0 mm²).
Withstand Capacity Comparison (k²S² ≥ I²t)
Enter an existing CPC in Section 3 to evaluate withstand.
Proves whether the existing conductor possesses sufficient thermal inertia to absorb the fault energy without overheating.
Worked Example & Calculation Breakdown
Scenario: A 32 A radial socket circuit protected by a BS EN 60898 Type B circuit breaker experiences an earth fault at the distribution board. Prospective fault current I = 1,200 A, disconnection time t = 0.1 s, using twin and earth cable with 70°C PVC insulated copper conductors (k = 115 per Table 54.2). The circuit incorporates a 1.5 mm² CPC.
- Calculate Energy Let-Through:
I²t = 1,200² × 0.1 = 1,440,000 × 0.1 = 144,000 A²s - Calculate Minimum Theoretical CPC:
S = √(144,000) / 115 = 379.47 / 115 = 3.30 mm² - Check Existing 1.5 mm² CPC Withstand:
k²S² = 115² × 1.5² = 13,225 × 2.25 = 29,756 A²s - Withstand Evaluation:
k²S² (29,756 A²s) < I²t (144,000 A²s) ⇒ FAIL. The 1.5 mm² CPC is inadequate for a 1.2 kA fault at 0.1s. An upgraded CPC of at least 4.0 mm² (k²S² = 211,600 A²s) is required.
BS 7671 Regulatory Framework & Limits
- Reg 543.1.3: Where the cross-sectional area of a protective conductor is determined by calculation, it shall be not less than the value given by the adiabatic equation.
- Table 54.2 vs Table 54.3: Table 54.2 applies when the protective conductor is incorporated in a multi-core cable (where the conductor starts at running temperature, e.g. 70°C). Table 54.3 applies when the protective conductor is separate or not bunched with live conductors (initial temperature 30°C).
- Limits of Adiabatic Validity: The adiabatic assumption relies on negligible heat escaping the conductor into the surrounding insulation during the fault. It is valid for fault durations between 0.1 seconds and 5.0 seconds. For
t > 5 s, heat dissipation occurs and non-adiabatic conditions apply.
⚠️ Engineering design aid: Always verify calculations against the current BS 7671 edition and protective device manufacturer data. Not a substitute for professional design certification.
Frequently Asked Questions
What is the adiabatic equation and when is it required?
The adiabatic equation k²S² ≥ I²t (or S = √(I²t) / k), defined in BS 7671 Regulations 434.5.2 and 543.1.3, calculates the minimum safe cross-sectional area of a conductor or CPC to prevent thermal damage before the protective device disconnects under earth fault or short-circuit current.
What k-factor applies to a standard flat Twin & Earth CPC?
Under BS 7671 Table 54.3, for a 70°C thermoplastic (PVC) copper protective conductor incorporated inside a cable or bunched (such as the bare CPC in 6242Y flat Twin & Earth), k = 115. If the CPC is a separate standalone single-core cable, Table 54.2 specifies k = 143.
What does "adiabatic" mean in electrical engineering?
"Adiabatic" describes a thermodynamic condition where zero heat escapes to the environment. For rapid electrical faults lasting under 5 seconds (especially under 0.1s), all I²t thermal energy is assumed to remain trapped within the copper conductor, meaning the temperature rise depends entirely on conductor mass and material factor k.
Built by a UK electrical engineer. If you spot a calculation discrepancy, want a specific breaker or fuse curve added, or have on-site test feedback, drop Adrian a line or email .