Calculate the minimum CPC cross-sectional area instantly using the adiabatic equation. Built-in k values for all conductor types, disconnection time references, and 70 electrical calculators — all on your phone.
Calculate minimum cable CSA to withstand fault current per BS 7671
Prospective fault current at connection point
Empty: Prospective Fault Current (I), Custom Time (t).
S = I × √t / kS= Minimum CSA (mm²)I= Fault current (A)t= Disconnection time (s)k= Material factor (Table 54.3)Want this calc and 69 others built into a mobile app, with saved projects, PDF export and offline use? Start a 7-day free trial.
The adiabatic equation is the fundamental formula used to determine whether a protective conductor is large enough to withstand the heating effect of a fault current. When an earth fault occurs in an electrical circuit, the fault current flows through the circuit protective conductor (CPC) until the protective device (MCB, fuse, or RCBO) disconnects the supply. During this time, the fault current heats the conductor. The adiabatic equation calculates the minimum conductor size that can absorb this heat energy without the insulation reaching a damaging temperature.
The term "adiabatic" means "without heat transfer to the surroundings." The equation assumes that all the heat generated by the fault current is absorbed by the conductor itself, with no heat being dissipated to the surrounding insulation, cable sheath, or environment during the fault. This is a valid assumption because fault durations are very short (typically fractions of a second), and in such a short time, virtually no heat escapes the conductor. The calculation therefore gives a conservative (worst-case) result.
The equation is given in BS 7671 Regulation 543.1 and is the method used to verify that protective conductors are adequately sized. It applies to circuit protective conductors (CPCs) and main earthing conductors. Regulation 543.1.1 explicitly excludes protective bonding conductors, which have separate sizing requirements. It is one of the most important calculations in electrical installation design and verification.
S = √(I²t) / k
S = Minimum cross-sectional area of the protective conductor (mm²)
I = Fault current in amperes (A) — the earth fault current flowing through the CPC
t = Disconnection time in seconds (s) — the time taken by the protective device to clear the fault
k = A factor dependent on the conductor material, insulation type, and initial/final temperatures
The expression I²t (I squared t) represents the energy let-through — the total energy dissipated in the conductor during the fault. It is measured in A²s (ampere-squared seconds). A high fault current for a short time, or a lower fault current for a longer time, can both produce the same I²t value. The protective conductor must be sized to withstand whatever I²t value the protective device allows through before it disconnects.
The k value encapsulates the thermal properties of the conductor — essentially how much energy per unit volume the conductor material can absorb before reaching the maximum permitted temperature. A higher k value means the conductor can absorb more energy, so a smaller conductor is acceptable. Copper has a higher k value than aluminium (115 vs 76 for PVC-insulated conductors), which is one reason copper conductors can be smaller than aluminium ones for the same duty.
Where an RCD is the limiting device — that is, where the highest prospective earth fault current everywhere in the circuit does not exceed the RCD's conditional rated current (Iq) — the RCD's I²t let-through energy may be used in the adiabatic equation in place of MCB or fuse data (OSG 3.6.4.5). This is common on long radial circuits where the fault level is modest. In all other cases, use the time/current characteristics of the overcurrent device.
The k value is the most important factor in the adiabatic equation because it reflects the conductor material's ability to absorb fault energy. BS 7671 provides k values in Tables 54.2 to 54.6 for different combinations of conductor material and insulation type. Here are the most commonly used values.
The k value for steel (51 for PVC) is significantly lower than for copper (115 for PVC), meaning a steel CPC (such as the steel wire armour of an SWA cable used as the protective conductor) needs to have a much larger cross-sectional area than an equivalent copper CPC to carry the same fault energy. This is an important consideration when relying on cable armour as the sole CPC — the adiabatic check must always be performed to verify the armour is adequate.
A ring final circuit protected by a 32 A Type B MCB.
Earth fault current at the furthest point: I = 800 A
Disconnection time of the MCB at 800 A: t = 0.01 s (magnetic trip)
CPC is copper with PVC insulation: k = 115
S = √(800² × 0.01) / 115
S = √(6,400) / 115
S = 80 / 115
S = 0.70 mm²
The minimum CPC is 0.70 mm². The installed 1.5 mm² CPC in a standard 2.5/1.5 mm² twin and earth cable is more than adequate.
A 100 A sub-main protected by a BS 88 fuse. The SWA armour is used as the CPC.
Earth fault current: I = 2,500 A
Disconnection time of the BS 88 fuse at 2,500 A: t = 0.1 s
Steel wire armour with PVC insulation: k = 51
S = √(2,500² × 0.1) / 51
S = √(625,000) / 51
S = 790.6 / 51
S = 15.50 mm²
The minimum armour CSA is 15.50 mm². The actual armour CSA of the cable must be checked against the manufacturer data to verify it meets this requirement.
These examples illustrate why the adiabatic check is important. In Example 1, the CPC is well within limits — the installed 1.5 mm² CPC is more than double the minimum required. In Example 2, the check is critical — if the SWA cable chosen has armour with less than 15.50 mm² effective CSA, the armour is inadequate as a CPC and either a larger cable must be used or a separate CPC must be installed alongside the SWA cable.
Rounding to the next standard size (Reg 543.1.3): When the adiabatic formula produces a non-standard CSA — such as 0.70 mm² in Example 1 or 15.50 mm² in Example 2 — you must select a conductor with the next larger standard cross-sectional area. The Regulation is explicit: where the formula gives a non-standard size, a conductor of the next larger standard CSA shall be used. Never round down, even if the calculated value is only marginally above a standard size.
The adiabatic equation involves looking up k values, finding disconnection times from device characteristics, and running the calculation — all of which are straightforward individually but time-consuming when done repeatedly for every circuit in a large installation. Elec-Mate automates the entire process.
Select the conductor material and insulation from a dropdown, and the k value is applied automatically. Enter the fault current and disconnection time, and the minimum CPC size appears instantly. The calculator shows the nearest standard cable size above the calculated minimum and compares the result to the simplified Table 54.7 method, so you can see at a glance which requirement governs.
The adiabatic equation calculator works seamlessly with the prospective fault current calculator — calculate the fault current in one, feed it into the adiabatic equation in the other, and verify your CPC sizing in seconds. Both calculators work offline on your phone. Use the EICR certificate tool to record your test results and verified conductor sizes on site.
These are two of 70 electrical calculators available in Elec-Mate — 56 technical calculators plus 14 business calculators. Combined with 16 certificate types, 8 Elec-AI agents, 12 AI tools, 46+ training courses, and integration with Xero and QuickBooks, it is the complete platform for UK electricians.
In the app
Free adiabatic equation calculator: S = root(I squared t) / k. Check minimum CPC and conductor size for fault current to BS 7671. k-values built in.
Enter fault current, disconnection time, and conductor type — get the minimum CPC size in mm squared instantly.
k values for copper, aluminium, and steel with PVC, XLPE, thermoplastic, and bare conductors — all from BS 7671 Tables 54.2 to 54.6.
The calculator shows the nearest standard cable CSA above the calculated minimum, so you can select the correct cable immediately.
Compares the adiabatic result against the simplified Table 54.7 method to confirm which requirement governs the CPC size.
Designed around BS 7671:2018+A4:2026 Regulation 543.1 — the requirement to verify protective conductor sizing against fault energy.
The adiabatic equation is one of 70 electrical calculators in Elec-Mate — 56 technical and 14 business calculators, all on your phone.
Use the prospective fault current calculator to find I, then feed it directly into the adiabatic equation. Seamless workflow.
Access worked examples for domestic and commercial circuits showing how the adiabatic equation is applied in real installations.
All calculators work offline. Size CPCs on site in basements, plant rooms, and areas with no mobile signal.
Follow these steps to verify that a protective conductor is adequately sized using the adiabatic equation in the Elec-Mate app.
Launch Elec-Mate and navigate to the calculators section. Tap "Adiabatic Equation" from the list of 70 available calculators. The calculator opens with fields for the three input values: fault current, disconnection time, and k value.
Enter the earth fault current in amperes at the point in the circuit where the CPC size is being verified. This is typically the prospective earth fault current (PEFC) measured or calculated at the furthest point of the circuit, which gives the lowest fault current and therefore the most onerous condition for disconnection time.
Enter the disconnection time of the protective device in seconds at the given fault current. For MCBs operating in the magnetic trip region, this is typically 0.01 seconds. For fuses, read the time from the published time/current characteristic at the calculated fault current. The calculator includes a reference library of common device characteristics.
Select the conductor material (copper, aluminium, or steel) and insulation type (PVC, XLPE, or bare) from the dropdown. The calculator automatically applies the correct k value from BS 7671 Tables 54.2 to 54.6. You can also enter a custom k value if needed.
The calculator instantly displays the minimum CPC cross-sectional area in mm squared. It also shows the nearest standard cable size above the calculated minimum and compares the result to the Table 54.7 simplified method to confirm which requirement governs.
Save the calculation to your project records or include it in your design documentation. The result can be cross-referenced with your cable schedule and circuit design to verify that all CPCs are adequately sized.
Regulation 543.1 of BS 7671 sets out the requirements for sizing protective conductors. It states that the cross-sectional area of every protective conductor, other than a protective bonding conductor, shall be calculated by the adiabatic equation or selected in accordance with Table 54.7. The regulation makes it clear that the adiabatic equation is the definitive method — Table 54.7 is a simplified alternative that gives conservative (larger) sizes.
The regulation specifies that the calculated cross-sectional area shall be not less than the value determined by the equation S = √(I²t) / k, where the symbols have the meanings described above. It also notes that the k values are given in Tables 54.2 to 54.6, and that the value of I²t shall not exceed the value given by the manufacturer for the protective device.
In practice, this means that for every circuit in an installation, the designer or verifier must either confirm that the CPC size meets Table 54.7 (the simpler check) or perform the adiabatic calculation to verify that the installed CPC is at least as large as the minimum calculated. The adiabatic method is particularly important for non-standard situations — for example, when the CPC is not the same material as the line conductor, when steel wire armour is used as the CPC, or when the designer wants to use a smaller CPC than Table 54.7 would require to reduce costs.
Amendment 4 to BS 7671 (A4:2026), published 15 April 2026, did not change the fundamental adiabatic equation requirements but added Regulation 530.3.201 covering requirements for bidirectional and unidirectional protective devices. The core CPC sizing requirements in Regulation 543.1 remain as established in the 18th Edition.
Zs and the adiabatic check interact for small cables (GN3 Reg 1.25): For smaller cross-sectional area cables, the earth fault loop impedance (Zs) may be limited by the adiabatic equation as well as by the maximum Zs disconnection requirement. A circuit can pass the Zs limit check — meaning the fault current is high enough to operate the device within the permitted disconnection time — yet still fail the adiabatic check if the fault current is modest and the device is slow. Both checks must always be carried out; satisfying one does not guarantee the other.
Elec-Mate is designed by electricians for electricians. The adiabatic equation calculator is one of 70+ calculators that work the way you actually need them to on site — fast, accurate, and available on your phone even without a signal. Enter your values, get the answer, verify the conductor, move on.
The platform also includes 16 certificate types (EICR, EIC, Minor Works, emergency lighting, fire alarm, EV charger, PAT testing, and solar PV), 8 Elec-AI agents, 12 AI tools, and 46+ training courses. Xero and QuickBooks integration means you can manage your jobs, certificates, and invoicing all from one mobile-first app.
Verified reviews from the UK App Store.
Elec-Mate is my go to app for business and electrical work. It's feature rich without feeling cluttered. A true all in one app for quotes, certs, calculations, RAMS, EICRs, and more. I use it every day without fail, and it makes my workflow much smoother since I'm not jumping between apps anymore. The price-to-feature ratio is excellent. Any issues I've had, the developer responds within the hour and usually fixes them the same day. 100% recommend.
I've used the app and the web based version for a while now and it's well worth the investment. If you're an apprentice or experienced Spark give it a go, you won't be disappointed.
I've been using Elec-Mate for a while now, and honestly, it's one of the best apps I've ever downloaded. Every aspect of it feels thoughtfully designed, from the clean and intuitive interface to the powerful features that make everything so easy to manage. It's clear that a lot of care and attention went into building this app, and it shows in every detail.
7-day free trial
Join 1,000+ UK electricians using 70 professional calculators on their phone. 7-day free trial, cancel anytime.
Start your free trialFrom £6.99/mo after the trial — no charge until day 8.
“Replaced three separate apps with Elec-Mate. Certs, quotes, and scheduling all in one place.”
Or download the app
We use cookies to improve the app and measure what works. Cookie Policy