How do you calculate Zs?

Zs is calculated from the prospective earth fault current using Ohm's law: Zs = U0 / Ia, where U0 is the nominal phase-to-earth voltage (usually 230 V in the UK) and Ia is the current that causes automatic disconnection of the protective device within the required time. In practice, BS 7671 provides tabulated maximum Zs values for common breakers and fuses.

What is the difference between Ze and Zs?

Ze is the external earth fault loop impedance provided by the supply network and earthing arrangement, measured at the origin of the installation. Zs is the total earth fault loop impedance at the end of a circuit and includes Ze plus the impedance of the line and protective conductors in the installation wiring. Zs is always greater than or equal to Ze.

What safety margin should I apply to Zs values?

BS 7671 tabulated Zs values are based on a conductor temperature of 80°C for thermoplastic insulation. To account for higher resistance at operating temperature and measurement tolerances, many designers apply a margin of 0.8 (i.e. design Zs ≤ 0.8 × tabulated Zs). This calculator allows you to apply an optional 0.8 factor when checking measured Zs.

Can I use this Zs calculator for TT systems?

Yes. For TT systems, disconnection is normally provided by an RCD. In that case the relevant parameter is the earth electrode resistance RA and the RCD residual operating current IΔn. BS 7671 requires RA × IΔn ≤ 50 V. This tool includes a TT mode where you can enter RA and IΔn and it will check compliance with the 50 V touch voltage limit.

BS 7671 Earth Fault Loop Impedance (Zs) Calculator

Q: What is Zs in BS 7671?

In BS 7671, Zs is the earth fault loop impedance of a final circuit or distribution circuit. It is the total impedance of the fault path from the point of fault, through the line conductor, protective conductor and supply, back to the source. Zs determines the fault current and therefore whether protective devices will disconnect within the required time.

What is earth fault loop impedance (Zs)?

In BS 7671, the earth fault loop impedance Z_s is the total impedance of the fault path from the point of fault, through the line conductor, protective conductor and supply, back to the source. It determines the earth fault current and therefore whether protective devices will disconnect within the required time.

Basic relationship

For a single-phase circuit:

Z_s = U₀ / I_a

U₀ – nominal phase-to-earth voltage (typically 230 V)
I_a – current causing automatic disconnection of the protective device within the required time

Relationship between Ze, R1+R2 and Zs

The measured Z_s at the end of a circuit is made up of the external earth fault loop impedance Z_e plus the impedance of the line and protective conductors in the installation:

Z_s = Z_e + (R₁ + R₂)

Designers often calculate R₁ + R₂ from cable length and resistance per metre, then add Z_e supplied by the DNO to estimate Z_s and compare it with the maximum permitted value.

How this Zs calculator works

This tool implements the core BS 7671 principle that the fault current must be high enough to operate the protective device within the required disconnection time. For MCBs, it uses typical multiples of rated current; for RCDs and TT systems it uses the 50 V touch voltage limit.

1. TN systems with MCBs

For MCBs to BS EN 60898-1, the instantaneous (magnetic) trip is typically:

Type B: 3–5 × In (we conservatively use 5 × In)
Type C: 5–10 × In (we conservatively use 10 × In)
Type D: 10–20 × In (we conservatively use 20 × In)

The calculator sets I_a to the chosen multiple of In and applies Ohm’s law:

Z_s,max = U₀ / I_a

This gives a conservative maximum Z_s for the selected breaker type and rating. In practice, you should compare with the tabulated values in BS 7671 or manufacturer data; this tool is designed to be on the safe side.

2. RCD-based disconnection (TN or TT)

For RCDs, BS 7671 requires that the product of earth resistance and residual operating current does not exceed the permissible touch voltage (usually 50 V):

R × I_Δn ≤ 50 V

In TN systems, R is effectively Z_s; in TT systems, R is the earth electrode resistance R_A plus the resistance of the protective conductor. This calculator:

Computes the maximum permitted Z_s or R_A as R_max = 50 / I_Δn
Checks your measured Z_s or R_A against this limit

3. Optional 0.8 design factor

Many designers apply a factor of 0.8 to tabulated Z_s values to allow for increased conductor resistance at operating temperature and measurement tolerances. When you tick “Apply 0.8 design factor”, the calculator checks:

Z_s,measured ≤ 0.8 × Z_s,max

Worked example

Consider a 32 A Type B MCB on a 230 V TN system, final circuit ≤ 32 A:

Select TN, MCB Type B, In = 32 A, U₀ = 230 V.
The calculator uses I_a = 5 × 32 A = 160 A.
Maximum Z_s is: Z_s,max = 230 / 160 ≈ 1.44 Ω.
If your measured Z_s is 0.95 Ω, with 0.8 factor applied, the design check is 0.95 ≤ 0.8 × 1.44 ≈ 1.15 Ω → Pass.

Limitations and good practice

This tool uses simplified assumptions and conservative multiples of In; always refer to the latest BS 7671 tables and manufacturer data.
Use an approved loop impedance tester and follow safe isolation procedures when measuring Z_s.
For complex installations (three-phase, high prospective fault currents, special locations), a full design calculation and coordination study is recommended.

FAQ

Is Zs the same as loop impedance on my tester?

Yes. Most multifunction testers label the measurement as “loop impedance” or “Zs”. Some instruments also allow a separate “Ze” test at the origin.

What if my measured Zs is slightly above the tabulated value?

If Z_s exceeds the tabulated maximum, the fault current may be insufficient to guarantee disconnection within the required time. Options include:

Using a larger conductor size to reduce R₁ + R₂
Shortening the circuit length
Using a more sensitive protective device (e.g. RCD)

Always document your design assumptions and verify against BS 7671.