Ib, In and Iz Explained
Ib ≤ In ≤ Iz is the rule that ties a circuit's load, its protective device and its cable together. Here is what each term means and how to apply the inequality on a real circuit.
Ib, In and Iz are three currents at the heart of BS 7671 circuit design. Get the relationship between them right and the protective device will carry the load without nuisance tripping, while still protecting the cable against overload.
The core requirement, from Regulation 433.1.1, is simple to state: Ib ≤ In ≤ Iz. This guide defines each term, explains why the inequality has to hold, and works through a shower circuit so you can see the numbers line up.
Key takeaways
- Ib = design current — the load the circuit is designed to carry, in amps.
- In = nominal (rated) current of the protective device — the fuse or MCB/RCBO rating.
- Iz = continuous current-carrying capacity of the cable as installed, after correction factors.
- The rule is Ib ≤ In ≤ Iz: the device must be big enough for the load but no bigger than the cable can take.
- A fourth check, I2 ≤ 1.45 × Iz, is satisfied automatically by modern BS EN 60898/61009 devices.
What each term means
The three quantities describe the load, the device protecting it, and the cable carrying it — in that order.
| Symbol | Name | What it is |
|---|---|---|
| Ib | Design current | The current the circuit is designed to carry in normal service — the actual load, in amps. |
| In | Nominal current of the device | The rated current of the protective device (e.g. a 32 A MCB has In = 32 A). |
| Iz | Current-carrying capacity | The continuous current the cable can carry in its installed conditions, after correction factors. |
Why Ib ≤ In ≤ Iz
Read the inequality in two halves. Ib ≤ In means the device must be rated at least as high as the load, or it would trip in normal use. In ≤ Iz means the device must not be rated higher than the cable can safely carry, or an overload could sit below the trip point and cook the cable.
In other words, the protective device sits between the load and the cable: large enough to pass the design current, small enough to protect the conductor. If In ends up larger than Iz, you either increase the cable size (raise Iz) or drop to a smaller device.
The fourth condition
Regulation 433.1.1 also requires I2 ≤ 1.45 × Iz, where I2 is the current that reliably operates the device. For devices to BS EN 60898 and BS EN 61009 (MCBs and RCBOs) I2 = 1.45 × In, so once In ≤ Iz the 1.45 condition is met automatically. It only needs a separate check for older BS 3036 rewireable fuses, where a 0.725 factor is applied instead.
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Where Iz comes from
Iz is not the raw tabulated figure. You start with It — the tabulated current-carrying capacity from Appendix 4 for the cable, reference method and insulation — then apply correction factors for the installed conditions: ambient temperature (Ca), grouping (Cg), thermal insulation (Ci) and, for buried cables, a soil/ depth factor.
The design condition is It ≥ In ÷ (Ca × Cg × Ci × …). The installed capacity Iz is the tabulated It multiplied by those same factors, and the design is sound when Iz is at least In. In practice you size the cable so that, after derating, it still comfortably carries the device rating.
Worked example: a 9.5 kW shower
Design current: a 9.5 kW shower at 230 V draws Ib = 9,500 ÷ 230 ≈ 41.3 A.
Device: pick In so that In ≥ Ib. A 45 A MCB works (45 ≥ 41.3); a 40 A device would be too small and nuisance-trip.
Cable: the cable's Iz must be ≥ 45 A after correction. 10 mm² twin-and-earth clipped direct (reference method C) has a tabulated It of about 64 A; even with some grouping and ambient derating its Iz stays well above 45 A, so Ib (41.3) ≤ In (45) ≤ Iz (≈60) holds. Had the cable run through insulation and dropped below 45 A, you would move up to 16 mm² or reduce the device.
Don't forget voltage drop
Passing Ib ≤ In ≤ Iz proves the cable is protected against overload — it does not prove the circuit is acceptable. You still have to check voltage drop and that the earth fault loop impedance (Zs) allows disconnection in time.
From guidance to action
Frequently asked questions
What does Ib mean in electrical terms?
Ib is the design current of a circuit — the current it is intended to carry in normal service, worked out from the connected load. For a 9.5 kW shower at 230 V, Ib is about 41.3 A.
What is Iz in BS 7671?
Iz is the continuous current-carrying capacity of the cable in its actual installed conditions — the tabulated capacity (It) after applying correction factors for ambient temperature, grouping and thermal insulation.
What is the difference between In and Iz?
In is the rated current of the protective device (the fuse or MCB rating). Iz is how much current the cable can carry. The device rating must not exceed the cable capacity, so In ≤ Iz.
Why must Ib ≤ In ≤ Iz?
So the protective device is big enough to pass the load without tripping (Ib ≤ In) but small enough to protect the cable against overload (In ≤ Iz). It is the overload-protection requirement of Regulation 433.1.1.
Related guides
Cable Sizing to BS 7671
The full cable sizing method — design current, correction factors, tabulated ratings and volt drop.
Cable Reference Methods Explained
How cable installation reference methods affect current-carrying capacity, correction factors and final cable selection.
Voltage Drop Explained (BS 7671)
The 3% and 5% limits, the mV/A/m method, and how to correct a circuit that fails on volt drop.
