R1+R2 Zs Ze Calculator
Calculate combined conductor resistance (R1+R2) and total loop impedance (Zs). Verify Ze values and protective device compliance according to BS 7671 earth fault loop requirements.
R1+R2 Zs Ze Calculator
How to Use R1+R2 Zs Ze Calculator
Verifying earth loop impedance is one of the most critical safety verification steps carried out by electricians during electrical installation testing, inspection, and EICR reporting. Follow these simple steps to calculate loop values and verify safety margins:
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1Measure Ze. Use a loop tester to measure the external loop impedance at the supply origin (main intake or distribution board) with the installation isolated from the earth.
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2Measure R1. Perform a dead continuity test on the line conductor from the distribution board to the furthest point of the circuit.
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3Measure R2. Test the circuit protective conductor (CPC) continuity to measure its end-to-end resistance.
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4Select protective device type. Choose the circuit breaker or fuse type (e.g. Type B MCB or BS 88 fuse) from the dropdown list.
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5Select protective device rating. Pick the rating (In) of the installed breaker or fuse.
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6Calculate. Click "Calculate" to automatically determine the combined conductor resistance ($R_1+R_2$), the total loop impedance ($Z_s$), and check compliance.
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7Review compliance result. Ensure the calculated value PASSES against the tabulated maximum permitted Zs limit, which includes voltage factors ($C_{\text{min}} = 0.95$) under BS 7671.
These calculations are essential when issuing an Electrical Installation Condition Report (EICR) to guarantee that circuits are safe for automatic disconnection of supply under earth fault conditions.
How to Calculate R1+R2 Zs Ze
To verify that the automatic disconnection of supply (ADS) works as designed, the circuit's total earth loop impedance must be low enough to flow a high fault current that instantly trips the protective device. The mathematical calculations follow basic resistance series formulas defined by BS 7671:
Formula 1 — Conductor Resistance (R1 + R2)
The total resistance of the circuit's line conductor (R1) and earth protective conductor (R2) is calculated as follows:
Formula 2 — Total Loop Impedance (Zs)
The total loop path impedance at the end of the circuit is the sum of the external grid supply path impedance (Ze) and the circuit's internal resistance:
Worked Example: TN-C-S Installation
Let's calculate loop impedance and safety compliance based on standard on-site measurements:
- Measured Ze: 0.35 Ω (typical TN-C-S origin value)
- Measured R1: 0.28 Ω
- Measured R2: 0.22 Ω
- Installed Device: 32A Type B MCB (BS EN 60898)
Step 1 — Calculate R1 + R2
Combine the line and CPC resistances:
Step 2 — Calculate Total Zs
Add the external impedance Ze to R1+R2:
Step 3 — Verify Compliance against BS 7671 limits
Under BS 7671 Table 41.3, the maximum permitted Zs for a 32A Type B MCB (at 230V, Cmin = 0.95) is 1.37 Ω. We compare the calculated Zs with this limit:
Result: Since the loop impedance is well below the maximum limit, the circuit disconnects in less than 0.4 seconds under fault conditions, achieving a PASS status.
Why Loop Impedance Matters for ADS
Under the IET Wiring Regulations, automatic disconnection of supply (ADS) is the primary method of shock protection. If an electrical fault occurs (such as a live wire touching a metal casing), the current travels through the earth path. A low loop impedance ensures that this fault current is large enough to trigger the circuit breaker instantaneously. If the loop impedance is too high, the fault current will be too low, the breaker will not trip, and metal enclosures will remain live at 230V, presenting a fatal hazard.
R1+R2 Zs Ze Calculator Chart
This reference chart displays maximum permitted earth loop impedance values (Zs) for standard Type B and Type C miniature circuit breakers (MCBs) at UK nominal supply voltage (230V) with a minimum voltage factor of 0.95 applied.
| Device Type | Rating (In) | Maximum Zs (Uncorrected) | Maximum Zs (Corrected Cmin = 0.95) |
|---|---|---|---|
| Type B MCB (BS EN 60898) | 6A | 7.67 Ω | 7.28 Ω |
| Type B MCB (BS EN 60898) | 10A | 4.60 Ω | 4.37 Ω |
| Type B MCB (BS EN 60898) | 16A | 2.88 Ω | 2.73 Ω |
| Type B MCB (BS EN 60898) | 20A | 2.30 Ω | 2.19 Ω |
| Type B MCB (BS EN 60898) | 32A | 1.44 Ω | 1.37 Ω |
| Type B MCB (BS EN 60898) | 40A | 1.15 Ω | 1.09 Ω |
| Type B MCB (BS EN 60898) | 50A | 0.92 Ω | 0.87 Ω |
| Type B MCB (BS EN 60898) | 63A | 0.73 Ω | 0.69 Ω |
| Type C MCB (BS EN 60898) | 6A | 3.83 Ω | 3.64 Ω |
| Type C MCB (BS EN 60898) | 10A | 2.30 Ω | 2.19 Ω |
| Type C MCB (BS EN 60898) | 16A | 1.44 Ω | 1.37 Ω |
| Type C MCB (BS EN 60898) | 20A | 1.15 Ω | 1.09 Ω |
| Type C MCB (BS EN 60898) | 32A | 0.72 Ω | 0.68 Ω |
| Type C MCB (BS EN 60898) | 40A | 0.58 Ω | 0.55 Ω |
| Type C MCB (BS EN 60898) | 50A | 0.46 Ω | 0.44 Ω |
| Type C MCB (BS EN 60898) | 63A | 0.37 Ω | 0.35 Ω |
Note: Values may vary depending on BS 7671 amendment edition and manufacturer documentation. Always verify current regulations.
R1+R2 Zs Ze Calculator Frequently Asked Questions
In electrical testing, R1+R2 is the combined resistance of the line (phase) conductor and the circuit protective conductor (CPC or earth) measured from the distribution board to the furthest point of the circuit. This value is critical for verifying that all conductors are continuous and that the earth path resistance is low enough to allow protective devices to operate during a fault.
Zs is calculated by adding the external earth fault loop impedance (Ze) of the installation to the circuit conductor resistance (R1+R2) using the formula Zs = Ze + (R1+R2). This calculation helps verify the total loop path impedance, which must be lower than the maximum permitted values specified in BS 7671 to ensure automatic disconnection.
In BS 7671, Ze represents the external earth fault loop impedance measured at the origin of the electrical installation. It is the impedance of the supply network up to the consumer unit or distribution board, including the supply transformer windings, distributor line conductors, and the earth return path back to the source substation.
The maximum Zs is the highest allowable earth fault loop impedance for a protective device to trip and disconnect the supply within the safety time limits of BS 7671. For a Type B 32A MCB protecting a final circuit, the tabulated maximum permitted Zs is 1.44 Ω, which corrected for voltage fluctuations (Cmin = 0.95) yields a safe design limit of 1.37 Ω.
Zs testing is critical to verify the automatic disconnection of supply (ADS) under fault conditions. If the loop impedance is too high, the fault current will be too low to trip the circuit breaker or blow the fuse fast enough, leaving exposed metallic parts of the installation energized and creating a severe risk of electric shock and fire.
Yes, Zs can be calculated by summing the measured external loop impedance (Ze) and the dead continuity test results (R1+R2). BS 7671 allows this calculation as a valid method for proving disconnection compliance, particularly when live testing at the end of the line presents safety risks or is impractical.
All three major UK earthing systems use Ze to define the external fault loop. In TN-C-S installations, Ze is usually low (maximum 0.35 Ω). In TN-S systems, the maximum typical Ze is 0.8 Ω, while TT earthing systems rely on earth electrodes and typically exhibit much higher Ze values, requiring RCDs for disconnection.
If the calculated or measured Zs exceeds the maximum permitted BS 7671 limits, the circuit does not comply with safety regulations. In the event of a fault, the protective device will not trip within the required time (e.g. 0.4s). Corrective actions include increasing conductor sizes, changing the breaker type/rating, or installing an RCD or RCBO for earth fault protection.