R1 R2 Calculator
Calculate R1 + R2 (line and earth conductor resistance) from the total earth fault loop impedance and the source impedance. Enter both values in ohms to verify circuit earth continuity.
Resistance Split Calculator from Ze and Zs
R1 + R2 Formula
Where:
- \(R_1\) — resistance of the line (phase) conductor of the circuit (Ω)
- \(R_2\) — resistance of the circuit protective conductor, CPC (Ω)
- \(Z_e\) — total earth fault loop impedance measured at the furthest point of the circuit (Ω)
- \(Z_s\) — source impedance, i.e. the part of the loop contributed by the supply transformer and incoming cables (Ω)
The formula rearranges the earth fault loop relationship \(Z_e = Z_s + (R_1 + R_2)\): the impedance measured at the end of the circuit, minus the impedance contributed by the supply, leaves the combined resistance of the circuit's own line and protective conductors.
R1 + R2 – Calculation Example
Example: a final circuit is tested at the point furthest from the consumer unit. The measured total earth fault loop impedance is 0.76 Ω, and the impedance of the source side of the installation is 0.28 Ω.
\[ R_1 + R_2 = 0.76 - 0.28 = 0.48~\Omega \]
Result: \(R_1 + R_2 = 0.48~\Omega\). These are the calculator's default values, so you can reproduce the result directly.
How to use the calculator
- Enter the Total circuit impedance \(Z_e\) — the earth fault loop impedance measured at the furthest point of the circuit, in ohms.
- Enter the Source impedance \(Z_s\) — the impedance of the supply transformer and incoming service, in ohms. Typical declared values are 0.35 Ω for TN-C-S and 0.8 Ω for TN-S supplies in the UK.
- The calculator returns R1 + R2, the combined resistance of the line and protective conductors. The source impedance must not exceed the total impedance, or the calculator shows an error.
What are R1 and R2?
\(R_1\) is the resistance of the line (live) conductor of a circuit, measured from the consumer unit to the furthest outlet or accessory. \(R_2\) is the resistance of the circuit protective conductor (CPC, the earth wire) over the same route. Together they form the part of the earth fault loop that lies inside the installation, and their sum is one of the key numbers recorded when testing a new circuit or certifying an installation under BS 7671 (the UK Wiring Regulations).
When a line-to-earth fault occurs, fault current flows through the line conductor, back through the CPC, and around the supply source. The total impedance of this path — the earth fault loop impedance — determines how large the fault current will be, and therefore how quickly the protective device (fuse, MCB or RCBO) can operate. If the loop impedance is too high, the fault current is too small to trip the breaker within the required disconnection time, leaving exposed metalwork live and dangerous.
Splitting the measured loop impedance into the source part and the installation part lets you check the wiring itself. An \(R_1 + R_2\) value that is much higher than expected for the cable size and length points to loose connections, damaged conductors, undersized cable, or joints with high resistance — problems that a whole-loop measurement alone might not isolate. The result is also used to verify conductor sizing against the adiabatic equation and to confirm that the calculated \(Z_s\) at the design stage will keep the protective device within its maximum permitted impedance.
Assumptions, limitations and practical tips
- Notation warning: conventions vary. In BS 7671 the total measured loop impedance is usually written \(Z_s\) and the external (supply) part \(Z_e\). In this calculator, "Total circuit impedance" is the full measured value at the end of the circuit and "Source impedance" is the upstream part — always check which convention your test instrument or form uses before entering values.
- Temperature: tabulated conductor resistances apply at 20 °C, but during a fault the conductors heat up and their resistance rises. Design and verification tables in BS 7671 apply correction factors for this; a measured \(R_1 + R_2\) that looks marginally acceptable cold may not be acceptable in fault conditions.
- The result is a sum: this calculator gives \(R_1 + R_2\), not the individual values. If you need \(R_1\) and \(R_2\) separately, measure them individually with a low-resistance ohmmeter (the standard \(R_1 + R_2\) test method) or split the sum in the measured ratio.
- System type: the earth fault loop concept applies to TN systems (TN-S, TN-C-S). In a TT system most of the loop impedance is in the earth electrode and the supply's earth return, so \(R_1 + R_2\) is a small part of a much larger loop that normally requires an RCD for fault protection.
- Cable size: to check whether the result is reasonable, compare it against the resistance per metre of the installed cable — our Wire Gauge calculator helps with conductor sizes, and the Parallel Resistance calculator is useful when conductors run in parallel.
- Source impedance: if you don't have a measured value, use the supply operator's declared figure; for a privately owned transformer you can estimate it from the nameplate data with the Single Phase Transformer calculator.
Frequently Asked Questions
How do I measure R1 + R2 directly instead of calculating it?
The standard method is the R1 + R2 test: isolate the circuit, link the line conductor to the CPC at the consumer unit, then measure resistance between line and earth at the furthest point with a low-resistance ohmmeter. The instrument reads the sum of both conductor resistances directly. Null the test leads first, and record the value at 20 °C or apply the relevant correction factor before comparing against design figures.
What is a normal value for R1 + R2?
There is no single fixed limit — the acceptable value depends on cable size, length and the maximum earth fault loop impedance allowed by the protective device. As a rough guide, a typical final circuit in 2.5 mm² / 1.5 mm² twin-and-earth cable has about 0.02 Ω per metre, so a 20 m run gives roughly 0.4 Ω. If your measured value is far above the figure calculated from cable length and resistance per metre, suspect a loose or corroded connection.
Can I predict R1 + R2 from cable length and cross-section?
Yes. Multiply the route length by the combined resistance per metre of the line and protective conductors. For copper, use about 0.0074 Ω/mm² per metre per conductor:
\[ R_1 + R_2 \approx \frac{0.0074 \times L \times (1/A_1 + 1/A_2)}{1} \]
where \(L\) is length in metres and \(A_1\), \(A_2\) are the conductor cross-sections in mm². Compare this design value with your test result — a large difference indicates a wiring fault.
Why does the calculator show an error when I enter my values?
The total measured loop impedance must always be greater than or equal to the source impedance, because the installation's own conductors add resistance on top of the supply side. If you get an error or a negative result, you have almost certainly swapped the two inputs, or you are mixing measurement conventions (some instruments label the total \(Z_s\) and the external part \(Z_e\) — the opposite of this calculator). Check your meter's labels and re-enter.
How do I convert between ohms and milliohms for test results?
Test instrument readouts and cable resistance tables often use milliohms (mΩ). Convert by dividing by 1000: 480 mΩ equals 0.48 Ω. The calculator works in ohms, so a loop impedance shown as 760 mΩ should be entered as 0.76. Working consistently in ohms avoids factor-of-1000 mistakes, which are among the most common errors when recording earth loop test results.
Does temperature affect my measured R1 + R2 value?
Yes. Conductor resistance rises about 0.4 % per °C for copper. Tests are usually carried out near 20 °C, the temperature at which tabulated values apply, so a cold measurement is directly comparable. However, during a real fault the conductors heat up significantly, and BS 7671 verification tables account for this. A value that passes with little margin at room temperature may still be inadequate under fault conditions, so treat borderline results with caution.
How is R1 + R2 used to check the protective device will trip?
Add the source impedance to your \(R_1 + R_2\) to get the total loop impedance, then compare it with the maximum Zs permitted for the fuse, MCB or RCBO. If the total exceeds the device's limit, the fault current will be too small to guarantee disconnection within the required time (0.4 s or 5 s depending on the circuit). Only qualified persons should certify this — verification requires the correct tables and test equipment.