Your Voltage Drop Calculation Is Wrong — The Reactance Error

There is a calculation that nearly every electrical engineer performs weekly, and the majority get it subtly wrong. Not catastrophically wrong — the cables don't catch fire. But wrong enough that circuits either fail commissioning voltage drop tests they should have passed, or pass tests they should have failed. The calculation is voltage drop, and the error is the simplified mV/A/m method.

The simplified method treats cable impedance as purely resistive. It works acceptably for small cables on short runs. For cables above 95mm2, particularly feeding motor loads at power factors below 0.90, it produces results that diverge from reality by 20-40%. And here is the part that surprises most engineers: for large cables at typical industrial power factors, the accurate method sometimes gives a LOWER voltage drop than the simplified method predicts.

The Simplified Method Everyone Uses

The mV/A/m method is elegant in its simplicity. Look up a single value from a table, multiply by current, multiply by length, done:

The mV/A/m values published in cable tables (AS/NZS 3008 Tables 35-42, BS 7671 Table 4D1B-4D4B) combine resistance and reactance into a single number. The problem is that this combined value is calculated at a specific assumed power factor — typically 0.8 for three-phase and sometimes 1.0 for single-phase. If your load's actual power factor differs from the table assumption, the combined value is wrong for your circuit.

Most engineers either do not realise the combined mV/A/m value embeds a power factor assumption, or they know but consider the difference negligible. For small cables, they are right. For large cables, they are not.

The Accurate Method Nobody Uses

The accurate voltage drop formula separates the resistive and reactive components and accounts for the load's actual power factor:

Where R is the cable resistance in ohms per metre, X is the cable reactance in ohms per metre, and phi is the phase angle of the load (cos(phi) = power factor).

This is the formula specified in AS/NZS 3008.1.1:2017 Clause 4.4.2 and BS 7671:2018 Appendix 4, Section 6. It is not optional — it is the standard method. The simplified mV/A/m values are a convenience derived from this formula at a fixed power factor.

AS/NZS 3008.1.1, Clause 4.4.2 — Calculation of voltage drop

Why Reactance Matters More Than You Think

Here is the physical insight that makes the accurate method non-intuitive. As cable cross-section increases:

• Resistance DECREASES (bigger conductor, less resistance)
• Reactance stays approximately CONSTANT (determined by conductor spacing, not cross-section)

This means for large cables, reactance becomes the dominant impedance component:

At 240mm2, the X/R ratio is 0.755 — reactance is 75% of resistance. At 400mm2, reactance exceeds resistance. For these cables, ignoring reactance or using it at the wrong power factor produces a fundamentally wrong result.

The Counter-Intuitive Result: Lower PF Can Mean Lower Voltage Drop

Here is where most engineers' intuition fails. Consider the accurate formula:

At unity power factor (cos(phi) = 1.0, sin(phi) = 0):

At 0.8 power factor (cos(phi) = 0.8, sin(phi) = 0.6):

For a 240mm2 cable: R = 0.098, X = 0.074

• At PF = 1.0: factor = 0.098 x 1.0 + 0.074 x 0.0 = 0.098
• At PF = 0.8: factor = 0.098 x 0.8 + 0.074 x 0.6 = 0.0784 + 0.0444 = 0.1228

So at 0.8 PF, the voltage drop is 0.1228/0.098 = 1.253 times the unity PF result — 25% higher. The reactive component adds significantly.

But now compare two different calculations for the same cable at PF = 0.8:

Simplified method (using the resistance-only mV/A/m, ignoring reactance entirely): The engineer looks up a combined mV/A/m value that was computed at PF = 1.0 or uses only R. This UNDERSTATES the voltage drop because it misses the X sin(phi) term.

The critical flip: For very large cables (400mm2+) at high power factors approaching unity, the voltage drop is dominated by R. But the same cable at 0.8 PF has a component from X sin(phi) that partially replaces the R cos(phi) reduction. Depending on the X/R ratio, the net voltage drop at 0.8 PF can be either higher or lower than at 1.0 PF. The simplified method cannot capture this trade-off at all.

Worked Example 1: 240mm2 Cable at 200m

Scenario: 240mm2 single-core XLPE cables in trefoil, 200m run, 415V three-phase, load = 350A at PF = 0.80.

Cable data (from AS/NZS 3008 Table 35, 75C operating temperature):

• R = 0.098 ohm/km = 0.000098 ohm/m
• X = 0.074 ohm/km = 0.000074 ohm/m

Simplified method (resistance only):

Accurate method (R cos(phi) + X sin(phi)):

The error: 14.88V vs 11.88V — the simplified method UNDERSTATES the voltage drop by 25.3%. The simplified result says 2.86%, comfortably within a 5% limit. The accurate result says 3.58%, which is still within limits but has significantly less margin.

Now consider a longer run or higher current, and the difference between "pass with margin" and "fail" can depend entirely on whether the engineer used the correct formula.

Worked Example 2: The Cable That "Passed" Then Failed

Scenario: 150mm2 4-core XLPE/SWA cable, 280m run, 415V three-phase, motor load = 250A at PF = 0.75 (partially loaded motor).

Cable data:

• R = 0.157 ohm/km
• X = 0.076 ohm/km

Simplified method:

Engineer's conclusion: 4.59%, within the 5% limit. Pass.

Accurate method (PF = 0.75, sin(phi) = 0.661):

Still within the 5% limit, but only just. Now factor in that cable resistance increases with temperature. At 90C (the maximum operating temperature for XLPE), resistance increases by approximately 17% over the 75C value used above:

The cable fails at 5.50%. The simplified calculation said 4.59% — a comfortable pass. The accurate calculation at operating temperature says 5.50% — a clear fail.

This is the scenario that leads to motors with "intermittent starting problems" and "unexplained undervoltage trips." The cable was sized using a simplified method that indicated compliance. The physics says otherwise.

What the Standards Actually Require

AS/NZS 3008.1.1:2017

Clause 4.4.2 provides the full voltage drop formula incorporating both R and X components. Clause 4.4.3 requires the use of conductor resistance at the actual operating temperature, not reference temperature. Tables 35-42 provide both combined mV/A/m values (at assumed PF = 0.8) AND separate R and X values, but the combined values are only valid at the stated power factor.

AS/NZS 3008.1.1, Clause 4.4.3 — Conductor resistance at operating temperature

BS 7671:2018

Appendix 4, Section 6 provides the methodology. Tables 4D1B through 4D4B provide separate R (r) and X (x) columns in mV/A/m format. The standard states that for loads at power factors other than those used to derive the tabulated combined values, the separate R and X columns must be used with the full formula.

BS 7671, Appendix 4, Section 6 — Voltage drop in consumers' installations

NEC (NFPA 70)

Chapter 9, Table 9 provides separate R (effective impedance at 0.85 PF) and X columns. Unlike BS 7671 and AS/NZS 3008, the NEC also provides an "effective Z at 0.85 PF" column that pre-computes the combined value at 0.85 PF. However, Informational Note No. 2 to Chapter 9, Table 9 explicitly provides the formula for other power factors: Vd = sqrt(3) x I x L x (R cos(theta) + X sin(theta)).

What To Do About It

For cables 95mm2 and above, or any run over 100m with motor loads:

1. Always use the full formula with separate R and X values from the cable tables. Never use the combined mV/A/m value unless the load power factor exactly matches the table assumption.

2. Use the correct operating temperature for resistance. At full load, XLPE cables run at 75-90C, and PVC cables at 70C maximum. The resistance at operating temperature can be 15-20% higher than the reference value.

3. Know your actual load power factor. Motors at partial load (the normal operating condition) have lower power factor than at full load. A motor rated at PF = 0.85 at full load may operate at PF = 0.70 at 50% load. Use the actual operating power factor, not the nameplate value.

4. Check both starting and running conditions. Motor starting current is typically 6-8x full load current at a very low power factor (0.15-0.30). The voltage drop during starting is a separate and often more critical check.

5. Add margin for cable ageing. Conductor resistance increases slightly over the cable's life due to oxidation and annealing. A 5% allowance on resistance is good engineering practice for cables expected to operate near their thermal limit for 20+ years.

The Bottom Line

The simplified mV/A/m method is a convenience approximation from an era when calculations were done by hand. With modern software (or even a spreadsheet), there is no reason not to use the full formula for every circuit. The additional effort is negligible. The consequence of getting it wrong — motors that won't start, circuits that fail commissioning, or cables that pass a desk check but fail in service — is not.

If you have motor circuits that start reluctantly, trip on undervoltage intermittently, or show "unexpected" voltage drop during commissioning, recalculate using the full impedance formula at operating temperature. The answer is likely in the cable impedance, not the motor.

Related Resources

• Why Your Cable Sizing Is Wrong: The Reactive Component Most Engineers Ignore — Deep dive into the R + X impedance problem
• Motor Voltage Drop: Startup vs Running — Two Different Problems — Starting current voltage drop is the harder calculation
• Voltage Drop: The 100m Workshop Cable — Four standards compared on the same cable run
• View all worked examples