Why do three-phase calculations omit the square root of 3 multiplier when using Table 4D4B?

In BS 7671 Appendix 4 tables, tabulated three-phase mV/A/m figures are already line-to-line values pre-scaled by root 3. Calculating with balanced line current Ib and length L directly provides line-to-line voltage drop.

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Voltage Drop Calculator UK (BS 7671 mV/A/m Limits)

BS 7671 Appendix 4 voltage-drop calculation from first principles: VD = (mV/A/m × Ib × L) / 1000. You supply your own mV/A/m value from the standard - no BS 7671 tables are republished here.

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⚠️ Appendix 4 Cumulative Intake Budget:The 3% (6.9 V) lighting and 5% (11.5 V) power limits under BS 7671 Reg 525.1 represent the total cumulative budget from the origin of the installation (DNO cut-out) to the final load. If an upstream distribution submain has already consumed 2% (4.6 V), your final circuit must not exceed the remaining allowance.

SupplySupply voltage

230 V single-phase400 V three-phase

CircuitmV/A/m value Voltage drop per amp per metre, from BS 7671 Appendix 4 tables. For single-phase (230 V), use the single-phase mV/A/m column. For three-phase (400 V), use the three-phase mV/A/m column: the formula VD = (mV/A/m × Ib × L) / 1000 already accounts for this; do NOT apply an additional √3 factor.Design current (Ib) [A] Amperes.Length of run (L)Metres.

Circuit typeLimit to check against

Lighting (3 %)Other uses (5 %)

BS 7671 limits for final circuits supplying lighting (3 %) or other uses (5 %).

Results & Summary

⚡ UK ELECTRICAL WORKSTATIONWITHIN LIMIT

Circuit: Circuit C1

Voltage Drop: -

Allowed Limit: 3% (6.9 V)

BS 7671:2018+A4:2026 Reg 525.1Verified On-Site

Voltage drop -

Percentage of supply -

BS 7671 limit used -

Show Full Mathematical Derivation (AM2 Working Standard)

BS 7671:2018+A4:2026

AM2 PORTFOLIO & DESIGN AUDIT FORMATTRANSPARENT FIRST-PRINCIPLES MATHS

Step 1 · Circuit Parameters & Unit Value

Tabulated Millivolt Drop Formula

Vd = (mV/A/m × Ib × L) / 1000

Vd = (18.0 × 20.0 × 15.0) / 1000 = 5.40 V

mV/A/m: 18.0 mV/(A·m) (BS 7671 Appendix 4 tabulated value)
Ib (Design Current): 20.0 A
L (Route Length): 15.0 m

Step 2 · Percentage Voltage Drop Calculation

Supply Voltage Basis

% Drop = (Vd / Vsupply) × 100

% Drop = (5.40 / 230) × 100 = 2.35 %

Nominal Voltage: 230 V

Step 3 · Permitted Limit Verification

BS 7671 Reg 525.1 Threshold Check

Permitted: ≤ 3.0 % (6.90 V for lighting)

Result: 2.35 % ≤ 3.00 % (✔ WITHIN PERMITTED LIMIT)

BS 7671:2018+A4:2026 Reg 525.1 · Appendix 4

Statutory Compliance Note:Worked example to BS 7671:2018+A4:2026. To be verified by a competent person against current standards and manufacturer data before use (EAWR 1989).

Worked example

230 V single-phase, 2.5 mm² cable, mV/A/m = 18, Ib = 20 A, L = 15 m, lighting circuit.

VD = (18 × 20 × 15) / 1000 = 5.4 V

5.4 / 230 = 2.35 %: within the 3 % limit (6.9 V).

Statutory Compliance Note:Worked example to BS 7671:2018+A4:2026. To be verified by a competent person against current standards and manufacturer data before use (EAWR 1989).

Table columns: BS 7671 Appendix 4 voltage drop tables (e.g. Table 4A2) have separate columns for single-phase and three-phase mV/A/m values. Ensure you enter the value from the correct column for your supply type. The three-phase column already includes the √3 factor in the tabulated value.

Regulation reference: Per BS 7671 Appendix 4, Table 4A2 for voltage-drop values per metre. The 3 % / 5 % limits are from BS 7671 Table 4A2 (or 4B1 for the older layout).

Frequently Asked Questions

What are the statutory voltage drop limits under BS 7671?

Under BS 7671:2018+A4:2026 Appendix 4 (Section 6.4), for low-voltage installations supplied directly from a public distributor network, maximum voltage drop between the installation origin and equipment terminals is 3% for lighting circuits (6.9 V at 230 V / 12.0 V at 400 V) and 5% for other uses such as heating and power sockets (11.5 V at 230 V / 20.0 V at 400 V). If supplied from a private substation, limits increase to 6% and 8% respectively.

Why do three-phase calculations omit the √3 multiplier when using Table 4D4B?

In BS 7671 Appendix 4, tabulated mV/A/m values in three-phase columns are already line-to-line values pre-multiplied by √3. When calculating three-phase voltage drop using VD = (mV/A/m × Ib × L) / 1000, entering the balanced phase current Ib and route length L gives the exact line-to-line drop directly without applying an additional √3 multiplier.

How does conductor operating temperature affect mV/A/m voltage drop?

Standard tabulated mV/A/m values in BS 7671 assume conductors operate at their maximum permissible temperature (70°C for thermoplastic PVC, 90°C for thermosetting XLPE). When design current Ib is significantly below cable tabulated capacity It, conductors run cooler and have lower electrical resistance, producing less voltage drop. Appendix 4 Section 6.1 provides the temperature correction formula for precise assessments.