Enter the supply voltage, load current, one-way cable run length, conductor material, cross-sectional area, and power factor. Typical copper resistivity at 20 °C is 17.2 nΩ·m; aluminium is 28.2 nΩ·m.
Conductor Material
Source (nominal) voltage
V_s:=230V=230 V
Load current
I:=40A=40 A
One-way cable run length
L:=50m=50 m
A_csa:=10mm^2=1e-05 m^2
Conductor cross-sectional area
Load power factor (cos φ)
pf:=0.9=0.9
Calculations
The conductor resistance for one-way length L is calculated from the resistivity formula R = ρ × L / A. The total loop resistance is double this value because current flows out through one conductor and returns through the other.
R_one:=(rho·L)/(A_csa)=0.09 Ω
One-way conductor resistance
Total loop resistance (out + return)
R_loop:=2·R_one=0.17 Ω
For circuits with a lagging power factor, the reactive component of the voltage drop adds to the resistive component. The power factor angle φ is recovered from the cosine, and tan φ gives the ratio of reactive to active current component.
Cable reactance for standard PVC/XLPE cables is typically 0.08–0.10 Ω/km per conductor. A representative value of 0.08 Ω/km one-way is used here; adjust for your cable type.
phi:=arccos(pf)=0.45 rad
Power factor angle φ (radians)
tan_phi:=(sin(phi))/(pf)=0.48
tan φ = sin φ / cos φ
Cable reactance per km (one conductor)
x_km:=0.08Ohm/km=8e-05 kg·m/A^2/s^3
One-way conductor reactance
X_one:=x_km·L=4e-03 Ω
X_loop:=2·X_one=8e-03 Ω
Total loop reactance (out + return)
The voltage drop across the cable loop is calculated using the standard formula that accounts for both the resistive and reactive voltage drop components:
V_drop = I × (R_loop × cos φ + X_loop × sin φ)
This is the approximate formula valid for most practical circuits where the phase angle between source and load is small.
sin_phi:=sin(phi)=0.44
sin φ
V_drop:=I·(R_loop·cos(phi)+X_loop·sin(phi))=6.33 V
Voltage drop along cable
Results
The voltage at the load terminals and the percentage voltage drop relative to the nominal supply voltage are the key outputs checked against code limits.
Voltage at load terminals
V_load:=V_s-V_drop=223.67 V
V_pct:=(V_drop)/(V_s)·100=2.75
Percentage voltage drop
Interpretation
The percentage voltage drop result should be compared against the applicable code limit — typically 3 % for lighting circuits and 5 % for power/motor circuits per IEC 60364-5-52 and BS 7671.
If the calculated percentage exceeds the limit, the remedy is to increase the conductor cross-sectional area, reduce the circuit length, reduce the load, or redistribute loads across multiple circuits.
The load terminal voltage shows the actual voltage available at the equipment. For a 230 V nominal supply, the voltage should remain above approximately 218 V (3 % drop) or 218.5 V to keep equipment within its rated tolerance band (typically ±10 %).
Assumptions & Limitations
Single-phase or DC circuit only — for three-phase circuits replace the factor of 2 with √3.
Resistivity value applies at 20 °C; at full operating temperature (75–90 °C for PVC/XLPE) resistance increases by approximately 20–30 %, increasing voltage drop.
The reactive voltage drop term uses the approximate formula; it is accurate when the voltage drop angle is small (typical for LV distribution).
Cable reactance is assumed uniform at 0.08 Ω/km; multicore armoured cables and busbar trunking have different reactance values.
Skin effect and proximity effect are neglected — these are only significant for conductors larger than about 300 mm².
Voltage drop on the source impedance (transformer, main switchboard) is not included.
Voltage Drop Calculator
This worksheet calculates the voltage drop along a conductor in a single-phase or equivalent DC circuit, as well as the resulting voltage at the load end and the percentage voltage drop relative to the source voltage.
Voltage drop is a critical consideration in electrical system design. Excessive voltage drop leads to poor equipment performance, overheating, and energy waste. Most electrical codes (IEC 60364, NEC, BS 7671) recommend that the total voltage drop from the supply to any outlet should not exceed 3–5% of the nominal supply voltage.
The governing principle is Ohm's Law applied to the resistance (and optionally reactance) of the cable conductors. For a single-phase circuit the total conductor length is twice the one-way run length (out and return), so the formula is:
Voltage Drop: V_drop = 2 × I × (R_conductor + X_conductor × tan φ)
Resistivity method: R_conductor = ρ × L / A, where ρ is the conductor resistivity, L the one-way length, and A the cross-sectional area.