Voltage Drop Formula & Calculator

Every conductor has some resistance, and any current flowing through that resistance produces a voltage drop — the voltage at the load end of a cable is always somewhat lower than at the source end. For short, heavily-loaded circuits this drop is negligible, but for long cable runs (a distant pump house, a remote lighting circuit, a large facility's far corner) it can become large enough to affect equipment performance, which is why voltage drop is checked as a standard part of cable sizing, alongside ampacity.

Single-Phase Voltage Drop Formula

VD (V) = 2 × I × L × R ÷ 1000, where I is load current in amps, L is the one-way cable length in metres, and R is the conductor's resistance in ohms per kilometre. The factor of 2 accounts for the round trip — current flows out through one conductor and back through the other, so the total resistive path is twice the one-way length.

3-Phase Voltage Drop Formula

VD (V) = √3 × I × L × R ÷ 1000. The √3 (approximately 1.732) factor replaces the single-phase factor of 2, reflecting the different current-voltage relationship in a balanced three-phase system compared to a single-phase circuit. This resistance-only three-phase voltage-drop equation is a useful approximation for balanced three-phase circuits, giving the approximate line-to-line voltage drop assuming a balanced load and equal conductor impedance. For detailed design, especially with large conductors, long runs, or significant reactance, use the cable manufacturer's R and X data and the applicable design standard.

Estimating conductor resistance: for a simplified calculation, conductor resistance can be estimated as R (Ω/km) = resistivity ÷ cross-sectional area. This calculator uses approximate reference resistivity values of 17.5 Ω·mm²/km for copper and 28 Ω·mm²/km for aluminum, so a 16 mm² copper conductor has an estimated R = 17.5 ÷ 16 ≈ 1.094 Ω/km. For a final cable calculation, use the conductor resistance published by the cable manufacturer, preferably at the applicable operating temperature.

Worked example: a single-phase circuit carries 40 A over a 60 m one-way cable run, using 16 mm² copper conductor (R ≈ 1.094 Ω/km), on a 230 V supply. VD = 2 × 40 × 60 × 1.094 ÷ 1000 ≈ 5.25 V. Percentage voltage drop = 5.25 ÷ 230 × 100 ≈ 2.28% — within the commonly used 5% total guideline, but worth checking against the specific limit for this particular circuit type (motor starting circuits, for example, often need a tighter limit).

Why voltage drop matters beyond just meeting a code limit: excessive voltage drop reduces the actual voltage available at the load, which has real performance consequences depending on the equipment. A significant reduction in motor terminal voltage can increase current and heating under some operating conditions and reduce available torque, though the actual response depends on motor type, load characteristics, and operating condition. Lighting can dim and, for some lamp types, shift color temperature. Electronic equipment can behave erratically, trip on undervoltage protection, or in severe cases fail to start reliably. These aren't just theoretical code-compliance concerns — they're practical reliability and efficiency issues that voltage drop calculations exist to prevent.

The relationship between voltage drop and conductor upsizing: since voltage drop is inversely proportional to conductor area (larger area, proportionally lower resistance, proportionally lower voltage drop for the same current and length), the standard remedy for excessive voltage drop is simply increasing conductor size beyond what ampacity alone would require. This is a common and often economically significant outcome for long cable runs — a circuit feeding a remote pump house or a distant lighting panel frequently needs a conductor one or two sizes larger than its ampacity requirement alone would suggest, purely to keep voltage drop within acceptable limits.

Impedance vs pure resistance — when the difference matters: the formula used here treats the conductor's opposition to current flow as purely resistive, which provides a useful estimate for preliminary or simplified cable-sizing calculations, but actual voltage drop can also depend on conductor reactance, load power factor, cable construction, installation arrangement, and conductor temperature. For larger conductors and installations where reactance is significant, a more accurate voltage drop calculation is needed. For a typical lagging AC load, an approximate three-phase R-X voltage-drop calculation can be written as VD = √3 × I × L × (R×cosφ + X×sinφ) ÷ 1000 (with an analogous single-phase version), incorporating both resistance (R) and reactance (X) along with the load's power factor angle (φ). Cable manufacturers publish both R and X values per km for their larger cable sizes specifically because this full calculation becomes necessary at that scale — the exact size threshold depends on the applicable standard, cable construction, and installation method, so check the manufacturer's data rather than a fixed size cutoff.

Summary: use VD = 2 × I × L × R ÷ 1000 for single-phase or VD = √3 × I × L × R ÷ 1000 for three-phase, calculate R from your conductor's cross-sectional area and material (or use the manufacturer's published value directly for the most accuracy), check the result against the appropriate percentage limit for your specific circuit type, and always check voltage drop alongside ampacity, using whichever constraint requires the larger conductor.

Voltage drop and energy losses: voltage drop isn't just a performance concern for the load — the power dissipated in the cable as I²R losses (heat) represents real, wasted energy that's paid for but never reaches the load. For circuits that carry substantial current over long distances for extended periods (a continuously running large motor on a long feeder, for example), the cumulative cost of this resistive loss over the equipment's service life can sometimes justify upsizing the conductor beyond the minimum required by either ampacity or the standard voltage drop limit, purely on energy-cost grounds — a more detailed lifecycle cost calculation, weighing the extra upfront conductor cost against ongoing energy savings, can identify this optimal point for high-utilization circuits.

1. Using total cable length (both directions) instead of one-way length. The formula's factor of 2 (single-phase) or √3 (three-phase) already accounts for the return path — entering the round-trip length instead of one-way length double-counts this and overstates voltage drop.

2. Using the wrong resistivity constant for the actual conductor material. Copper and aluminum have meaningfully different resistivity (aluminum's resistance is roughly 1.6× copper's for the same cross-sectional area) — using copper's constant for an aluminum conductor, or vice versa, gives a significantly wrong result.

3. Ignoring reactance for larger conductors and installations. This resistance-only calculation provides a useful estimate for many ordinary cases, but for larger conductor sizes reactance can become a meaningful fraction of total impedance — the exact size threshold depends on the applicable standard, cable construction, and installation method, so using resistance alone for large-conductor, long-run calculations without checking manufacturer's data can understate actual voltage drop.

4. Checking voltage drop at a light or average load instead of the design load current. Voltage drop scales directly with current, so use the circuit's design load or maximum expected operating current as required by the applicable standard — a calculation done at typical operating current rather than this design current can pass a check that would actually fail under legitimate full-load conditions.

5. Sizing a cable for ampacity alone without also checking voltage drop. A conductor that's thermally adequate (correct ampacity) for a long run can still produce excessive voltage drop — always check both constraints and use whichever requires the larger conductor size, especially for long cable runs with relatively light current.

6. Applying a steady-state voltage-drop limit directly to motor starting. Motor starting should be evaluated separately because starting current can be several times running current — the acceptable starting-voltage reduction is application-dependent and should be checked against the motor, starting method, driven load, and applicable design requirements, rather than applying a tight steady-state limit to the starting condition.

7. Ignoring starting current voltage drop for motor circuits. For many induction motors, locked-rotor (starting) current can be several times full-load running current — the actual value should be taken from the motor nameplate, datasheet, or applicable design data. Checking voltage drop only at running current misses a potentially much larger, if brief, starting voltage drop that can prevent the motor from starting reliably.

8. Not accounting for the conductor's temperature-dependent resistance change. This calculator uses fixed reference resistivity values and does not automatically adjust conductor resistance for operating temperature. Because conductor resistance increases with temperature, a cable running hot under load has somewhat higher actual resistance, and therefore somewhat higher actual voltage drop, than this calculation alone suggests.

A practical checklist for a complete cable sizing exercise: (1) determine the circuit's design load current; (2) select a conductor size meeting ampacity requirements after applying temperature and grouping derating; (3) calculate voltage drop at that conductor size and design load current; (4) if voltage drop exceeds the applicable limit, increase conductor size and recheck both ampacity margin and voltage drop; (5) for motor circuits, additionally check starting current voltage drop separately. Working through these steps in order, rather than checking only one constraint, is what a complete and defensible cable sizing calculation actually requires.