How to Calculate Voltage Drop: DC, Single-Phase, and Three-Phase Formulas

Voltage drop is the difference between the voltage at the source and the voltage available at the load while current is flowing. For a two-wire DC circuit, use 2LIR ពេលណា អិល is the one-way length and រ is the resistance of one conductor per unit length. For single-phase AC, include resistance, reactance, and power factor. For a balanced three-phase circuit, replace the factor 2 ជាមួយ sqrt(3).

សៀគ្វី	Steady-state voltage-drop formula	Voltage used for percent drop
Two-wire DC	Delta V = 2 x L x I x R	DC system voltage
Two-wire single-phase AC	Delta V = 2 x L x I x (R x cos phi + X x sin phi)	The circuit’s line-to-line or line-to-neutral voltage, as applicable
AC បីហ្វាមានតុល្យភាព	Delta V_LL = sqrt(3) x L x I x (R x cos phi + X x sin phi)	Line-to-line voltage

បន្ទាប់មកធ្វើការគណនា៖

Voltage drop (%) = 100 x Delta V / nominal circuit voltage

The formulas are only valid when the units match. If រ និង X are in ohms per kilometre, enter អិល in kilometres. If they are in ohms per 1,000 feet, enter the one-way length as a fraction of 1,000 feet.

The AC expressions shown here use the usual approximate form for a lagging load power factor. A leading-power-factor circuit can change the sign of the reactive term; use the applicable phasor model rather than copying the lagging-load formula unchanged.

For a quick preliminary result, use the ម៉ាស៊ីនគណនាការធ្លាក់ចុះតង់ស្យុង VIOX. The manual method below shows what the calculator inputs mean and when a more detailed engineering study is necessary.

Variables and Units

និមិត្តសញ្ញា	អត្ថន័យ	Use it correctly
Delta V	Calculated voltage drop, in volts	Compare it with the voltage at the same circuit basis
អិល	ប្រវែងផ្លូវតែមួយទិស	Do not double it before using a formula that already contains 2
ខ្ញុំ	Load current, in amperes	Use the current in the segment being calculated
រ	AC or DC conductor resistance per unit length	Use data for the conductor material, size, construction, and relevant operating temperature
X	Conductor reactance per unit length	Use the cable or installation data for the actual conductor arrangement
cos phi	កត្តាថាមពលនៃការផ្លាស់ទី (Displacement power factor)	Do not substitute efficiency or total harmonic distortion
sin phi	sqrt(1 - cos^2 phi) for the assumed sinusoidal lagging load	It represents the reactive component in the approximate AC formula; leading power factor requires the correct sign convention

The one-way-length convention is the most common source of calculation errors. A two-wire DC or single-phase circuit has an outgoing conductor and a return conductor, so the formula multiplies the one-way length by 2. A balanced three-phase calculation uses the phase relationship between conductors, which produces the sqrt(3) factor instead.

If a cable table already gives loop resistance, do not multiply by 2 again. Confirm whether the published value is per conductor, per pair, per kilometre, or per 1,000 feet before calculating.

Why Resistance Alone Is Not Always Enough

For a purely resistive DC circuit, voltage drop follows Ohm’s law:

Delta V = I x R_loop

For AC circuits, conductor impedance has both resistance and reactance. The common steady-state approximation is:

Delta V = I x (R x cos phi + X x sin phi) x phase-and-length factor

នេះ។ R cos phi term represents the in-phase component. The X sin phi term accounts for the voltage component associated with conductor reactance and load power factor. Seattle Public Utilities presents this approximation and applies a factor of 2 to single-phase circuits and approximately 1.73 to three-phase circuits in its electrical design calculation guidance.

For short, small-conductor, near-unity-power-factor circuits, a resistance-only calculation may be adequate for screening. For long feeders, large conductors, low-power-factor loads, parallel conductors, or unusual conductor arrangements, use verified AC resistance and reactance data rather than assuming X = 0.

DC Voltage-Drop Example

Assume a 48 V DC load has these design inputs:

• load current: 20 A;
• one-way cable length: 30 m = 0.030 km;
• resistance of one conductor at the selected operating condition: 3.08 ohm/km;
• equal outgoing and return conductors.

Calculate the loop voltage drop:

Delta V = 2 x L x I x R
Delta V = 2 x 0.030 km x 20 A x 3.08 ohm/km
Delta V = 3.696 V

Calculate the percentage:

Voltage drop (%) = 100 x 3.696 V / 48 V
Voltage drop = 7.70%

The load would receive approximately:

48.0 V - 3.696 V = 44.304 V

This result does not automatically prove that the conductor is unacceptable. Compare it with the load’s permitted input range, the project voltage-drop criterion, conductor ampacity, terminal limits, and the applicable installation rules. If the drop is too high, possible design changes include a larger conductor, a shorter route, a lower current, or a higher distribution voltage where the system permits it.

Single-Phase AC Voltage-Drop Example

Assume a 230 V single-phase circuit has:

• current: ១៦ ក;
• one-way length: 40 m = 0.040 km;
• AC resistance: 4.61 ohm/km;
• reactance: 0.08 ohm/km;
• power factor: 0.90;
• sin phi = sqrt(1 - 0.90^2) = 0.436.

Use the single-phase formula:

Delta V = 2 x L x I x (R x cos phi + X x sin phi)
Delta V = 2 x 0.040 x 16 x (4.61 x 0.90 + 0.08 x 0.436)
Delta V = 5.36 V

បន្ទាប់មក:

Voltage drop (%) = 100 x 5.36 / 230
Voltage drop = 2.33%

The receiving-end voltage is approximately 224.64 V, before adding any upstream source, transformer, feeder, connection, or contact voltage drop.

Three-Phase Voltage-Drop Example

Assume a balanced 400 V three-phase load has:

• line current: 63 A;
• one-way route length: 80 m = 0.080 km;
• AC resistance per phase conductor: 0.727 ohm/km;
• reactance: 0.08 ohm/km;
• power factor: 0.85;
• sin phi = sqrt(1 - 0.85^2) = 0.527.

Use the balanced three-phase formula:

Delta V_LL = sqrt(3) x L x I x (R x cos phi + X x sin phi)
Delta V_LL = 1.732 x 0.080 x 63 x (0.727 x 0.85 + 0.08 x 0.527)
Delta V_LL = 5.76 V

The line-to-line percentage drop is:

Voltage drop (%) = 100 x 5.76 / 400
Voltage drop = 1.44%

The estimated receiving-end line-to-line voltage is 394.24 V.

These three examples use declared hypothetical រ និង X values so the arithmetic can be checked. For an actual project, replace them with conductor data appropriate to the cable construction, operating temperature, frequency, route, and installation arrangement.

Calculate Multi-Segment Circuits Separately

Do not apply the final load current to the entire route when loads branch off along the feeder. Calculate each segment using the current that actually flows through that segment, then add the voltage drops.

For a three-segment radial circuit:

Delta V_total = Delta V_segment_1 + Delta V_segment_2 + Delta V_segment_3

For example, if the source-to-panel feeder carries 60 A, the next section carries 35 A, and the final branch carries 12 A, each segment must use its own length, current, resistance, reactance, and power factor. The same principle applies when conductor size changes between the feeder and branch circuit.

This segment method also prevents a common error: calculating only the final branch while ignoring voltage already lost in the transformer, feeder, busway, protective devices, terminals, or upstream conductors. Include an element only when you have a defensible impedance or measured drop for it.

Use This Calculation Workflow

1. Identify the circuit topology. Select two-wire DC, two-wire single-phase AC, or balanced three-phase AC. Do not use the balanced formula for a materially unbalanced circuit.
2. Set the voltage basis. For balanced three-phase results, use line-to-line voltage when calculating percentage drop. For a phase-to-neutral branch, use the applicable phase-to-neutral voltage and circuit model.
3. Measure one-way route length. Follow the conductor route, not the straight-line distance between equipment.
4. Determine design current by segment. Use the expected load current for the operating condition being checked. Starting, charging, or other transient conditions require their own study.
5. Obtain compatible conductor data. Use resistance and reactance values with the same units and appropriate temperature, material, construction, and installation arrangement.
6. Calculate volts and percent. Keep all units visible, then calculate the receiving-end voltage.
7. Compare with the correct limit. Check the adopted code, project specification, equipment input range, and performance requirement. There is no single universal voltage-drop percentage for every circuit.
8. Verify the complete design. Ampacity, temperature correction, grouping, terminals, protective-device coordination, fault-loop performance, and voltage drop are separate checks.

Common Errors That Change the Answer

កំហុស	Why the result is wrong	វិធីសាស្រ្តត្រឹមត្រូវ
Doubling a measured loop length	នេះ។ 2 factor is applied twice	Use one-way length with the standard two-wire formula, or use loop resistance without another factor of 2
Using DC resistance for every AC feeder	It omits AC resistance effects and reactance	Use cable or manufacturer data appropriate to the AC installation
Ignoring conductor temperature	Resistance rises as the conductor warms	Use resistance at the relevant operating condition or apply a documented correction
Dividing three-phase drop by phase-to-neutral voltage	The percentage basis does not match the line-to-line result	ចែក Delta V_LL by nominal line-to-line voltage
Treating voltage drop as ampacity	A low-drop conductor can still be thermally unsuitable, and vice versa	Verify ampacity and voltage drop independently
Applying one current to a distributed feeder	Upstream and downstream segments carry different current	Calculate each segment and sum the drops
Using steady-state current for motor starting	Starting current and source impedance can dominate the temporary dip	Perform a motor-starting or dynamic voltage study

When the Simplified Formulas Are Not Enough

Use a more complete circuit model or engineering study when the system includes:

• materially unbalanced three-phase loads;
• significant neutral current or triplen harmonics;
• nonlinear loads where displacement power factor does not describe the waveform adequately;
• motor starting, transformer energization, or other transient events;
• parallel conductors or complex conductor geometry;
• long feeders where source, transformer, and connection impedances materially affect terminal voltage;
• distributed generation where the concern may be voltage rise rather than load-side voltage drop;
• safety-critical loads with a narrow operating-voltage window.

នេះ។ VIOX line-loss guide explains the separate relationship between current, resistance, and real-power loss. Voltage drop and power loss are related, but they are not interchangeable: voltage drop concerns the voltage difference seen by the load, while conductor real-power loss is primarily I^2R.

For cable selection in control-panel applications, continue with the IEC cable sizing, derating, voltage-drop, and trunking guide. If you need to reconcile metric and North American conductor designations before checking manufacturer data, use the AWG to mm2 cable-size conversion guide.

Voltage-Drop Limits Depend on the Applicable Rules

IEC 60364-5-52:2009+A1:2024 covers the selection and erection of low-voltage wiring systems; its Clause 525 addresses voltage drop and points to the relevant annex for maximum values. The applicable value depends on the installation context and adopted rules, so the standard must be used with the project requirements and national implementation.

In US work, the commonly quoted 3% និង 5% values appear in National Electrical Code informational-note context as recommendations for reasonable efficiency of operation, not as a universal rule for every circuit. Some applications contain separate mandatory requirements. Verify the adopted edition, authority having jurisdiction, equipment instructions, and project specification rather than using one percentage globally. The distinction is visible in NFPA’s official 2025 NEC code-development material.

Calculation Checklist

Before accepting a result, confirm that:

• the circuit topology and voltage basis are correct;
• length means the actual one-way route unless the data explicitly uses loop length;
• រ, X, និង អិល use compatible units;
• resistance reflects the relevant conductor and operating condition;
• current and power factor describe the segment and operating state being checked;
• feeder and branch drops are added where both contribute;
• the result is compared with equipment, project, and jurisdictional requirements;
• conductor ampacity and protection are verified independently.

ប្រើ ម៉ាស៊ីនគណនាការធ្លាក់ចុះតង់ស្យុង VIOX to check a preliminary design quickly. For final design, retain the inputs, conductor source data, assumptions, formula, and acceptance criterion so another engineer can reproduce the result.

ប្រភព និងស្តង់ដារ

• IEC 60364-5-52:2009+A1:2024, Low-voltage electrical installations – Wiring systems
• Seattle Public Utilities, Design Calculations for Electrical Design, February 2024
• NFPA 70 2025 code-development material

Technical review note: This article provides a transparent steady-state calculation method, not a substitute for project-specific conductor selection, code review, or a power-system study.