Medium Voltage Drop Calculator and Formula

A medium voltage drop calculator estimates the voltage lost along a three-phase AC feeder from its length, load current, conductor resistance and reactance, and power factor. Enter those electrical values to get the estimated drop in volts and as a percentage of the system voltage; use the result as a calculation aid, not as a design approval.

Formula

For a balanced three-phase AC circuit, this calculator uses the approximate line-to-line voltage-drop formula:

ΔV = √3 × I × L × (R cos φ + X sin φ)

Here, ΔV is the estimated voltage drop in volts; I is line current in amperes; L is one-way route length in kilometres; R is conductor resistance in ohms per kilometre; X is conductor reactance in ohms per kilometre; and φ is the phase angle, with power factor cos φ. The calculator obtains sin φ as √(1 − power factor²), assuming a lagging load. Its percentage result is 100 × ΔV / V, where V is nominal line-to-line system voltage in volts. Estimated receiving-end voltage is V − ΔV.

Use resistance and reactance values that correspond to the actual conductor, operating frequency, and relevant operating temperature. The default values are illustrative calculation inputs, not a recommendation for a particular cable or installation. For an unbalanced, single-phase, or more detailed network calculation, this formula may not apply.

Worked Example

Using the calculator’s default values: system voltage 4,160 V, route length 100 m, current 100 A, resistance 0.2 Ω/km, reactance 0.1 Ω/km, and power factor 0.9:

1. Convert the one-way length to kilometres: 100 m ÷ 1,000 = 0.1 km.
2. Find the sine of the phase angle: √(1 − 0.9²) = √0.19 ≈ 0.43589.
3. Calculate the impedance-weighted term: 0.2 × 0.1 × 0.9 + 0.1 × 0.1 × 0.43589 ≈ 0.0213589 Ω.
4. Calculate drop: √3 × 100 A × 0.0213589 Ω ≈ 3.70 V.
5. Calculate the percentage: 100 × 3.70 ÷ 4,160 ≈ 0.09%.
6. Estimate receiving-end voltage: 4,160 − 3.70 ≈ 4,156.30 V.

The displayed outputs are 3.70 V, 0.09%, and 4,156.30 V, rounded to two decimal places. Intermediate calculations retain more precision, so hand calculations rounded earlier may differ slightly.

What the Calculator Is For

“Medium voltage” commonly refers to distribution systems above low voltage and below high voltage, but exact boundaries vary by standard and jurisdiction. The term alone does not specify a voltage, cable construction, grounding arrangement, or acceptable voltage-drop target. A calculator provides a first estimate for a stated set of circuit assumptions; it cannot determine whether an installation is suitable or compliant.

Voltage drop occurs because current flows through conductor impedance. Resistance contributes a component associated with the in-phase current, while reactance contributes a component associated with the out-of-phase current. Longer routes and higher currents generally increase the drop. The resistance and reactance terms also mean that power factor matters; a resistance-only calculation can miss a meaningful part of the estimate on an AC feeder.

The percentage helps compare the estimated drop with the nominal voltage. For example, a small number of volts can represent different proportions on systems with different nominal voltages. Do not assume that a particular percentage is universally acceptable: requirements depend on the system, equipment, operating conditions, and applicable design rules.

Choosing and Entering the Inputs

• Voltage: Enter nominal line-to-line voltage for a three-phase system, not phase-to-neutral voltage. The result’s percentage uses this value as its reference.
• Length: Enter one-way route length in metres. The formula uses the full outgoing feeder length; do not double it as if it were a two-conductor single-phase circuit.
• Current: Enter line current in amperes for the operating condition being evaluated. A nameplate rating, a measured value, and a calculated demand current are not interchangeable without context.
• Resistance and reactance: Enter each in ohms per kilometre. Manufacturer or engineering data should match the conductor and conditions as closely as possible. If data are supplied per metre, convert them before entering them; multiply ohms per metre by 1,000 to obtain ohms per kilometre.
• Power factor: Enter a value from 0 to 1, such as 0.9. The formula interprets this as the magnitude of a lagging power factor. A leading power factor can change the reactive contribution’s sign and needs an appropriately adjusted calculation.

Interpretation, Assumptions, and Limits

This is an approximate voltage-drop calculation for a balanced three-phase circuit, using a common impedance-based expression. It assumes the entered current and power factor represent the same operating condition and treats conductor resistance and reactance as uniform along the route. It does not model transformer impedance, upstream network voltage variation, motor starting, harmonics, temperature rise, load changes, or interactions with other feeders.

In particular, conductor resistance rises as conductor temperature rises. Using a resistance value specified at a lower temperature may understate operating drop. For long routes or cases where the drop is a significant part of nominal voltage, a more complete circuit or power-flow analysis may be appropriate. The simple receiving-end result is just nominal voltage minus the estimated feeder drop; it does not account for the source voltage varying under load.

The calculation is not a cable-sizing tool and does not establish ampacity, short-circuit withstand, insulation suitability, protection coordination, or safe clearances. Medium-voltage systems present serious electrical hazards. Selection, installation, and verification require qualified electrical professionals and applicable standards; do not use this estimate alone to approve equipment or work on an energized system.

Common Errors and Useful Checks

• Mixing units: A length entered in metres is converted to kilometres inside the formula. Resistance and reactance must still be entered in Ω/km, and current in A.
• Using the wrong voltage basis: For the three-phase formula, use line-to-line voltage in the percentage calculation.
• Using total circuit length incorrectly: The formula uses one-way feeder route length and includes the three-phase factor √3. Do not apply an additional round-trip multiplier.
• Ignoring reactance or power factor: The result includes both R and X contributions. Entering zero reactance is only appropriate when justified by the data or intentionally used as a simplified estimate.
• Rounding too early: Keep full precision through the calculation and round only the displayed result. A difference in the last decimal place is normal.

For a quick reasonableness check, verify that doubling the route length or current approximately doubles the estimated drop when all other values stay fixed. The percentage should decrease if nominal voltage increases while the absolute drop remains unchanged.

Frequently Asked Questions

What does a medium voltage drop calculator calculate?
It estimates the voltage lost along a feeder from its length, current, conductor resistance and reactance, and power factor. This version reports volts, percentage of nominal line-to-line voltage, and a simple estimated receiving-end voltage.

Is this formula for a three-phase circuit?
Yes. It uses the balanced three-phase approximation with the √3 factor. Do not apply it directly to a single-phase, unbalanced, or otherwise different circuit without using a suitable formula.

Should I enter one-way or round-trip cable length?
Enter one-way route length. The expression is written for a three-phase feeder and already uses the appropriate three-phase relationship; adding a round-trip multiplier would generally overstate the estimate.

Why does power factor affect voltage drop?
Power factor describes the phase relationship between voltage and current. Resistance and reactance contribute differently to voltage drop, so the estimate includes both the power-factor and phase-angle terms.

Can I use the result to choose a medium-voltage cable?
No. The result addresses estimated voltage drop only. Cable selection also depends on current-carrying capacity, fault conditions, installation, insulation, protection, and applicable requirements, which need professional evaluation.

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in v | System voltage | V | 4160 | 0 | 1000000
in l | One-way route length | m | 100 | 0 | 1000000
in i | Load current | A | 100 | 0 | 1000000
in r | Conductor resistance | ohm/km | 0.2 | 0 | 1000
in x | Conductor reactance | ohm/km | 0.1 | 0 | 1000
in pf | Power factor | - | 0.9 | 0 | 1
out drop | Estimated line-to-line voltage drop | V | sqrt(3) * i * (r * l / 1000 * pf + x * l / 1000 * sqrt(1 - pf ^ 2)) | 2
out pct | Voltage drop | % | 100 * drop / v | 2
out recv | Estimated receiving-end voltage | V | v - drop | 2