3 Phase Cable Calculation Formula Calculator
Use this premium calculator to estimate three phase current, minimum cable size by ampacity, minimum cable size by voltage drop, and a recommended standard cable size for copper or aluminum conductors. It is designed for fast planning and engineering pre checks.
Expert Guide to the 3 Phase Cable Calculation Formula
The 3 phase cable calculation formula is one of the most practical tools in electrical design because it connects load demand, current, voltage drop, conductor material, and cable cross sectional area into a single engineering workflow. Whether you are sizing a cable for a motor, panel feeder, industrial machine, pump, compressor, or building distribution board, the goal is the same: choose a cable that can safely carry current while keeping voltage drop within acceptable limits.
In a three phase system, electrical power is delivered more efficiently than in a single phase circuit, especially for large loads. That is why factories, commercial buildings, pumping stations, HVAC plants, workshops, and process facilities commonly use three phase supply. However, the cable still must be correctly selected. A cable that is too small may overheat, waste energy, produce excessive voltage drop, and shorten equipment life. A cable that is too large may unnecessarily increase project cost. Good cable sizing is about balancing safety, compliance, performance, and economics.
Core 3 phase cable current formula
The starting point is to calculate line current. For a three phase load in kilowatts, the standard planning formula is:
Where:
- I = line current in amperes
- P = real power in watts
- √3 = 1.732
- V = line to line voltage in volts
- PF = power factor
- η = efficiency as a decimal
If the load is expressed in kVA instead of kW, the current formula simplifies to:
Where S is apparent power in volt amperes. For horsepower based motor loads, a common estimate is to convert horsepower to watts first, then divide by voltage, power factor, and efficiency in the same way.
How cable size is estimated from current
Once current is known, a first pass cable area can be estimated using current density:
Where:
- A = conductor area in mm²
- I = current in amperes
- J = allowable current density in A/mm²
This is useful for planning, budgeting, and concept design. In many practical installations, designers use a current density estimate that reflects conductor material, insulation, ambient temperature, cable grouping, and installation method. For many rough calculations, values around 3 to 6 A/mm² are often used as a screening range, but final selection should always be checked against the applicable code table or manufacturer data.
Why voltage drop matters in three phase cable sizing
Current carrying capacity is not the only design limit. Long cable runs can suffer from voltage drop, and this can be a major issue for motors and sensitive equipment. Low voltage at the load can increase current, reduce starting torque, create nuisance tripping, and lower efficiency. The simplified three phase voltage drop relation for conductor sizing is:
Where:
- ρ = conductor resistivity in ohm mm²/m
- L = one way cable length in meters
- Vd = allowable voltage drop in volts
This formula helps estimate the conductor area required so that voltage drop stays below a chosen limit, such as 3% or 5%. In many real world projects, the final recommended cable size is the larger of the ampacity based result and the voltage drop based result.
Typical material data used in planning
Copper and aluminum are the two most common conductor materials. Copper is more conductive and mechanically robust, while aluminum is lighter and often less expensive per unit of carrying capacity. The difference in conductivity directly affects cable size for the same current and voltage drop target.
| Material | Typical resistivity at 20°C | Relative conductivity | Density | General sizing impact |
|---|---|---|---|---|
| Copper | 0.0172 to 0.0175 ohm mm²/m | About 100% IACS reference | 8.96 g/cm³ | Smaller cross section for the same electrical duty |
| Aluminum | 0.0282 ohm mm²/m | About 61% IACS | 2.70 g/cm³ | Larger cross section needed for equal voltage drop and resistance |
These values are standard engineering data points commonly used in preliminary design. They explain why an aluminum feeder often requires a larger nominal area than a copper feeder for the same load and run length.
Step by step example of the 3 phase cable calculation formula
Assume the following design case:
- Load = 75 kW
- Voltage = 415 V three phase
- Power factor = 0.90
- Efficiency = 95%
- Length = 60 m one way
- Conductor = copper
- Current density = 4 A/mm²
- Allowed voltage drop = 3%
- Convert efficiency to decimal: 95% = 0.95
- Calculate current: I = 75,000 / (1.732 × 415 × 0.90 × 0.95)
- The result is about 122 A
- Calculate cable area by ampacity estimate: A = 122 / 4 = 30.5 mm²
- Allowable voltage drop = 415 × 0.03 = 12.45 V
- Calculate cable area by voltage drop: A = (1.732 × 122 × 0.0175 × 60) / 12.45
- The result is about 17.8 mm²
- Select the larger result, then round up to the next standard size
- In this example, the planning recommendation becomes 35 mm² copper
This example shows something important: sometimes ampacity governs, and sometimes voltage drop governs. On short runs with high current, ampacity can dominate. On long runs with modest current, voltage drop can become the controlling factor.
Common standard cable sizes used in low voltage design
After calculating the theoretical minimum area, engineers typically round up to the next standard cable size. This ensures the selected conductor is available in the market and gives practical design margin.
| Standard size mm² | Typical use case | Planning comment |
|---|---|---|
| 1.5 | Lighting and control circuits | Not for large three phase power feeders |
| 2.5 | Small branch circuits | Useful for light machinery and socket circuits where permitted |
| 4 | Small motors and feeders | Check starting current and installation method |
| 6 | Moderate branch loads | Often selected when voltage drop margin is needed |
| 10 | Sub feeders and medium equipment | Common commercial power size |
| 16 | Heavier motor loads | Good step up from 10 mm² |
| 25 | Large branch feeders | Frequently used in industrial panels |
| 35 | Short to medium feeder runs | Common result for 75 kW class loads at 400 to 415 V |
| 50 | Longer runs and higher current | Often chosen when voltage drop becomes more restrictive |
| 70 and above | Main feeders and high demand equipment | Final selection should include full code and derating checks |
Factors that change the final cable size
The calculator on this page provides a strong preliminary result, but final engineering selection should also evaluate the following:
- Ambient temperature: hotter locations reduce allowable ampacity.
- Cable grouping: bundled or closely spaced cables run hotter and require derating.
- Installation method: tray, conduit, direct buried, and free air all affect heat dissipation.
- Insulation type: PVC, XLPE, and other insulations have different thermal ratings.
- Motor starting current: motors can draw several times full load current during start.
- Harmonics: variable frequency drives and nonlinear loads may increase conductor heating.
- Short circuit withstand: large systems may require cable checks for fault thermal stress.
- Terminal ratings and local code: conductor selection must match lugs, breakers, and regional electrical rules.
Comparison of copper and aluminum for three phase cable design
From a pure electrical perspective, copper performs better per unit area because of lower resistivity. However, aluminum remains widely used in utility and building feeders because it is much lighter and can be cost effective when the installation is properly designed. The tradeoff is straightforward: aluminum usually needs a larger cross section to deliver similar resistance and voltage drop performance.
For that reason, the same three phase current may lead to two different cable recommendations depending on conductor material. The calculator reflects this by using different resistivity values for copper and aluminum when estimating voltage drop based cable area.
When to use 3% versus 5% voltage drop
Many designers use 3% as a tighter target for branch circuits or sensitive equipment and 5% as an upper planning limit for total feeder plus branch circuit drop, subject to local standards and project specifications. Motor circuits often benefit from tighter control because starting torque can be affected by reduced terminal voltage. If the cable run is long, lowering the drop target can substantially increase the selected conductor size.
Why simple formulas are still useful
Even though professional cable software can model reactance, conductor temperature, installation grouping, fault levels, and harmonic content, the classic 3 phase cable calculation formula remains valuable. It gives fast visibility into order of magnitude cable size, lets estimators price jobs early, helps engineers compare copper and aluminum options, and offers a transparent method for checking whether a selected feeder seems reasonable.
Best practice workflow for reliable cable sizing
- Identify the real load and its operating duty.
- Use the correct three phase current formula for kW, kVA, or HP.
- Estimate minimum area from current carrying capacity.
- Estimate minimum area from voltage drop.
- Select the larger result and round up to a standard size.
- Apply derating for ambient temperature, grouping, and installation method.
- Check short circuit withstand and protective device coordination.
- Verify compliance with the governing code and manufacturer data.
Authoritative references for deeper study
For broader electrical safety, efficiency, and measurement context, review the following authoritative resources:
- OSHA electrical safety guidance
- U.S. Department of Energy guidance on motor load and efficiency
- NIST SI units for electricity and magnetism
Final takeaway
The 3 phase cable calculation formula is not just an academic equation. It is the basis for safe and efficient low voltage power design. Start with line current, check voltage drop, compare copper and aluminum intelligently, and always round to a practical standard cable size before performing detailed code based verification. If you use the calculator above as a planning tool and then confirm the result with local standards and manufacturer ampacity tables, you will have a much stronger basis for selecting the right three phase cable.