3 Phase Cable Size Calculation Formula Calculator
Estimate current, minimum cable cross-sectional area, selected standard cable size, and voltage drop for a 3 phase electrical circuit. This calculator uses the core 3 phase current formula and compares ampacity sizing with voltage drop sizing for a practical recommendation.
Results
Enter your values and click Calculate Cable Size to see the recommended cable area, estimated current, and voltage drop.
1) 3 phase current: I = P / (1.732 x V x PF x eta)
2) Area by ampacity: A = I / J
3) Area by voltage drop: A = (1.732 x I x rho x L x design factor x 100) / (V x allowed drop percent)
4) Final recommendation: choose the larger area from ampacity and voltage drop, then round up to the next standard cable size.
Sizing Chart
The chart compares calculated load current with estimated cable ampacity, and compares minimum required area with the selected standard cable size.
Expert Guide: Understanding the 3 Phase Cable Size Calculation Formula
The 3 phase cable size calculation formula is one of the most important practical tools in electrical design. Whether you are sizing feeders for motors, distribution boards, HVAC systems, industrial machinery, or commercial building services, the cable has to do more than simply carry current. It must operate safely, limit voltage drop, tolerate installation conditions, and satisfy code requirements. A cable that is too small can overheat, waste energy, damage insulation, and create serious reliability and fire risks. A cable that is too large may be safe, but it can add unnecessary project cost and make terminations more difficult.
At the heart of the calculation is the standard 3 phase current formula. For a balanced three phase load, current is typically determined from real power using:
I = P / (1.732 x V x PF x eta)
Where I is line current in amperes, P is load power in watts, V is line to line voltage, PF is power factor, and eta is equipment efficiency expressed as a decimal. If your load is already known in amperes, you may not need this step. But for motors and many building services loads, the current is often derived from kilowatts and system voltage. This makes the formula especially useful during preliminary engineering and equipment selection.
Why current alone is not enough
A common mistake is assuming that cable size can be selected only from load current. In real projects, current is just the starting point. Professional cable sizing also considers:
- Current carrying capacity, also called ampacity
- Voltage drop over the cable run
- Conductor material, usually copper or aluminum
- Installation method, such as in air, conduit, tray, or direct buried
- Ambient temperature and grouping or derating factors
- Insulation type and maximum conductor temperature
- Short circuit withstand requirements
- Applicable electrical code and local authority requirements
That is why a good 3 phase cable size calculator checks both ampacity and voltage drop, then selects the larger requirement. This approach reflects how many engineers perform an initial design check before moving to a full code-based verification.
Step 1: Calculate the 3 phase load current
Assume a 45 kW load on a 415 V three phase system, with power factor 0.90 and efficiency 95 percent. The current would be:
- Convert efficiency to decimal: 95 percent = 0.95
- Apply the formula: I = 45000 / (1.732 x 415 x 0.90 x 0.95)
- The result is approximately 73.4 A
This is the design current before any future capacity margin, service factor, or code-specific adjustment. If the load is a motor, some designers also compare the result to motor full load current values published by manufacturers or code tables.
Step 2: Estimate minimum cross-sectional area by ampacity
Once current is known, you can estimate the conductor area using a practical current density method:
A = I / J
Where A is conductor area in mm² and J is allowable current density in A/mm². The value of current density changes with conductor material and installation method. Copper often allows a higher current density than aluminum because of its better conductivity. Cables in free air can usually dissipate heat more effectively than cables in conduit or buried installation.
For early-stage estimation, engineers often use conservative design current density assumptions. For example, copper in air may be estimated around 6 A/mm², copper in conduit around 4.5 A/mm², and copper buried around 4 A/mm². Aluminum is lower. This calculator uses this style of practical approximation to provide a fast recommendation, but detailed final design should still be validated against the relevant code tables and manufacturer data sheets.
Step 3: Check voltage drop
Even if the cable can carry the current thermally, it may still be too small if the circuit is long. Excessive voltage drop causes motors to run hotter, lighting to dim, electronic equipment to misbehave, and energy losses to increase. For a simplified three phase design estimate using conductor resistance, the required area by voltage drop can be written as:
A = (1.732 x I x rho x L x design factor x 100) / (V x allowable drop percent)
Where rho is conductor resistivity in ohm mm²/m, L is one-way cable length in meters, and the design factor allows a more conservative result for warmer operating conditions or general uncertainty. Copper has lower resistivity than aluminum, so for the same current and distance it usually achieves lower voltage drop at the same cross-sectional area.
Copper vs aluminum in 3 phase cable sizing
Copper and aluminum are both widely used in three phase power systems, but they behave differently. Copper offers lower resistivity, smaller conductor size for the same current, stronger terminations, and generally better corrosion resistance in many indoor settings. Aluminum is lighter and often less expensive per unit conductor volume, but it typically requires a larger cross-sectional area for equivalent performance and may need more careful termination practices.
| Conductor Material | Electrical Resistivity at 20 C | Relative Conductivity | Practical Design Impact |
|---|---|---|---|
| Copper | 0.0172 to 0.0178 ohm mm²/m | About 100 percent IACS reference | Lower voltage drop and smaller cable size for the same load |
| Aluminum | 0.0280 to 0.0283 ohm mm²/m | About 61 percent IACS | Needs larger cross-sectional area to match copper performance |
The resistivity ranges above are standard engineering values at 20 C and are commonly used in electrical calculations. In actual operation, conductor resistance rises with temperature, which is one reason conservative design factors are helpful during preliminary sizing.
Typical standard cable sizes
After calculating the minimum area, the next step is to round upward to a standard cable size. Common metric power cable sizes include 1.5, 2.5, 4, 6, 10, 16, 25, 35, 50, 70, 95, 120, 150, 185, 240, and 300 mm². The exact availability depends on your market, insulation system, and cable construction. Multi-core cables, single-core runs, armoring, and insulation type can all influence final ampacity.
| Standard Area | Approximate Copper Ampacity in Air | Approximate Copper Ampacity in Conduit | Typical Use Case |
|---|---|---|---|
| 10 mm² | 50 to 65 A | 40 to 50 A | Small sub-feeders and machinery circuits |
| 16 mm² | 68 to 85 A | 55 to 70 A | Medium motors and commercial branch feeders |
| 25 mm² | 89 to 115 A | 75 to 95 A | Distribution circuits and larger motor feeders |
| 35 mm² | 110 to 140 A | 95 to 115 A | Longer feeders with tighter voltage drop limits |
| 50 mm² | 135 to 175 A | 115 to 145 A | Industrial panels, larger HVAC, process loads |
These values are approximate planning ranges only. Final ampacity must be confirmed using the applicable standard, installation conditions, conductor temperature rating, cable grouping, and manufacturer data. Still, they illustrate an important reality: there is not a single universal ampacity for a cable size. Installation conditions matter a lot.
How installation method changes the answer
If the same 3 phase cable is installed in open air, in conduit, or directly buried, its ability to shed heat changes. Lower heat dissipation means lower allowable current. That is why identical loads can require different cable sizes depending on the installation route. This also explains why tray systems may allow smaller conductors than tightly grouped conduit runs. In underground systems, soil thermal resistivity and burial depth can significantly influence performance.
How voltage drop affects motor circuits
Motor loads deserve special attention. Starting current can be several times higher than running current, and low voltage during starting can reduce torque and increase heating. In long feeder runs, a cable that satisfies steady-state ampacity may still produce too much voltage drop during motor starting. Engineers often review both running and starting scenarios, especially for large motors, pumps, compressors, and conveyors.
Common mistakes in 3 phase cable size calculation
- Using single phase formulas on a three phase system
- Ignoring power factor or efficiency when deriving current from kW
- Sizing only by ampacity and skipping voltage drop
- Not adjusting for installation method or ambient temperature
- Forgetting that aluminum usually requires a larger area than copper
- Selecting the exact calculated area instead of the next standard size up
- Neglecting local electrical code, fault level, and protective device coordination
Best practice workflow for accurate sizing
- Determine the real load power in kW or known current in A
- Identify system voltage, phase arrangement, power factor, and efficiency
- Calculate line current using the 3 phase formula
- Estimate minimum area based on current carrying capacity
- Calculate minimum area based on allowable voltage drop
- Select the larger result and round up to the next standard size
- Verify against applicable code tables and manufacturer data
- Check short circuit withstand, protective device settings, and terminations
Important standards and authority references
For safety, compliance, and deeper design guidance, consult recognized authorities and technical references. Useful starting points include the U.S. Occupational Safety and Health Administration electrical safety resources, the U.S. Department of Energy industrial energy and motor system resources, and the National Institute of Standards and Technology electrical metrology resources. These sources do not replace your local code book, but they do provide high-authority technical and safety information relevant to electrical system design and performance.
When to use this calculator
This calculator is ideal for preliminary design, budget estimation, quick engineering checks, tender reviews, and educational use. It is especially useful when you need to compare copper versus aluminum, judge the effect of longer cable runs, or understand how voltage drop can force a larger cable than thermal capacity alone. Because it rounds upward to standard sizes and shows both ampacity and voltage drop results, it gives a practical recommendation rather than only a theoretical area.
Final takeaway
The most reliable way to approach a 3 phase cable size calculation formula is to think in layers. First, calculate the line current correctly. Second, estimate the area needed to carry that current safely. Third, confirm that the same cable keeps voltage drop within acceptable limits. Fourth, round up to a standard size and validate against code and manufacturer data. If you follow that sequence, your cable selection will be safer, more efficient, and more defendable from both engineering and cost perspectives.
Engineering note: this page provides a planning-level calculation intended for fast decision support. Final cable sizing should always be checked against your local electrical code, product data sheets, installation derating factors, and short circuit requirements.