3-Phase Formula Guide | kW, Amps & kVA

Quick Answer

What are the key three-phase formulas to choose before calculating?

Where √3 = 1.732

→ Choose the known values first, then use the 3-Phase Calculator or the related tools below for the actual voltage, current, kW, kVA, and power-factor inputs.

After the Formula Result

Use the formula result as the first calculation, then close the workflow with the right calculator handoff:

For code-sensitive conductor, breaker, or equipment decisions, verify the adopted NEC edition, equipment listings, manufacturer instructions, and AHJ requirements before treating the formula result as final.

For a chart record, use the Single-Phase vs Three-Phase Chart when the next question is which voltage and phase model applies. Use the kVA to Amps Chart when the formula result needs line-current documentation before transformer, feeder, load-bank, or equipment review.

Three-Phase Power Formulas

Real Power (Watts/kW)

Calculator checkpoint: real power from line values

Before solving real power, collect the actual line-to-line voltage, line current, and power factor. Then run the formula or calculator for that specific load and carry the result into the next equipment check instead of reusing a sample result.

Apparent Power (VA/kVA)

Reactive Power (VAR/kVAR)

Q = √3 × V_L × I_L × sin(θ)
Q = √(S² - P²)

Line vs Phase Values

Understanding the Difference

Star (Wye) Connection Formulas

V_L = √3 × V_ph
V_ph = V_L / √3

I_L = I_ph

Common Wye Voltages:

Delta Connection Formulas

V_L = V_ph

I_L = √3 × I_ph
I_ph = I_L / √3

Star vs Delta Comparison

Voltage and Current Relationships

When to Use Each

Three-Phase Current Calculations

Current from Power (Most Common)

I = P / (√3 × V × PF)

Example: 50 kW motor, 480V, PF = 0.87

I = 50,000W / (1.732 × 480V × 0.87)
I = 50,000 / 723.5
I = 69.1A per phase

Current from kVA

I = kVA × 1000 / (√3 × V)

Example: 75 kVA transformer, 480V

I = 75,000 / (1.732 × 480)
I = 75,000 / 831.4
I = 90.2A

Current from HP (Motors)

I = HP × 746 / (√3 × V × Eff × PF)

Example: 50 HP motor, 480V, Eff = 0.92, PF = 0.87

I = 50 × 746 / (1.732 × 480 × 0.92 × 0.87)
I = 37,300 / 665.6
I = 56.0A

Three-Phase Voltage Calculations

Standard Three-Phase Voltages

Voltage Drop in Three-Phase

V_drop = √3 × I × (R × cos(θ) + X × sin(θ)) × L

For approximate calculation (copper wire):

V_drop (%) = (√3 × I × L × ρ) / (A × V) × 100

Where:

• I = Line current (A)
• L = One-way length (feet)
• ρ = Resistivity constant
• A = Wire cross-section area

→ Use Voltage Drop Calculator for accurate sizing.

Motor Full Load Current (FLC) Tables

Three-Phase Motor FLC at 460V

Based on NEC Table 430.250:

Motor FLC at Different Voltages

→ Use Full Load Current Calculator for NEC table FLC values, or Motor Current Calculator for formula-current comparison.

Transformer Sizing

Three-Phase Transformer kVA

kVA = √3 × V × I / 1000

Or from load:

kVA = kW / PF

Standard 3-Phase Transformer Sizes

15, 30, 45, 75, 112.5, 150, 225, 300, 500, 750, 1000, 1500, 2000, 2500 kVA

Sizing Example:

Load: 200 kW, PF = 0.85

kVA = 200 / 0.85 = 235.3 kVA
Select next size: 300 kVA transformer

Worked Examples

Example 1: Calculate 3-Phase Power

Given: 480V system, 50A per line, PF = 0.9

Solution:

P = √3 × V × I × PF
P = 1.732 × 480 × 50 × 0.9
P = 37,413W = 37.4 kW

Example 2: Current for Known Load

Given: 100 kW load, 208V, 3-phase, PF = 0.85

Solution:

I = P / (√3 × V × PF)
I = 100,000 / (1.732 × 208 × 0.85)
I = 100,000 / 306.2
I = 326.6A

Example 3: Star to Delta Conversion

Given: Star-connected motor, V_ph = 230V, I_ph = 10A

For Star:

V_L = √3 × V_ph = 1.732 × 230 = 398.4V
I_L = I_ph = 10A

If reconnected in Delta at same line voltage:

V_ph = V_L = 398.4V
I_ph = V_ph / Z = 398.4 / 23 = 17.3A (assuming same impedance)
I_L = √3 × I_ph = 1.732 × 17.3 = 30A

Power increases 3× in Delta!

Example 4: Generator Sizing

Given: Facility load 150 kW, PF = 0.8, want 25% reserve

Solution:

Required kVA = kW / PF = 150 / 0.8 = 187.5 kVA
With 25% reserve: 187.5 × 1.25 = 234.4 kVA
Select: 250 kVA generator

Unbalanced Load Calculations

Single-Phase Load on Three-Phase

For single-phase load connected line-to-neutral:

I_line = kW × 1000 / (V_ph × PF)

Balancing Three-Phase Loads

To balance loads across phases:

1. Calculate total load per phase
2. Move loads to equalize current
3. Target within 10% imbalance

Common Mistakes to Avoid

Related Calculators

Summary

Essential Three-Phase Formulas:

Star vs Delta:

• Star: V_L = √3 × V_ph, I_L = I_ph
• Delta: V_L = V_ph, I_L = √3 × I_ph

Remember: √3 = 1.732

FAQ

What does √3 represent in three-phase?

√3 (1.732) is the mathematical factor that relates line and phase values due to the 120° phase shift between phases. It appears in all balanced three-phase power calculations.

How do I convert single-phase to three-phase current?

Three-phase current is lower than single-phase for the same power. Divide single-phase current by √3 (1.732) for equivalent three-phase current at the same voltage.

What is the difference between Star and Delta?

Star (Wye) has a neutral connection and different line/phase voltages (V_L = √3 × V_ph). Delta has no neutral, and line voltage equals phase voltage, but line current is √3 times phase current.

Why is 480V common for industrial?

480V three-phase offers efficient power transmission with lower currents than 208V or 240V systems. Lower current means smaller conductors and lower losses for heavy industrial loads.

How do I calculate amps from HP for a 3-phase motor?

Use I = (HP × 746) / (√3 × V × Eff × PF) or refer to NEC Table 430.250 for standard FLC values. Always use nameplate data when available.