3-Phase Formulas | 480V 100A = 70.7 kW

Quick Answer

What are the key three-phase formulas?

Calculate	Formula
Power (kW)	P = √3 × V_L × I_L × PF ÷ 1000
Current (A)	I = P × 1000 ÷ (√3 × V × PF)
Apparent Power (kVA)	S = √3 × V_L × I_L ÷ 1000

Where √3 = 1.732

→ Use the 3-Phase Calculator for instant calculations.

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After the Formula Result

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

If the result is...	Next check
A motor running-current estimate	Compare against the Motor Current Calculator and nameplate data
A service or feeder load in kVA	Review current and transformer relationships with the Transformer Calculator
A long circuit run	Check the same current in the Voltage Drop Calculator
A low power factor load	Continue with the Power Factor Calculator before sizing correction equipment

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)

Method	Formula	When to Use
Line Values	P = √3 × V_L × I_L × PF	Most common (line-to-line voltage)
Phase Values	P = 3 × V_ph × I_ph × PF	When phase values known

Example: 480V, 100A, PF = 0.85

P = √3 × 480V × 100A × 0.85
P = 1.732 × 480 × 100 × 0.85
P = 70,666W = 70.7 kW

Apparent Power (VA/kVA)

Method	Formula
Line Values	S = √3 × V_L × I_L
Phase Values	S = 3 × V_ph × I_ph

Reactive Power (VAR/kVAR)

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

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Line vs Phase Values

Understanding the Difference

Term	Description	Symbol
Line Voltage	Voltage between any two lines (L-L)	V_L or V_LL
Phase Voltage	Voltage from line to neutral (L-N)	V_ph or V_LN
Line Current	Current in the supply line	I_L
Phase Current	Current through each winding	I_ph

Star (Wye) Connection Formulas

V_L = √3 × V_ph
V_ph = V_L / √3

I_L = I_ph

Common Wye Voltages:

Line Voltage	Phase Voltage
208V	120V
400V	230V
480V	277V
600V	347V

Delta Connection Formulas

V_L = V_ph

I_L = √3 × I_ph
I_ph = I_L / √3

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Star vs Delta Comparison

Voltage and Current Relationships

Parameter	Star (Y)	Delta (Δ)
Line Voltage	V_L = √3 × V_ph	V_L = V_ph
Phase Voltage	V_ph = V_L ÷ √3	V_ph = V_L
Line Current	I_L = I_ph	I_L = √3 × I_ph
Phase Current	I_ph = I_L	I_ph = I_L ÷ √3
Power	P = √3 × V_L × I_L × PF	P = √3 × V_L × I_L × PF
Neutral	Available	Not available

When to Use Each

Configuration	Best For
Star (Wye)	Distribution systems, single-phase loads from 3-phase, motors that need reduced starting current
Delta	Motor running, higher starting torque, transmission (no neutral needed)

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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

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Three-Phase Voltage Calculations

Standard Three-Phase Voltages

Nominal	Line-to-Line	Line-to-Neutral	Use
208/120V	208V	120V	Commercial
240V	240V	139V	Commercial Delta
480/277V	480V	277V	Industrial
600/347V	600V	347V	Industrial (Canada)

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.

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Motor Full Load Current (FLC) Tables

Three-Phase Motor FLC at 460V

Based on NEC Table 430.250:

HP	FLC (A)	HP	FLC (A)
1	2.1	30	40
2	3.0	40	52
3	4.8	50	65
5	7.6	60	77
7.5	11	75	96
10	14	100	124
15	21	125	156
20	27	150	180
25	34	200	240

Motor FLC at Different Voltages

HP	208V	230V	460V	575V
10	30.8	28	14	11
25	74.8	68	34	27
50	143	130	65	52
100	273	248	124	99

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

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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

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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

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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

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Common Mistakes to Avoid

Mistake	Why It's Wrong	Correct Approach
Forgetting √3 factor	Power calculation off by 1.732	Always use √3 for 3-phase
Using wrong voltage	Line vs phase confusion	Clarify V_LL or V_LN before calculating
Ignoring power factor	Undersized conductors	Include PF for AC loads
Same current Star/Delta	Currents differ by √3	Apply correct conversion

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Related Calculators

Calculator	Use When...
3-Phase Power Calculator	Power and current calculations
Full Load Current Calculator	Motor FLC lookup
Motor Current Calculator	Formula-current comparison
Transformer Sizing	Transformer kVA selection
Voltage Drop Calculator	Wire sizing for distance

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Summary

Essential Three-Phase Formulas:

Calculate	Formula
Power	P = √3 × V_L × I_L × PF
Current	I = P / (√3 × V × PF)
kVA	S = √3 × V_L × I_L

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

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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.