Electrical Power Formulas & Calculations Reference

Quick Answer

What is the electrical power formula?

P = V × I (Power = Voltage × Current)

System	Formula	Example
DC	P = V × I	12V × 5A = 60W
Single-Phase AC	P = V × I × PF	120V × 10A × 0.9 = 1080W
Three-Phase AC	P = √3 × V × I × PF	1.732 × 480V × 20A × 0.85 = 14,117W

→ Use the Power Calculator for instant calculations.

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After the Power Result

Use the formula answer to decide which workflow owns the next step:

Result you calculated	Continue with
Watts, amps, or voltage for a basic circuit	Power Calculator for the exact input set
Motor kW, HP, or shaft output	Motor Power Calculator with efficiency and power factor
kWh or operating cost	Electricity Cost Calculator with runtime and utility rate assumptions
Low power factor or kVA-to-kW gap	Power Factor Calculator before sizing correction equipment
Long-run conductor loss	Voltage Drop Calculator before selecting wire size

This keeps the formula page as the reference layer and sends project-specific sizing, cost, and conductor checks to the calculator built for that workflow.

For a chart record, use the Power Factor Triangle Chart when the result needs kW, kVAR, kVA, phase angle, and correction notes. Use the kVA to Amps Chart when an apparent-power result needs single-phase or three-phase line-current review before transformer, feeder, or equipment checks.

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DC Power Formulas

Basic DC Power Equations

Find	Formula	Units
Power (P)	P = V × I	Watts (W)
Power (P)	P = I² × R	Watts (W)
Power (P)	P = V² / R	Watts (W)
Voltage (V)	V = P / I	Volts (V)
Current (I)	I = P / V	Amperes (A)

DC Power Wheel

All 12 formulas for DC calculations:

Power (P):

P = V × I
P = I² × R
P = V² / R

Voltage (V):

V = P / I
V = I × R
V = √(P × R)

Current (I):

I = P / V
I = V / R
I = √(P / R)

Resistance (R):

R = V / I
R = P / I²
R = V² / P

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Single-Phase AC Power Formulas

Three Types of AC Power

Type	Symbol	Unit	Formula	Description
Real Power	P	Watts (W)	P = V × I × PF	Actual work done
Reactive Power	Q	VAR	Q = V × I × sin(θ)	Energy stored in L/C
Apparent Power	S	VA	S = V × I	Total power in circuit

Power Triangle Relationship

S² = P² + Q²

 S (VA)
 /|
 / |
 / | Q (VAR)
 /θ |
 ------
 P (W)

Where:

• P = Real Power (Watts)
• Q = Reactive Power (VAR)
• S = Apparent Power (VA)
• θ = Phase angle
• PF = cos(θ) = Power Factor

Single-Phase Formulas

Calculate	Formula	Example
Real Power	P = V × I × PF	120V × 15A × 0.9 = 1620W
Apparent Power	S = V × I	120V × 15A = 1800VA
Reactive Power	Q = √(S² - P²)	√(1800² - 1620²) = 784.5VAR
Power Factor	PF = P / S	1620W / 1800VA = 0.9
Current	I = P / (V × PF)	1620W / (120V × 0.9) = 15A

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Three-Phase Power Formulas

Balanced Three-Phase Systems

Configuration	Real Power (P)	Apparent Power (S)
Line Values	P = √3 × V_L × I_L × PF	S = √3 × V_L × I_L
Phase Values	P = 3 × V_ph × I_ph × PF	S = 3 × V_ph × I_ph

Where:

• √3 = 1.732 (square root of 3)
• V_L = Line voltage (line-to-line)
• I_L = Line current
• V_ph = Phase voltage (line-to-neutral)
• I_ph = Phase current
• PF = Power factor

Star (Wye) vs Delta Connection

Relationship	Star (Y)	Delta (Δ)
V_line to V_phase	V_L = √3 × V_ph	V_L = V_ph
I_line to I_phase	I_L = I_ph	I_L = √3 × I_ph
Power	P = √3 × V_L × I_L × PF	P = √3 × V_L × I_L × PF

Three-Phase Power Examples

Example 1: 480V Industrial Motor

Given: 480V, 3-phase, 50A, PF = 0.85

P = √3 × V × I × PF
P = 1.732 × 480V × 50A × 0.85
P = 35,353W = 35.4 kW

Example 2: 208V Commercial System

Given: 208V, 3-phase, 100A, PF = 0.9

P = √3 × V × I × PF
P = 1.732 × 208V × 100A × 0.9
P = 32,423W = 32.4 kW

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Power Factor

Power Factor Formulas

Calculate	Formula
Power Factor	PF = P / S = W / VA
Power Factor	PF = cos(θ)
True Power	P = S × PF
Apparent Power	S = P / PF
Reactive Power	Q = S × sin(θ) = S × √(1 - PF²)

Power Factor Correction

To find capacitor kVAR needed:

kVAR = kW × (tan(θ₁) - tan(θ₂))

Where:

• θ₁ = arccos(current PF)
• θ₂ = arccos(target PF)

Example: Correct 100kW load from PF 0.7 to PF 0.95

θ₁ = arccos(0.7) = 45.57°
θ₂ = arccos(0.95) = 18.19°
kVAR = 100 × (tan(45.57°) - tan(18.19°))
kVAR = 100 × (1.02 - 0.33)
kVAR = 69 kVAR capacitor needed

→ Use Power Factor Calculator for correction sizing.

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Power Conversion Formulas

Watts, kW, HP Conversions

From	To	Formula
Watts	Kilowatts	kW = W / 1000
Kilowatts	Watts	W = kW × 1000
HP	Watts	W = HP × 746
Watts	HP	HP = W / 746
HP	kW	kW = HP × 0.746
kW	HP	HP = kW / 0.746 = kW × 1.341

kW / kVA Conversions

From	To	Formula
kW	kVA	kVA = kW / PF
kVA	kW	kW = kVA × PF

Quick Reference: HP to kW

HP	kW	HP	kW
1	0.746	15	11.2
2	1.49	20	14.9
3	2.24	25	18.6
5	3.73	30	22.4
7.5	5.59	40	29.8
10	7.46	50	37.3

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Common Voltage Systems

US Standard System Voltages

System	Voltage	Typical Use
Single-Phase	120V	Residential, lighting
Single-Phase	240V	Residential appliances
Three-Phase	208V	Commercial (Y from 120V)
Three-Phase	240V	Commercial (Delta)
Three-Phase	480V	Industrial, large motors
Three-Phase	600V	Industrial (Canada/Heavy Industry)

Voltage Relationships

3-Phase System	Line Voltage	Phase Voltage (Y)
208V system	208V	120V
240V system	240V	139V
480V system	480V	277V
600V system	600V	347V

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Worked Examples

Example 1: Calculate Heater Power

Given: 240V heater with 20Ω resistance

Solution:

P = V² / R
P = (240V)² / 20Ω
P = 57,600 / 20
P = 2,880W = 2.88 kW

Example 2: Industrial Motor Power

Given: 3-phase 480V motor, 30A per phase, PF = 0.87

Solution:

P = √3 × V × I × PF
P = 1.732 × 480V × 30A × 0.87
P = 21,706W = 21.7 kW

HP = 21.7 kW / 0.746 = 29.1 HP ≈ 30 HP motor

Example 3: Current from Power

Given: 5 kW load, 240V single-phase, PF = 0.95

Solution:

I = P / (V × PF)
I = 5000W / (240V × 0.95)
I = 5000 / 228
I = 21.9A

Example 4: kVA Sizing for Transformer

Given: Load 150 kW, PF = 0.8

Solution:

kVA = kW / PF
kVA = 150 kW / 0.8
kVA = 187.5 kVA

Select next standard size: 200 kVA transformer or 225 kVA transformer

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Power Loss in Conductors

Line Loss Formula

P_loss = I² × R

Where:

• P_loss = Power lost in wire (Watts)
• I = Current (Amperes)
• R = Wire resistance (Ohms - check AWG charts)

Percentage Loss

% Loss = (P_loss / P_total) × 100

Example: 50A circuit, 0.5Ω total round-trip wire resistance

P_loss = (50A)² × 0.5Ω = 1,250W

If load is 10kW:
% Loss = (1250 / 10000) × 100 = 12.5% (This is too high! NEC requires <3% to 5% drop max)

→ Use Voltage Drop Calculator to properly size conductors.

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Common Mistakes to Avoid

Mistake	Why It's Wrong	Correct Approach
Ignoring power factor	Undersized equipment	Always include PF for AC circuits containing motors/transformers
Using P=VI for 3-phase	Missing √3 factor	Use P = √3 × V × I × PF for three-phase power
Confusing kW and kVA	These differ by PF	kW = kVA × PF
Using 1 HP = 1 kW	Inaccurate (1 HP = 746W)	1 HP = 0.746 kW exactly

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Related Calculators

Calculator	Use When...
Power Calculator	Basic V, I, P calculations
3-Phase Power Calculator	Three-phase systems
Power Factor Calculator	PF correction sizing
Motor Power Calculator	Motor load calculations

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Summary

Key Formulas:

System	Power Formula
DC	P = V × I = I²R = V²/R
Single-Phase AC	P = V × I × PF
Three-Phase AC	P = √3 × V × I × PF

Key Conversions:

• 1 HP = 746W = 0.746 kW
• kVA = kW / PF
• √3 = 1.732

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FAQ

What is the difference between kW and kVA?

kW (kilowatts) is real power that does actual work. kVA (kilovolt-amperes) is apparent power, the total power in the circuit. They differ by the power factor: kW = kVA × PF. Equipment like transformers and utility generators are rated in kVA.

Why use √3 in three-phase calculations?

The √3 (1.732) factor mathematically accounts for the 120° phase shift between the three phases in a balanced three-phase system. It correctly converts between line and phase values ensuring an accurate power calculation.

How do I calculate motor running power?

Use P = √3 × V × I × PF for three-phase motors, where I is the actual running current under load. Or use the nameplate HP rating × 0.746 for rated maximum output power in kW. Remember that actual electrical power input is higher due to motor efficiency losses.

What is a good power factor?

Residential loads typically run at PF 0.85-0.95. Industrial targets are usually strictly maintained above 0.9 or 0.95 to avoid costly utility penalties. Unity (1.0) is mathematically ideal but practically rare in factories. Anything below 0.85 usually dictates a firm need for correction capacitors.

How do I convert between HP and kW?

Multiply HP by 0.746 to get kW. Divide kW by 0.746 (or multiply by 1.341) to calculate HP. These conversions are for mechanical power equivalents; electrical input may be slightly higher due to the motor's internal efficiency.