Motor Power Formula | 25 HP 480V = 28.6A

Quick Answer: kW = HP × 0.746 | HP = kW ÷ 0.746. Torque (lb-ft) = HP × 5,252 / RPM | Torque (N·m) = kW × 9,549 / RPM. 3-phase formula current: I = HP × 746 / (1.732 × V × η × PF). Example: 25 HP, 480V, η=92%, PF=0.85 → I = 28.6A. Synchronous speed: n = 120 × f / poles (4-pole, 60Hz → 1,800 RPM). For NEC circuit sizing, use Table 430.250 FLC values, not calculated current. → Motor Power Calculator

Key Motor Power Formulas

Calculate	Formula	Example
kW from HP	kW = HP × 0.746	25 HP = 18.65 kW
HP from kW	HP = kW ÷ 0.746	18.65 kW = 25 HP
Output Power	P_out = P_in × η	19.73 kW × 0.95 = 18.7 kW shaft
Torque (lb-ft)	T = HP × 5,252 / RPM	25 HP @ 1,750 = 75 lb-ft
Torque (N·m)	T = kW × 9,549 / RPM	18.65 kW @ 1,750 = 101.7 N·m
3ϕ FLC	I = HP×746 / (1.732×V×η×PF)	25HP, 480V, 92%, 0.85 = 28.6A
Sync Speed	n = 120×f / poles	4-pole, 60Hz = 1,800 RPM

Power Conversion Formulas

HP and kW Conversions

Convert	Formula	Example
HP → kW	kW = HP × 0.746	10 HP = 7.46 kW
kW → HP	HP = kW ÷ 0.746	7.5 kW = 10.05 HP
HP → Watts	W = HP × 746	5 HP = 3,730 W
Watts → HP	HP = W ÷ 746	2,238 W = 3 HP

Quick Reference: HP to kW

HP	kW	HP	kW
1	0.746	25	18.6
2	1.49	30	22.4
3	2.24	40	29.8
5	3.73	50	37.3
7.5	5.59	75	55.9
10	7.46	100	74.6
15	11.2	150	112
20	14.9	200	149

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Motor Efficiency

Efficiency Formula

Efficiency (η) = Output Power / Input Power × 100%

Or:

η = P_shaft / P_electrical × 100%

Rearranged Formulas

Find	Formula
Output Power	P_out = P_in × η
Input Power	P_in = P_out / η
Efficiency	η = P_out / P_in

Typical Motor Efficiencies

Motor Size	Standard (IE1)	High Efficiency (IE2)	Premium (IE3)
1 HP	78%	84%	86%
5 HP	85%	89%	90%
10 HP	88%	91%	92%
25 HP	90%	93%	94%
50 HP	92%	94%	95%
100 HP	93%	95%	96%
200 HP	94%	96%	96.5%

NEMA Premium Efficiency (4-Pole, 60 Hz) — NEMA MG1-2021 Table 12-12

HP	Min. Efficiency	HP	Min. Efficiency
1	85.5%	25	93.6%
1.5	86.5%	30	93.6%
2	86.5%	40	94.1%
3	89.5%	50	94.1%
5	89.5%	75	94.5%
7.5	91.0%	100	95.0%
10	91.7%	150	95.4%
15	92.4%	200	95.4%
20	93.0%	250	95.4%

Use the motor nameplate and manufacturer certified data for the specific frame, enclosure, and efficiency class before procurement or compliance review.

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Input vs Output Power

Understanding Motor Power

 ┌─────────────────┐
 P_in (kW) ──► │ MOTOR │ ──► P_out (HP/kW)
 Electrical │ Efficiency │ Mechanical
 │ Losses: Heat │ (Shaft Power)
 └─────────────────┘

Calculating Input Power

For a motor with known HP and efficiency:

P_input (kW) = (HP × 0.746) / Efficiency

Example: 20 HP motor, 91% efficiency

P_input = (20 × 0.746) / 0.91
P_input = 14.92 / 0.91
P_input = 16.4 kW

Calculating Current from HP

For three-phase motor:

I = (HP × 746) / (√3 × V × η × PF)

Example: 20 HP, 480V, η = 0.91, PF = 0.87

I = (20 × 746) / (1.732 × 480 × 0.91 × 0.87)
I = 14,920 / 658
I = 22.7A

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Torque Formulas

Torque from Power and Speed

In lb-ft (Imperial):

T = (HP × 5252) / RPM

In N·m (Metric):

T = (kW × 9549) / RPM

Or:

T = (P × 60) / (2π × n)

Where:

• T = Torque (lb-ft or N·m)
• P = Power (HP or kW)
• RPM/n = Rotational speed
• 5252 = 33,000 / (2π) for HP→lb-ft
• 9549 = 60,000 / (2π) for kW→N·m

Torque Examples

Example 1: 10 HP motor at 1750 RPM

T = (10 × 5252) / 1750
T = 52,520 / 1750
T = 30.0 lb-ft

Example 2: 7.5 kW motor at 1450 RPM

T = (7.5 × 9549) / 1450
T = 71,618 / 1450
T = 49.4 N·m

Torque Reference Table

HP	1200 RPM	1800 RPM	3600 RPM
1	4.4 lb-ft	2.9 lb-ft	1.5 lb-ft
5	21.9 lb-ft	14.6 lb-ft	7.3 lb-ft
10	43.8 lb-ft	29.2 lb-ft	14.6 lb-ft
25	109.4 lb-ft	72.9 lb-ft	36.5 lb-ft
50	218.8 lb-ft	145.8 lb-ft	72.9 lb-ft
100	437.7 lb-ft	291.8 lb-ft	145.9 lb-ft

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Motor Speed Formulas

Synchronous Speed

n_sync = (120 × f) / P

Where:

• n_sync = Synchronous speed (RPM)
• f = Frequency (Hz)
• P = Number of poles

Common Motor Speeds (60 Hz)

Poles	Synchronous	Typical Full Load
2	3600 RPM	3450-3550 RPM
4	1800 RPM	1725-1770 RPM
6	1200 RPM	1140-1175 RPM
8	900 RPM	850-875 RPM

Slip Formula

Slip (%) = (n_sync - n_actual) / n_sync × 100

Example: 4-pole motor running at 1750 RPM

Slip = (1800 - 1750) / 1800 × 100
Slip = 50 / 1800 × 100
Slip = 2.8%

Typical slip: 2-5% for induction motors

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Motor Sizing for Loads

Load Types and Motor Sizing

Load Type	Description	Sizing Factor
Constant Torque	Conveyors, pumps	1.0-1.15
Variable Torque	Fans, blowers	0.8-1.0
Constant HP	Machine tools	1.15-1.25
High Inertia	Flywheels, crushers	1.25-1.5
Cyclic	Compressors, saws	1.15-1.35

Power Required for Common Applications

Pumps:

HP = (Q × H × SG) / (3960 × η_pump)

Where:

• Q = Flow rate (GPM)
• H = Total head (feet)
• SG = Specific gravity
• η_pump = Pump efficiency

Fans/Blowers:

HP = (CFM × SP) / (6356 × η_fan)

Where:

• CFM = Air flow (cubic feet/minute)
• SP = Static pressure (inches WC)

Conveyors:

HP = (V × F) / (33,000 × η)

Where:

• V = Belt speed (ft/min)
• F = Total force (lbs)

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Worked Examples

Example 1: Motor Input Power

Given: 50 HP motor, 94% efficiency

Find: Input power in kW

Solution:

P_shaft = 50 HP × 0.746 = 37.3 kW
P_input = P_shaft / η = 37.3 / 0.94 = 39.7 kW

Example 2: Motor Current Draw

Given: 25 HP, 480V 3-phase, η = 92%, PF = 0.85

Find: Full load current

Solution:

P_input = (25 × 746) / 0.92 = 20,272 W

I = P / (√3 × V × PF)
I = 20,272 / (1.732 × 480 × 0.85)
I = 20,272 / 706.8
I = 28.7 A

Example 3: Torque at Different Speeds

Given: 15 HP motor

Find: Torque at 1200, 1800, and 3600 RPM

Solution:

At 1200 RPM: T = (15 × 5252) / 1200 = 65.7 lb-ft
At 1800 RPM: T = (15 × 5252) / 1800 = 43.8 lb-ft
At 3600 RPM: T = (15 × 5252) / 3600 = 21.9 lb-ft

Lower speed = Higher torque for same HP!

Example 4: Pump Motor Sizing

Given: Pump flow 200 GPM, head 100 ft, pump η = 75%

Find: Required motor HP

Solution:

HP = (Q × H × SG) / (3960 × η)
HP = (200 × 100 × 1.0) / (3960 × 0.75)
HP = 20,000 / 2,970
HP = 6.7 HP

Select next standard size: 7.5 HP motor

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Motor Nameplate Data

Understanding Nameplate Information

Data	Meaning	Use
HP	Rated output power	Load matching
Voltage	Operating voltage	Electrical connection
FLA	Full Load Amps	Circuit sizing
RPM	Full load speed	Application matching
SF	Service Factor	Overload capacity
Eff	Efficiency	Energy calculations
PF	Power Factor	Electrical sizing

Service Factor

Service Factor allows temporary overload:

• SF 1.0 = No overload allowed
• SF 1.15 = 15% overload capacity (most common)
• SF 1.25 = 25% overload capacity

Continuous rating with SF:

Max Continuous HP = Rated HP × SF

Example: 10 HP motor, SF = 1.15

Max Continuous = 10 × 1.15 = 11.5 HP

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Energy Cost Calculations

Annual Energy Cost

Annual Cost = (HP × 0.746 × Hours × Cost) / Efficiency

Example: 20 HP motor, 8,000 hrs/year, $0.12/kWh, η = 91%

Cost = (20 × 0.746 × 8,000 × 0.12) / 0.91
Cost = 14,323 / 0.91
Cost = $15,741/year

Efficiency Upgrade Savings

Savings = HP × 0.746 × Hours × Cost × (1/η_old - 1/η_new)

Example: 50 HP, 8,000 hrs, $0.12/kWh, upgrade 91%→95%

Savings = 50 × 0.746 × 8,000 × 0.12 × (1/0.91 - 1/0.95)
Savings = 35,808 × (1.099 - 1.053)
Savings = 35,808 × 0.046
Savings = $1,647/year

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Common Mistakes to Avoid

Mistake	Why It's Wrong	Correct Approach
Confusing HP and kW	Different by factor 0.746	Convert properly
Ignoring efficiency	Input ≠ Output power	Include efficiency
Wrong speed for torque	Torque varies with speed	Use actual operating speed
Oversizing motors	Runs inefficiently at partial load	Size for 75-100% load

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Related Calculators

Calculator	Use When...
Motor Power Calculator	Power and efficiency
Motor Current Calculator	Formula current and nameplate comparison
Full Load Current Calculator	NEC table FLC lookup
Motor Starting Current	Inrush sizing
3-Phase Power Calculator	Electrical power

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Summary

Key Formulas:

• HP to kW: kW = HP × 0.746
• Efficiency: η = P_out / P_in
• Torque: T = (HP × 5252) / RPM
• Speed: n = (120 × f) / Poles

Remember:

• 1 HP = 746 Watts = 0.746 kW
• Input Power > Output Power (losses)
• Lower speed = Higher torque at same HP

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FAQ

What's the difference between motor HP and input kW?

HP is the mechanical output power at the shaft. Input kW is the electrical power consumed, which is higher than output due to motor losses. Input kW = (HP × 0.746) / Efficiency.

How do I calculate motor efficiency?

Efficiency = (Output Power / Input Power) × 100%. Measure electrical input power and mechanical output (or use nameplate HP as rated output).

Why does torque decrease with speed?

For constant power (HP), torque and speed are inversely related: T = HP × 5252 / RPM. To maintain the same HP at higher speed, less torque is needed.

What service factor should I use?

For continuous duty at full load, use SF 1.0. For applications with occasional overload or harsh environments, SF 1.15 is standard. SF 1.25 is for severe conditions.

How do I size a motor for my application?

Calculate the required power for your load, add 10-25% margin for safety and efficiency, then select the next standard motor size. Consider starting torque requirements for high-inertia loads.