Motor Power Formulas Guide | HP, kW, Torque and Current

Quick Answer: Use this guide to choose the motor-power formula path first: HP or kW conversion, shaft torque, synchronous speed, input power, efficiency, power factor, voltage, and formula current. Then run the Motor Power Calculator for the specific motor data. For NEC conductor or protection sizing, use the separate Full Load Current Calculator instead of treating formula current as the table value.

This guide keeps motor formulas as a workflow, not a universal answer table. Reviewed 2026-07-07.

Motor power calculator workflow before examples

Use this sequence before copying any formula result into design notes:

1. Identify whether the task is HP-to-kW conversion, input power, torque, speed, formula current, energy cost, or motor sizing.
2. Enter the known HP or kW, voltage, phase, efficiency, power factor, speed, service factor, hours, and load type in the Motor Power Calculator.
3. Compare formula current with nameplate FLA and, when the task is NEC sizing, the Full Load Current Calculator.
4. Document whether the result is mechanical shaft output, electrical input, calculated operating current, nameplate FLA, or NEC table FLC.
5. Check the result against the driven load, duty cycle, enclosure, ambient temperature, and manufacturer data before selecting a motor.

Key Motor Power Formulas

Power Conversion Formulas

HP and kW Conversions

Quick Reference: HP to kW

Motor Efficiency

Efficiency Formula

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

Or:

η = P_shaft / P_electrical × 100%

Rearranged Formulas

Typical Motor Efficiencies

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

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

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

To use this path, enter the motor HP and the efficiency basis from the nameplate or manufacturer data. The calculator result should be labeled as electrical input power, not shaft output.

Calculating Current from HP

For three-phase motor:

I = (HP × 746) / (√3 × V × η × PF)

Use this path when the task is formula current, energy modeling, or a comparison against nameplate data. For NEC branch-circuit conductor or protection sizing, move to the full-load-current lookup instead of reusing the formula result.

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

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)

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

Motor Sizing for Loads

Load Types and Motor Sizing

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)

Calculator checks instead of static examples

Use these example paths as presets for the calculator workflow, then read the actual numeric result from the calculator output:

After each check, compare the result with the motor nameplate. If the next decision is conductor, overload, or short-circuit protection sizing under the NEC, use a table-FLC lookup and the applicable motor articles rather than treating the formula current as the code value.

Motor Nameplate Data

Understanding Nameplate Information

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

Use the nameplate service factor as a rating note, not as permission to run above normal load continuously without checking temperature, duty, enclosure, and manufacturer instructions.

Energy Cost Calculations

Annual Energy Cost

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

Enter HP or kW, efficiency, operating hours, load factor, and energy cost in the calculator or cost model. Label the result as an energy-cost estimate, not a motor sizing value.

Efficiency Upgrade Savings

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

Run the old and new efficiency values through the same load profile before claiming savings. Keep demand charges, runtime, process changes, and maintenance effects separate from the motor formula result.

Common Mistakes to Avoid

Related Calculators

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

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.