How to Calculate BLDC Motor Torque and Power: Practical Guide for Engineers
The most common mistake in BLDC motor selection is not a complex calculation error — it is neglecting a simple one. An undersized motor overheats and fails within weeks. An oversized motor wastes budget and space. This guide covers the essential formulas every engineer needs, three real-world sizing examples (AGV drive wheel, conveyor belt, water pump), safety factor selection, and the five most common calculation mistakes we see in customer specification sheets. Based on 15+ years of application engineering at Shenghe Motor.
1. Essential Formulas
| Formula | Description | Units |
|---|---|---|
| P = T × n / 9.55 | Power from torque and speed | P (W), T (Nm), n (RPM) |
| T = 9.55 × P / n | Torque from power and speed | T (Nm), P (W), n (RPM) |
| T = F × r | Torque from force and radius | T (Nm), F (N), r (m) |
| F = m × g × μ | Rolling resistance force (horizontal) | F (N), m (kg), g=9.81, μ=friction coeff |
| F = m × g × sin(θ) | Gravity force on incline | θ = incline angle |
| P_in = V × I | Input electrical power | P_in (W), V (V), I (A) |
| η = P / P_in | Motor efficiency | η (decimal, e.g. 0.85) |
| J = 0.5 × m × r² | Moment of inertia (solid cylinder) | J (kg·m²) |
| T_accel = J × α | Torque for angular acceleration | T_accel (Nm), α (rad/s²) |
The constant 9.55: Derived from 60/(2π). When you measure speed in RPM and want power in watts, this constant converts between angular velocity in rad/s and rotational speed in RPM.
2. Example 1: AGV Drive Wheel Motor
Scenario: An AGV weighing 800 kg (including payload) travels at 1.5 m/s on a level warehouse floor. Wheel diameter = 200mm (0.2m radius = 0.1m). Rolling friction coefficient μ = 0.02 (polyurethane wheel on concrete). Two driven wheels, each with its own motor.
Step 1 — Rolling resistance force (per wheel):
F = (m × g × μ) / 2 = (800 × 9.81 × 0.02) / 2 = 78.5 N
Step 2 — Required torque (per motor):
T = F × r = 78.5 × 0.1 = 7.85 Nm
Step 3 — Wheel RPM:
n = v / (2π × r) × 60 = 1.5 / (2π × 0.1) × 60 = 143 RPM
Step 4 — Motor power:
P = T × n / 9.55 = 7.85 × 143 / 9.55 = 117.5 W
Step 5 — Account for incline (5% grade, θ≈2.86°):
F_incline = 400 × 9.81 × sin(2.86°) = 196 N (per wheel)
T_incline = 196 × 0.1 = 19.6 Nm → P = 293 W
Selected motor: 300W BLDC + 15:1 planetary gearbox (output: 143 RPM × 15 = 2145 RPM motor speed). Continuous torque 10 Nm at gearbox output, peak 25 Nm for 30 seconds to handle ramp starts.
3. Example 2: Conveyor Belt Drive
Scenario: A horizontal belt conveyor moves 500 kg of material at 0.5 m/s. Drive pulley diameter = 150mm (radius 0.075m). Belt runs on steel rollers. System uses one motor via chain reduction.
Step 1 — Total load force:
F_load = m × g × μ = 500 × 9.81 × 0.035 (steel rollers) = 172 N
Add belt tension preload: +50 N = 222 N total
Step 2 — Pulley torque:
T = F × r = 222 × 0.075 = 16.7 Nm
Step 3 — Pulley RPM:
n = 0.5 / (2π × 0.075) × 60 = 63.7 RPM
Step 4 — With 3:1 chain reduction to motor shaft:
Motor torque = 16.7 / 3 = 5.6 Nm (÷3 because gearbox multiplies torque)
Motor speed = 63.7 × 3 = 191 RPM
Step 5 — Motor power:
P = 5.6 × 191 / 9.55 = 112 W
Selected motor: 150W BLDC + 10:1 worm gearbox. Continuous output torque 60 Nm (well above 16.7 Nm requirement). Worm gearbox provides self-locking — conveyor won't back-drive when motor stops — critical for inclined conveyors.
4. Example 3: Centrifugal Water Pump
Scenario: A pump moves water at 100 L/min against 25m head. Pump efficiency η_pump = 70%. Direct-drive, no gearbox.
Step 1 — Hydraulic power:
P_hydraulic = ρ × g × Q × H = 1000 × 9.81 × (100/60000) × 25 = 409 W
Step 2 — Motor shaft power:
P_motor = P_hydraulic / η_pump = 409 / 0.70 = 584 W
Step 3 — Motor speed: Pump rated at 2900 RPM
Step 4 — Motor torque:
T = 9.55 × 584 / 2900 = 1.92 Nm
Selected motor: 750W BLDC rated at 3000 RPM (next standard size up from 600W). Continuous torque 2.4 Nm. The oversize of 750W vs 584W provides headroom for higher viscosity fluids and pump wear over time. Variable-speed controller enables flow control without throttling valve — saves 15–30% pump energy.
5. Safety Factor Selection
| Application | Recommended Safety Factor | Reasoning |
|---|---|---|
| Fan / blower (clean air) | 1.1–1.2 | Predictable load, no shock, no stalling |
| Conveyor (light duty) | 1.3–1.5 | Belt tension variation, occasional overload |
| AGV / mobile robot | 1.5–2.0 | Ramp starts, obstacle climbing, floor debris |
| Crusher / shredder | 2.0–3.0 | High shock loads, unpredictable material size |
| Hoist / lift / winch | 2.5–4.0 | Safety-critical; must hold load on power loss |
| Pump (clean water) | 1.2–1.3 | System curve variation, wear margin |
| Machine tool spindle | 1.5–2.0 | Cutting force variation, intermittent overload |
Safety factor is applied to continuous torque, not peak. A motor rated at 5 Nm continuous with a 2× overload capacity already handles 10 Nm peaks. Adding a 2× safety factor on top means sizing for 10 Nm continuous — unnecessarily large. Apply the safety factor to the calculated continuous load torque, then check that peak demands fall within the motor's overload rating.
6. The 5 Most Common Sizing Mistakes
- 1. Specifying "power" without speed. "I need a 500W motor." — At what RPM? 500W at 500 RPM = 9.55 Nm. 500W at 5000 RPM = 0.96 Nm. These are completely different motors. Always specify torque at speed.
- 2. Neglecting acceleration torque. Steady-state torque may be 2 Nm, but accelerating the load from 0 to 3000 RPM in 0.2 seconds could require 8 Nm. Motor must deliver both continuous and peak torque.
- 3. Ignoring gearbox efficiency. A 100W motor with an 85% efficient gearbox delivers 85W to the load. That 15% loss generates heat in the gearbox (and adds to motor load). Factor gearbox efficiency (typically 70–90% depending on type and ratio) into your power calculation.
- 4. Room-temperature testing only. A motor that meets torque spec at 25°C may fall 20% short at -10°C (higher bearing grease viscosity, lower magnet strength in some materials) or at 60°C (winding resistance increases ~40% from 25°C to 85°C). Always specify the operating temperature range and derate accordingly.
- 5. Overlooking duty cycle. A motor rated "500W continuous" can only deliver 500W indefinitely in a 25°C ambient with free air convection. In a sealed enclosure at 40°C ambient with 60% duty cycle, the same motor may only deliver 350W. Provide your duty cycle and thermal environment when requesting a motor recommendation.
Send us your load profile (torque-speed points or application parameters) — our application engineers will validate the sizing and recommend the right motor. Free, no commitment, typically within 24 hours.