Skip to content
RFrftools.io
Motor

Gear Ratio Calculator

Calculate gear ratio, output speed, torque multiplication, and power transmission efficiency for gear trains.

Loading calculator...

Formula

GR=N2/N1,n2=n1/GR,T2=T1×GR×ηGR = N₂/N₁, n₂ = n₁/GR, T₂ = T₁ × GR × η
N₁— Driver teeth count
N₂— Driven teeth count
η— Gear efficiency (%)

How It Works

This calculator determines gear ratio, output speed, and torque multiplication for mechanical power transmission systems. Mechanical engineers, robotics designers, and industrial automation specialists use it to match motor characteristics to load requirements. Proper gear ratio selection optimizes efficiency—operating motors at 70-90% of no-load speed maximizes their efficiency curve per NEMA MG-1 guidelines.

Per Shigley's 'Mechanical Engineering Design' (11th ed.), gear ratio GR = N_driven/N_drive = ω_in/ω_out = T_out/(T_in×η), where η is gear efficiency. Output torque increases by GR while speed decreases by the same factor. Efficiency varies by gear type per AGMA 1010: spur gears achieve 97-99% per mesh, helical 97-99%, bevel 95-98%, worm 40-90% (ratio-dependent), and planetary 95-98%.

For multi-stage gearboxes, ratios multiply while efficiencies compound: a 3-stage gearbox with 5:1 per stage achieves 125:1 total ratio at 94-97% efficiency (0.98³ = 0.94 for three 98% meshes). Reflected inertia transforms as J_reflected = J_load/GR², meaning high gear ratios dramatically reduce motor acceleration torque requirements—a 10:1 ratio reduces reflected inertia 100×, enabling small motors to accelerate large loads.

Worked Example

Design a gear reducer for an AGV drive motor. Motor: 400W, 3000 RPM, 1.27 N·m rated torque. Wheel requirement: 150 RPM, 12 N·m minimum torque at wheel.

Step 1 — Calculate required gear ratio: GR = ω_motor / ω_wheel = 3000 / 150 = 20:1

Step 2 — Determine achievable output torque: Assuming 95% planetary gearbox efficiency (single-stage at 20:1): T_out = T_motor × GR × η = 1.27 × 20 × 0.95 = 24.1 N·m This exceeds 12 N·m requirement by 2× margin—acceptable

Step 3 — Consider two-stage alternative: Two 4.47:1 stages: total GR = 4.47 × 4.47 = 20:1 Efficiency: 0.97 × 0.97 = 0.94 (slightly lower) T_out = 1.27 × 20 × 0.94 = 23.9 N·m (similar result)

Step 4 — Calculate reflected wheel inertia to motor: Wheel + load inertia: J_wheel = 0.05 kg·m² J_reflected = J_wheel / GR² = 0.05 / 400 = 0.000125 kg·m² Motor rotor inertia: 0.0008 kg·m² (from datasheet) Total: 0.000925 kg·m² → wheel inertia is only 13.5% of total

Step 5 — Verify motor operating point: Motor speed at 150 RPM wheel: 3000 RPM = 100% of rated speed For best efficiency, consider 3600 RPM motor with 24:1 ratio → wheel at 150 RPM, motor at 83% speed (optimal efficiency band)

Result: Select 20:1 planetary gearbox with 95% efficiency. Output delivers 24 N·m, exceeding requirement by 100%. The reflected inertia of 0.125 g·m² is negligible compared to motor rotor inertia, enabling rapid acceleration.

Practical Tips

  • ✓Per AGMA efficiency guidelines, select worm gears only for ratios >20:1 where self-locking is required; efficiency drops below 50% at ratios >40:1, wasting over half input power as heat
  • ✓For backdrivable requirements (robotic joints, cobots), avoid worm gears with ratios >15:1—reverse efficiency falls below 50%, effectively locking the output; use planetary or cycloidal drives instead
  • ✓Per motor efficiency curves, target gear ratio that places motor speed at 70-90% of no-load RPM under typical load—this operating region maximizes motor efficiency by 3-8% versus operation near stall or no-load

Common Mistakes

  • ✗Forgetting cumulative efficiency losses: Per AGMA standards, a 4-stage spur gearbox at 97% per stage delivers only 88.5% overall (0.97⁴); neglecting this causes 12% torque shortfall versus single-stage assumptions
  • ✗Confusing speed ratio with gear ratio: GR = N_driven/N_drive = teeth_driven/teeth_drive; output speed = input speed / GR, not multiplied—reversing this causes 2× error in speed calculations
  • ✗Ignoring inertia reflection through gear ratio: J_reflected = J_load/GR²; a 10:1 ratio reduces effective load inertia 100×—this dominates acceleration calculations for high-ratio gearboxes

Frequently Asked Questions

Per servo sizing theory (Krishnan, 'Electric Motor Drives'): For minimum acceleration time, optimal GR = √(J_load/J_motor), which matches reflected load inertia to motor inertia. For maximum continuous torque delivery, select GR = T_required/(T_motor×η). These often differ—use the higher ratio for torque-limited applications and optimal inertia match for acceleration-limited (pick-and-place) applications. Typical industrial servo systems use 3:1 to 10:1 ratios.
Per AGMA design guidelines: Planetary gearboxes achieve higher torque density (3-5× for same volume) by distributing load across 3-5 planet gears in parallel. They provide coaxial input/output shafts and lower backlash (1-10 arc-min vs. 10-30 arc-min for spur trains). Efficiency is 95-98% per stage even at high ratios. Cost is 2-5× higher than equivalent spur gearbox. Planetary suits compact, high-torque applications; spur trains suit cost-sensitive, lower-torque applications.
Yes—ratios <1 (overdrive) multiply output speed while reducing torque. A 1:3 ratio (0.33:1) triples speed but delivers only 1/3 of input torque. Per mechanical design practice, this suits spindle drives, centrifuges, and turbine applications where high speed is needed from slower prime movers. Ensure the motor provides adequate torque at the reduced output—output torque = input torque × GR × η, so T_out = T_in × 0.33 × 0.97 = 0.32×T_in.

Shop Components

As an Amazon Associate we earn from qualifying purchases.

NEMA 17 Stepper Motor

NEMA 17 bipolar stepper motors for precision motion control

Amazon →

Stepper Motor Driver (A4988)

A4988 stepper driver modules for microstepping control

Amazon →

DC Motor with Encoder

12 V DC motors with encoders for closed-loop drive applications

Amazon →

Related Calculators

Motor

Servo Motor

Calculate servo motor torque, speed, efficiency, and back-EMF from electrical and load parameters.

Motor

DC Motor

Calculate DC motor speed, torque, power, and efficiency from electrical parameters

Motor

Torque Converter

Convert torque between Newton-metres, pound-feet, pound-inches, oz·in, kg·cm and dyne·cm — covers all motor datasheet units.

Motor

Stepper Motor

Calculate stepper motor speed, step frequency, and travel per revolution