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Motor

Gear Ratio Calculator

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

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Formula

GR = N₂/N₁, n₂ = n₁/GR, T₂ = T₁ × GR × η

N₁— Driver teeth count
N₂— Driven teeth count
η— Gear efficiency (%)

How It Works

A gear train transforms rotational speed and torque between a driving and a driven shaft. The gear ratio (GR) equals the number of teeth on the driven gear divided by the number of teeth on the driving gear (or equivalently, input speed divided by output speed). Output torque scales by GR (minus efficiency losses), while output speed is divided by GR. Compound gear trains multiply individual stage ratios, and efficiency per stage is typically 97–99% for helical gears and 95–97% for spur gears.

Worked Example

A two-stage gear train connects a 3000 RPM motor to a conveyor shaft. Stage 1: drive gear 20 teeth, driven gear 60 teeth → GR₁ = 60/20 = 3 Stage 2: drive gear 15 teeth, driven gear 45 teeth → GR₂ = 45/15 = 3 Step 1 — Total gear ratio: GR_total = GR₁ × GR₂ = 3 × 3 = 9 Step 2 — Output speed: N_out = 3000 / 9 = 333.3 RPM Step 3 — Output torque (assuming 98% efficiency per stage): η_total = 0.98 × 0.98 = 0.9604 If motor torque = 0.5 N·m: T_out = 0.5 × 9 × 0.9604 = 4.32 N·m Result: The conveyor shaft turns at 333 RPM and receives 4.32 N·m — nearly 9× the motor torque with 4% loss to gear friction.

Practical Tips

  • ✓Use a gear ratio that keeps motor speed in its peak-efficiency band (typically 70–90% of no-load RPM) at the design operating point
  • ✓For back-drivability requirements (e.g., robotic joints), avoid worm gears with ratios above ~20:1 as their reverse efficiency drops below 50%
  • ✓Always verify the gearbox's maximum input speed and rated torque separately — these are independent limits and both must be respected

Common Mistakes

  • ✗Forgetting cumulative efficiency losses in multi-stage trains — a 4-stage gearbox at 97% per stage is only 88.5% overall
  • ✗Confusing gear ratio with speed ratio — output speed = input speed / GR, not multiplied by it
  • ✗Ignoring gear inertia reflected back to the motor shaft, which is proportional to GR² and dominates acceleration calculations for high-ratio gearboxes

Frequently Asked Questions

Maximum power is transferred when the reflected load inertia equals the motor rotor inertia. The optimal gear ratio is sqrt(J_load / J_motor). For torque-limited rather than inertia-limited systems, choose the ratio that keeps the motor in its rated torque band.
A planetary gearbox achieves higher torque density and lower backlash in a compact, coaxial form. It distributes torque across multiple planet gears in parallel, giving efficiencies of 95–98% even at ratios up to 10:1 per stage. Spur gear trains are simpler and cheaper but require offset shaft placement.
Yes — a ratio less than 1 (overdrive) increases output speed while reducing output torque. This is common in spindle drives and turbine applications. Simply set the driven gear to have fewer teeth than the drive gear.

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