Free Gear Ratio & Output Speed Calculator

Calculate total reduction ratios across multi-stage gear trains, determine final output RPM, and calculate torque multiplication.

⚙️ Motor Speed & Gear Stages

Input Motor Speed (RPM)

Motor Torque (N·m)

Stage 1 Gear Pair

Driver 1 (Pinion Teeth)

Driven 1 (Gear Teeth)

Stage 2 Gear Pair (Compound)

Driver 2 (Pinion Teeth) Set 1:1 if single stage

Driven 2 (Gear Teeth)

Stage Mechanical Efficiency (%)

📊 Output Speed & Torque

Final Output Shaft Speed

200 RPM

15.00 : 1 Total Reduction Ratio

Output Torque

3.38 N·m

2.49 ft-lbs (30.0 in-lbs)

Overall Efficiency

90.3% Total

2 gear mesh stages

Stage 1 Reduction: 5.00 : 1 (600 RPM intermediate)

Stage 2 Reduction: 3.00 : 1

Shaft Output Mechanical Power: 70.9 Watts (0.095 HP)

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Understanding Compound Gear Trains

When high speed reduction (such as 20:1 or 100:1) is required, attempting it with a single gear pair requires an impractically massive driven gear. Compound gear trains mount a small driving pinion and a large driven gear on the same intermediate shaft, multiplying reduction ratios in compact enclosures.

Compound Gear Equations

GR_{\text{total}} = \frac{N_{\text{driven,1}}}{N_{\text{driver,1}}} \times \frac{N_{\text{driven,2}}}{N_{\text{driver,2}}}

RPM_{\text{out}} = \frac{RPM_{\text{in}}}{GR_{\text{total}}}

\tau_{\text{out}} = \tau_{\text{in}} \times GR_{\text{total}} \times \eta_{\text{total}}

P_{\text{watts}} = \tau_{\text{out}} \times \frac{2 \pi \cdot RPM_{\text{out}}}{60}

Idler Gears vs. Compound Gears

An idler gear placed between an input gear and an output gear changes the direction of shaft rotation but does not alter the gear ratio (the tooth count of the idler cancels out mathematically). To achieve compound ratio multiplication, the two intermediate gears must be locked together on a common shaft.

Frequently Asked Questions

Why does output torque not equal input torque times gear ratio?

Every mechanical gear mesh loses energy to tooth sliding friction, churning of grease or oil lubricant, and shaft bearing resistance. Spur gear pairs typically achieve 95% efficiency, meaning a 2-stage compound gearbox delivers roughly 90% of theoretical multiplied torque.

What is the minimum tooth count to prevent gear undercutting?

For standard 20-degree pressure angle spur gears, pinions with fewer than 14 to 17 teeth suffer from undercutting—where the generating cutter scoops out the base of the tooth, weakening tooth root strength and causing rough running.

How does back-drivability relate to gear ratio?

High reduction gearboxes (especially over 50:1, or any worm gear drive) are non-backdrivable: external torque applied to the output shaft cannot spin the motor due to internal friction locking.