Gear Ratio Calculator Formula

Understand the math behind the gear ratio calculator. Each variable explained with a worked example.

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Formulas Used

Gear Ratio

gear_ratio = ratio

Output Speed

output_speed = input_speed / ratio

Output Torque (ideal)

output_torque = input_torque * ratio

Variables

Variable	Description	Default
`teeth_driver`	Driver Gear Teeth (N1)	20
`teeth_driven`	Driven Gear Teeth (N2)	60
`input_speed`	Input Speed(RPM)	1800
`input_torque`	Input Torque(N-m)	50
`ratio`	Derived value`= teeth_driven / teeth_driver`	calculated

How It Works

Gear Ratio Fundamentals

Gears trade speed for torque (or vice versa) while transmitting rotational power.

Formulas

Gear Ratio = N2 / N1 (driven teeth / driver teeth)

Output Speed = Input Speed / Gear Ratio

Output Torque = Input Torque x Gear Ratio (assuming no losses)

A ratio greater than 1 is a speed reduction (torque multiplication). A ratio less than 1 is a speed increase (torque reduction).

Worked Example

A 20-tooth driver meshing with a 60-tooth driven gear, input 1800 RPM at 50 N-m.

teeth_driver = 20teeth_driven = 60input_speed = 1800input_torque = 50

01Gear ratio = 60 / 20 = 3.0 (speed reduction)
02Output speed = 1800 / 3.0 = 600 RPM
03Output torque = 50 x 3.0 = 150 N-m (ideal)
04Actual torque is slightly less due to mesh efficiency (typically 95-99% per stage).

Frequently Asked Questions

What is typical gear mesh efficiency?

Spur gears: 97-99% per stage. Helical gears: 96-99%. Worm gears: 40-90% depending on lead angle. Bevel gears: 95-98%. For multi-stage gearboxes, multiply efficiencies.

Does the gear ratio change the power?

Ideally no. Power = Torque x Angular Velocity. When torque increases, speed decreases proportionally so power is conserved. In practice, some power is lost to friction and heat.

What determines the minimum number of teeth?

For standard spur gears with 20-degree pressure angle, a minimum of 13 teeth avoids undercut interference. Below this, profile-shifted gears or a different tooth form is needed.

Learn More

Guide

How to Calculate Gear Ratios: Complete Engineering Guide

Learn how to calculate gear ratios for spur gears, compound gear trains, and planetary systems. Covers speed, torque, and efficiency relationships with practical examples.

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