Red Seal Exam Math Series

Gear Ratio & Speed
Calculations

Master gear, belt, chain, and worm drive calculations for the Red Seal Industrial Maintenance Mechanic (433A) exam — Blocks C & D.

mwredsealprep.ca · Industrial Maintenance Mechanic 433A · Blocks C & D

Why Gear Math Appears on the Red Seal Exam

Gear ratio and speed calculations appear across Block C and Block D. They're some of the most calculation-friendly questions on the exam — straightforward formulas with clean numbers — and a reliable source of marks for prepared candidates.

The same core formula applies to gears, belt drives, and chain drives. Master it once and you can handle all three.

The Core Formula

Output Speed

Input Speed × (Driver ÷ Driven)

Output Torque

Input Torque × (Driven ÷ Driver)

Inverse of speed — speed↑ means torque↓

When speed goes up, torque goes down — and vice versa. Power is conserved (minus losses).

Which Measurement to Use

Gear Drive

Number of teeth

Output RPM = Input × (Driver teeth ÷ Driven teeth)

Belt Drive

Sheave diameter

Output RPM = Input × (Driver dia. ÷ Driven dia.)

Chain Drive

Sprocket teeth

Output RPM = Input × (Driver teeth ÷ Driven teeth)

Worm Drive

Gear teeth ÷ Worm starts

Ratio = Worm Gear Teeth ÷ Worm Starts

Can you solve gear ratio problems under exam pressure?

Test yourself with timed Red Seal–style drive calculations.

Try Free Practice

Worked Examples

7 problems

Try to solve each problem before revealing the solution.

1

Worked Example

Gear Drive

Problem

A driving gear has 20 teeth and turns at 1,800 RPM. The driven gear has 60 teeth. What is the output speed?

DRIVERDRIVEN

Small driver → Large driven = Speed reduction, Torque increase

2

Worked Example

Torque

Problem

The driving gear in Example 1 produces 50 ft-lbs of torque. What is the output torque (ignoring losses)?

3

Worked Example

Compound Train

Problem

A gear train has three stages: Stage 1: 15-tooth driver → 45-tooth driven. Stage 2: 20-tooth driver → 80-tooth driven. Stage 3: 25-tooth driver → 50-tooth driven. Input is 1,200 RPM. What is the final output speed?

4

Worked Example

Belt Drive

Problem

A motor turns at 1,750 RPM and drives a 4" diameter sheave. The driven sheave is 12" diameter. What is the output speed?

DRIVER 4"DRIVEN 12"

Belt drive uses sheave diameter in the formula

5

Worked Example

Belt Drive

Problem

A motor runs at 1,750 RPM. You need an output speed of 875 RPM. The driver sheave is 6". What diameter driven sheave is required?

6

Worked Example

Chain Drive

Problem

A drive sprocket has 17 teeth and turns at 900 RPM. The driven sprocket has 51 teeth. What is the output speed?

7

Worked Example

Worm Drive

Problem

A single-start worm meshes with a 40-tooth worm gear. Input speed is 1,750 RPM. What is the output speed?

Common Exam Traps

Driver vs driven confusion

High Risk

Always identify which gear/sheave is the driver (power source side) and which is the driven (load side). Swapping them reverses your answer.

Compound trains — multiply, don't add

High Risk

For multi-stage gear trains, multiply all stage ratios together. Never add them.

Belt drives use diameter, not radius

Watch Out

Use the full diameter measurement in the formula, not the radius. A very common arithmetic error.

Idler gears don't affect the ratio

Watch Out

An idler gear changes rotation direction only. Do not include it in your ratio calculation — ratio is always first driver to last driven.

Speed up vs speed down

Watch Out

Driver smaller than driven → speed decreases, torque increases (reducer). Driver larger than driven → speed increases, torque decreases (increaser).

Quick Reference

You want
Formula
Output speed
Input speed × (Driver ÷ Driven)
Output torque
Input torque × (Driven ÷ Driver)
Required driven size
Driver size × (Input speed ÷ Output speed)
Compound ratio
Ratio₁ × Ratio₂ × Ratio₃ …
Worm gear ratio
Worm gear teeth ÷ Worm starts

Test Yourself

Randomized drive ratio problems — try to solve before revealing the answer.

Practice Problem

Randomized every time

Belt Drive — Output Speed

Solve This

A motor sheave is 4" diameter and turns at 1300 RPM. The driven sheave is 8" diameter. What is the output speed?

Frequently Asked Questions

Last updated: June 2026 · Based on the Red Seal Occupational Standard (RSOS) for Industrial Maintenance Mechanic (Millwright) 433A

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