Red Seal Exam Math Series

Belt & Chain Drive
Calculations

Sheave sizing, belt length, chain pitch, and chain length for the Red Seal Industrial Maintenance Mechanic (433A) exam — Block D.

mwredsealprep.ca · Industrial Maintenance Mechanic 433A · Block D

Why This Math Appears on the Red Seal Exam

Belt and chain drive calculations appear in Block D and test your ability to calculate speeds, select components, and determine centre distances. The math is straightforward — the challenge is keeping driver and driven components straight and using the right formula for the right drive type.

Belt drives use sheave diameter. Chain drives use sprocket teeth. The speed ratio formula is the same for both.

1

Belt Drives

Output Speed

Input speed × (Driver diameter ÷ Driven diameter)

Required Driven Sheave

Driver diameter × (Input speed ÷ Output speed)

Open Belt Length

2C + 1.57(D + d) + (D − d)² ÷ 4C

Belt Length Variables

LBelt length
CCentre distance
DLarge sheave diameter
dSmall sheave diameter

Can you solve drive calculations under exam pressure?

Test yourself with timed Red Seal–style belt and chain problems.

Try Free Practice

Worked Examples — Belt Drives

3 problems

Try to solve each problem before revealing the solution.

1

Worked Example

Belt Speed

Problem

A 6" driver sheave on a 1,750 RPM motor drives a fan with an 18" sheave. What is the fan speed?

2

Worked Example

Sheave Size

Problem

A motor runs at 1,750 RPM with a 5" driver sheave. You need to drive a pump at 700 RPM. What driven sheave diameter is required?

3

Worked Example

Belt Length

Problem

A drive has a 12" driven sheave and a 4" driver sheave with a 24" centre distance. What belt length is required?

2

Chain Drives

Output Speed

Input speed × (Driver teeth ÷ Driven teeth)

Chain Pitch from ANSI#

Chain number ÷ 8 = pitch (inches)

Chain Length (approx)

(N₁ + N₂) ÷ 2 + 2C/p — round up to even

ANSI Chain Pitch Reference

ANSI #
Calc
Pitch
#35
35 ÷ 8
0.4375"
#40
40 ÷ 8
0.500"
#50
50 ÷ 8
0.625"
#60
60 ÷ 8
0.750"
#80
80 ÷ 8
1.000"
#100
100 ÷ 8
1.250"

Chain Length Variables

LChain length (links)
N₁Driver sprocket teeth
N₂Driven sprocket teeth
CCentre distance
pChain pitch

Worked Examples — Chain Drives

3 problems

Try to solve each problem before revealing the solution.

4

Worked Example

Chain Speed

Problem

A 17-tooth drive sprocket at 900 RPM drives a conveyor with a 34-tooth sprocket. What is the conveyor sprocket speed?

5

Worked Example

Chain Pitch

Problem

What is the pitch of a #60 roller chain?

6

Worked Example

Chain Length

Problem

A #50 chain (0.625" pitch) connects a 17-tooth sprocket to a 34-tooth sprocket with a 20" centre distance. How many links are required?

Chain Sag — Horizontal Drives

Proper chain sag is 2–3% of the centre distance, measured at the midpoint of the slack side.

Example: 30" centre distance → sag = 0.6" to 0.9"

Too tight increases sprocket and chain wear. Too loose causes vibration, noise, and possible jumping. For drives with reversing or shock loads, use less sag (tighter tension).

Common Exam Traps

Open vs crossed belt formula

High Risk

The belt length formula is for open belts only. Crossed belt drives use a different formula. The exam will specify which type.

Chain length — round up to even

High Risk

Always round chain length up to the nearest even number. An odd-link chain requires an offset (half) link, which is weaker than a standard connecting link.

ANSI chain pitch — always divide by 8

Watch Out

Chain number divided by 8 = pitch in inches. This is always imperial, regardless of where the chain was manufactured.

Belt tension — over-tensioning is common

Watch Out

Over-tensioning loads bearings and shortens belt life. Correct deflection is 1/64" per inch of span. Exam troubleshooting may present over-tension as the root cause of premature failure.

Belt drives use diameter, not radius

Watch Out

Use full diameter measurements in all belt formulas. Using radius is a very common arithmetic error.

Quick Reference

You want
Formula
Belt output speed
Input speed × (Driver dia ÷ Driven dia)
Required driven sheave
Driver dia × (Input speed ÷ Output speed)
Open belt length
2C + 1.57(D+d) + (D-d)² ÷ 4C
Chain output speed
Input speed × (Driver teeth ÷ Driven teeth)
Chain pitch from ANSI#
Chain number ÷ 8 (inches)
Chain length (approx)
(N₁+N₂) ÷ 2 + 2C/p, round up to even
Chain sag
2–3% of centre distance

Test Yourself

Randomized belt and chain problems — try to solve before revealing the answer.

Practice Problem

Randomized every time

Chain Speed

Solve This

A 19-tooth drive sprocket runs at 1750 RPM and drives a 76-tooth sprocket. 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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