AtlasCalcsUtility Calculation Suite
August 2026 12 min read

Pulley Diameter Calculator

Free pulley diameter calculator. Size pulley diameters for a desired speed ratio (D₂ = D₁·n₁/n₂) or for a target belt speed (D₁ = 60000·v/(π·n₁)). Reports belt speed and ideal tension. Works for V-belt, flat and timing drives.

Pulley Diameter Calculator

Pulley Diameter Inputs

Unit System
SI — mm Imperial — in
Mode
Size from ratio Size from belt speed
Driver Speed n₁ (rpm)
Driven Speed n₂ (rpm)
Driver Diameter D₁ (mm)

D₂ = D₁·(n₁/n₂)

Power (kW)
Power Unit
kW hp
Auto-calculate instantly

Driven Diameter D₂

450mm

D₁·(n₁/n₂)

Belt speed is in a sensible range (5–30 m/s).
Speed Ratio i

3:1

Driver D₁

150mm

Belt Speed

11.78m/s

Belt Tension

424N

Speed Ratio i

3:1

n₁/n₂ = D₂/D₁

Driver D₁

150mm

Input

Belt Speed

11.78m/s

π·D·n/60

Belt Tension

424N

≈ P/v

Result Summary

Driver n₁1500 rpm
Driven n₂500 rpm
Speed Ratio3 : 1
Driver D₁150 mm
Driven D₂450 mm
Belt Speed11.78 m/s
Power5 kW
Belt Tension424 N
Estimated Result — Uses the open-belt relations i = n₁/n₂ = D₂/D₁ and v = π·D·n/60 (m/s, D in m; or π·D·n/60 000 with D in mm). In ratio mode D₂ = D₁·i; in speed mode D₁ = 60 000·v/(π·n₁), D₂ = D₁·i. Ideal belt tension F = P/v (P in watts, v in m/s) is an estimate; real designs add centrifugal/slack effects, a service factor and a wrap check (use the belt-length calculator for centre/wrap).

Interactive Diagram

The larger driven pulley turns slower; belt speed is the same on both.

Visualizations

Diameter Comparison

150mmD₁ driver
450mmD₂ driven

Belt Speed

v12m/s

Formula

For an open belt drive the speed ratio equals the diameter ratio: i = n₁/n₂ = D₂/D₁. Once you fix the driver diameter (or the target belt speed), the other diameters follow. Belt speed is set by the driver: v = π·D·n/60 (m/s, D in m). Ideal tension is roughly F = P/v; real drives add centrifugal and slack-side terms plus a service factor.

i = n₁/n₂ = D₂/D₁ , v = π·D₁·n₁/60000

Alternative Form

D₂ = D₁·i (ratio mode) ; D₁ = 60000·v/(π·n₁) (speed mode)

Variables

SymbolNameUnitDescription
n₁, n₂SpeedrpmDriver / driven
D₁, D₂DiametermmPitch dia
iRatio:1n₁/n₂ = D₂/D₁
vBelt speedm/sπ·D·n/60
FTensionN≈ P/v

Explanation

Pick ratio mode when you know the two speeds and a practical driver size; the tool gives the driven size and resulting belt speed. Pick speed mode when a belt-speed limit (or a desired surface speed) dictates the driver size. Both yield the ideal tension estimate F = P/v so you can sanity-check the drive.

Derivation

i = n₁/n₂. Open belt: D₂/D₁ = n₁/n₂ ⇒ D₂ = D₁·i. v = π·D₁·n₁/60 (D₁ m) = π·D₁·n₁/60 000 (D₁ mm). Speed mode: D₁ = 60 000·v/(π·n₁), D₂ = D₁·i. F = P/v (P W, v m/s).

Step-by-Step Calculation

Follow each step to understand how the result is calculated from your inputs.

Step 1

Speed ratio.

i = n₁/n₂ = D₂/D₁
n₁:1500
n₂:500
Intermediate: i = 1500/500 = 3
Result: 3 : 1
Step 2

Driven diameter.

D₂ = D₁·i
D₁:150
Intermediate: D₂ = 150·3
Result: 450 mm
Step 3

Belt speed.

v = π·D₁·n₁/60000
Intermediate: v = π·150·1500/60000
Result: 11.78 m/s
Step 4

Belt tension (ideal).

F = P/v
P:5 kW
Intermediate: F = 5,000/11.78
Result: 424 N
Final Answer
450 mm

Worked Examples

See how the calculator works with different scenarios.

Scenario

Ratio mode: n₁=1500, n₂=500, D₁=150 mm, P=5 kW.

Inputs

mode:ratio
n1:1500
n2:500
D1:150
P:5
pwrUnit:kw

Calculation

i=3; D₂=150·3=450; v=π·150·1500/60000=11.8 m/s; F=5000/11.8=424 N

Result

D₂=450 mm, v=11.8 m/s

Interpretation

3:1 reduction from a 150 mm driver.

Understanding Your Result

Your Result: 450 mm

Typical range: Belt speed 11.8 m/s; aim 5–25 m/s for V-belts, up to ~30 for timing. Ratio 3:1.

What This Means

With n₁=1500 rpm and n₂=500 rpm the ratio is 3:1, so the driver should be 150 mm and the driven 450 mm; belt speed is 11.8 m/s and ideal tension ≈ 424 N at 5 kW.

Why It Matters

Getting pulley diameters right sets the speed ratio and belt speed in one step. Wrong diameters mean the wrong output speed or a belt running too fast/slow — shortening life or losing power. The tension estimate flags whether the drive is heavily loaded.

Professional Interpretation

Round D₁/D₂ to standard pulley sizes, then re-check v. Confirm wrap and tension with the belt-length calculator and apply a service factor (≈1.2–1.6). Keep D₁ above the belt-section minimum.

Ratio

3 : 1

Belt speed

11.8 m/s

Recommendations

  • •Belt speed is reasonable.
  • •Round to standard pulley sizes.
  • •Check wrap with the belt-length calculator.
  • •Apply a service factor to tension.
  • •Keep driver above belt-section min diameter.

Educational Content

Introduction

A belt drive’s output speed is set entirely by pulley diameters. This calculator sizes those diameters either from a desired speed ratio or from a target belt speed, and reports the resulting belt speed and an ideal tension estimate — the essentials for a first-cut belt-drive design.

Concept Explanation

Open-belt ratio i = n₁/n₂ = D₂/D₁. Belt speed v = π·D·n/60 (m/s, D in m). Ratio mode: D₂ = D₁·i. Speed mode: D₁ = 60 000·v/(π·n₁) (D in mm), D₂ = D₁·i. Ideal tension F = P/v. Real designs add centrifugal/slack terms, a service factor and a wrap check.

Applications

▸Motor-to-machine drives
▸Fans and blowers
▸Pumps
▸Conveyors
▸HVAC
▸Workshop machinery

Benefits

  • •Exact ratio sizing
  • •Belt-speed control
  • •Tension estimate
  • •Ratio & speed modes
  • •SI/imperial units

Limitations

  • •No wrap check
  • •Ideal tension
  • •No rating
  • •Open belts only
  • •Single stage

Best Practices

  • •Round to standard sizes
  • •5–25 m/s belt speed
  • •Service factor on tension
  • •Check wrap separately
  • •Min diameter per section

Common Misconceptions

Myth: Diameter does not set speed.
Truth: n₂/n₁ = D₁/D₂ exactly (open belt).
Myth: Tension = P/v exactly.
Truth: It is an ideal estimate; add slack/centrifugal + SF.
Myth: Any speed is fine.
Truth: Belt life depends on v range.
Myth: Outside diameter matters.
Truth: Use pitch diameter for ratio.

Practical Tips

  • •D₁=150 mm, D₂=450 mm.
  • •Ratio 3:1
  • •Round to standard pulley sizes.
  • •Aim belt speed 5–25 m/s.
  • •Check wrap with belt-length calculator.

Common Mistakes

Wrong output speed
Use D₂ = D₁·(n₁/n₂).
Belt too fast
Increase D₁ or reduce n₁.
Tension ignored
Apply F=P/v + service factor.
Outside diameter used
Use pitch diameter.
No wrap check
Run belt-length calculator.

Assumptions

This calculator makes the following assumptions to provide estimates:

Open belt: Same direction.
Pitch dia: Not outside.
Ideal tension: F = P/v.
No slip: Design intent.
One unit: mm or in.

Limitations

Be aware of these limitations when using this calculator:

No wrap: Separate tool.
Ideal tension: Estimate.
No rating: Catalogue.
Single stage: No compound.

Frequently Asked Questions

Answers to common questions about this calculator.

What is a pulley diameter calculator for?
It sizes pulley diameters so a belt drive delivers the speed ratio you want, or so the belt runs at a target surface speed — and it reports the resulting belt speed and tension.
What is the speed ratio relation?
For an open belt, i = n₁/n₂ = D₂/D₁, where n is rpm and D pitch diameter. The driven pulley is larger for a speed reduction.
How is belt speed found?
v = π·D·n/60 (m/s) with D in metres. In mm: v = π·D·n/60 000. It is the same on both pulleys.
How do I size D₂ from a ratio?
D₂ = D₁·(n₁/n₂) = D₁·i. Pick the driver diameter D₁, multiply by the ratio.
How do I size for a target belt speed?
D₁ = 60 000·v/(π·n₁) (mm), then D₂ = D₁·(n₁/n₂). v in m/s.
What belt speed is reasonable?
For flat/V belts roughly 5–25 m/s; timing belts up to 30–60 m/s. Stay within the belt series rating.
What is belt tension from power?
Approximate ideal tension F = P/v (N) with P in watts and v in m/s. Real designs add slack/centrifugal effects and a service factor.
What is pitch diameter vs outside diameter?
Use pitch diameter for speed relations; outside diameter is larger by roughly 2× belt thickness (belts) or the tooth addendum (timing).
Can I use inches?
Yes — toggle Imperial; diameters convert at 25.4 mm/in and speed to ft/min.
What about wrap angle?
θ₁ = 180° − 2·asin((D₂−D₁)/(2C)); you need a centre distance for wrap, which this tool does not size. Check it on a belt-length calculator.
What if D₂ is huge?
Very large ratios need multiple stages or a different drive (gear/chain). Single belts are practical up to ~4–6:1.
What is the minimum pulley diameter?
Set by the belt section (smaller bends reduce belt life); follow the belt maker’s minimum.
How does diameter affect life?
Larger pulleys reduce belt bending stress and extend life; smaller pulleys raise it.
What is the difference from a gear ratio?
Same ratio concept, but belts can slip and need wrap/tension; gears are positive.
When do I use this vs chain?
Pulleys/belts for quiet, low-maintenance, shock-absorbing; chain for no-slip high torque.
What about compound drives?
Stack two stages; overall ratio is the product of stage ratios (and diameters).
How accurate is the sizing?
Exact for ideal geometry; real belts need standard diameters, tension and wrap checks.
What standards apply?
ISO 4184 / 5290 (V-belts), ISO 5296 (timing), plus manufacturer catalogues.
What is a step pulley?
A pulley with several diameters to give discrete speed steps on the same centre.
What is a variable-pitch pulley?
Sheaves whose effective diameter changes (e.g., CVT) to vary ratio continuously.
How do I read "D₂/D₁"?
It is the diameter ratio and equals the speed ratio n₁/n₂ — bigger driven pulley = slower output.
What is the effect of n₁?
Higher driver rpm lets you use a smaller driver diameter for the same belt speed.
What is the recommended driver size?
As large as space allows for belt life; never below the belt-section minimum.
How do I verify?
Recompute belt speed with the result: v = π·D₁·n₁/60 000 and confirm it matches the target or is in range.
What if the result is non-standard?
Round to a catalogue pulley size, then re-check speed/tension; small changes are usually fine.
What about torque?
T₁ = 9549·P/n₁ (N·m); the belt transmits torque via tension difference. F≈P/v is the mean tension estimate.
Does belt type change the formula?
The diameter/speed relations are the same; only pitch diameter definition and ratings differ.
What is backlash in belts?
Belts can slip under overload; timing belts do not (toothed). Keep loads within rating.
Can this size a pulley for a fan?
Yes — set target belt speed for the desired fan rpm given motor speed, or set ratio from the two rpms.
Explore the full collection:

Related Calculators

Explore more calculators related to this topic.

Next Logical Steps

Explore more calculators related to this topic.

Related Guides

Deepen your understanding with these educational resources.

Glossary

Technical terms used in mortgage calculations explained in plain language.

Pitch Dia D
Speed-setting diameter.
Ratio i
n₁/n₂ = D₂/D₁.
Belt Speed v
π·D·n/60.
Belt Tension F
P/v.
Open Belt
Same rotation.

Authoritative References

Trusted sources and standards referenced by this calculator.

Applicable Standards

ISO 4184ISO 5290ISO 5296RMA IP-20/25

Was This Calculator Helpful?

Page Information

Last Updated:

August 2026

Version:

2.1.0

License:

Free to use for educational and professional purposes.