August 2026 12 min read

Belt Length Calculator

Free belt length calculator for open belt drives. Compute belt pitch length from pulley diameters and centre distance (L = 2C + π(D+d)/2 + (D−d)²/4C) or solve centre distance from a known belt length, plus ratio, wrap angle and belt speed.

Belt Length Calculator

Belt Drive Inputs

Unit System

SI — mm Imperial — in

Calculation Mode

Choose what to solve for

Large Dia D (mm)

Small Dia d (mm)

Centre Distance C (mm)

Axis-to-axis distance

Pulley Speed n (rpm)

Optional — for belt speed

Auto-calculate instantly

Belt Length

1,277.5mm

Open belt, D=200, d=100.

Wrap angle is healthy (≥120°).

Speed Ratio

2:1

Wrap (small)

165.6°

Belt Speed

15.71m/s

Centre C

400mm

Speed Ratio

2:1

D/d

Wrap (small)

165.6°

Contact arc

Belt Speed

15.71m/s

π·D·n/60

Centre C

400mm

Axis distance

Result Summary

Large Dia D	200 mm
Small Dia d	100 mm
Speed Ratio	2 : 1
Centre Distance	400 mm
Belt Length	1,277.49 mm
Wrap (small)	165.6°
Belt Speed	15.71 m/s

Estimated Result — Uses the exact open-belt length expression L = 2C + π(D+d)/2 + (D−d)²/(4C) and its inverse (solve 8C² + (2π(D+d)−4L)C + (D−d)² = 0 for the positive root). Wrap angle θ_s = 180° − 2·asin((D−d)/(2C)). Belt speed v = π·D·n/60 (m/s with D in m). All lengths must share one unit; the tool converts mm↔in. It gives geometric pitch length, not the supplier take-up allowance.

Interactive Diagram

Open belt: both pulleys turn the same way; length = 2 spans + 2 arcs.

Visualizations

Belt Length Breakdown

800mm2C

471.2mmπ(D+d)/2

6.3mm(D−d)²/4C

Small-Pulley Wrap Angle

θ_s166°

Formula

An open belt wraps two pulleys. Its pitch length is two straight spans (2C) plus the belt arcs over both pulleys. The π(D+d)/2 term is the total arc contribution and (D−d)²/(4C) corrects for the size difference. Inverting the formula (solving the quadratic for C) lets you set the centre distance once you have chosen a standard belt length.

L = 2C + π(D+d)/2 + (D−d)²/(4C)

Alternative Form

θ_s = 180° − 2·asin((D−d)/(2C)) , v = π·D·n/60

Variables

Symbol	Name	Unit	Description
L	Belt length	mm	Pitch length
C	Centre distance	mm	Between axes
D	Large pulley dia	mm	Driver or driven
d	Small pulley dia	mm	Other pulley
θ_s	Wrap angle	°	On small pulley
v	Belt speed	m/s	π·D·n/60

Explanation

Belt length grows linearly with centre distance and the average pulley diameter, with a small extra term when pulleys differ. The wrap angle on the small pulley is what limits grip — keep it high by using a larger centre distance or closer pulley sizes. Belt speed is set only by the driving pulley diameter and its rpm; both pulleys run at that same belt speed.

Derivation

L = 2C + (arc over large) + (arc over small). Arc over large = (π + 2β)D/2, arc over small = (π − 2β)d/2 with β = asin((D−d)/(2C)); summing gives L = 2C + π(D+d)/2 + (D−d)²/(4C). For centre from length: multiply by 4C and rearrange to 8C² + (2π(D+d)−4L)C + (D−d)² = 0; the positive root is the physical centre distance.

Step-by-Step Calculation

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

Step 1

Two straight spans plus the arcs.

L = 2C + π(D+d)/2 + (D−d)²/(4C)

D:200 mm

d:100 mm

C:400 mm

Intermediate: L = 2·400 + π(200+100)/2 + (200−100)²/(4·400)

Result: 1,277.5 mm

Step 2

Speed ratio.

i = D/d

D:200

d:100

Intermediate: i = 200/100

Result: 2 : 1

Step 3

Wrap angle on the small pulley.

θ_s = 180° − 2·asin((D−d)/(2C))

Intermediate: θ_s = 180 − 2·asin((200−100)/(2·400))

Result: 165.6°

Step 4

Belt speed (if rpm given).

v = π·D·n/60

n:1500 rpm

Intermediate: v = π·200·1500/60000

Result: 15.71 m/s

Final Answer

1,277.5 mm

Worked Examples

See how the calculator works with different scenarios.

Scenario

Equal pulleys D=d=200 mm, C=400 mm.

Inputs

D:200

d:200

C:400

Calculation

L = 2·400 + π·400/2 + 0 = 800 + 628.3 = 1428.3 mm; ratio 1; wrap 180°

Result

L = 1428 mm

Interpretation

Equal pulleys give a simple 2C + πD length.

Understanding Your Result

Your Result: 1,277.5 mm

Typical range: Wrap should be ≥120° (ideally ≥150°) on the small pulley; yours is 166°. Centre distance is often 2–5× the large diameter.

What This Means

With D = 200 mm, d = 100 mm, the open belt is 1,277.5 mm long (at C = 400 mm) with a 166° wrap on the small pulley.

Why It Matters

Belts are stocked at standard pitch lengths. You either compute L to order the right belt, or pick a standard belt and back-solve the centre distance so the drive assembles with adjustment. Wrap angle governs grip and life.

Professional Interpretation

Select the nearest standard pitch length (ISO 4184 / RMA), then re-solve C for that belt including take-up. Belt speed ≈ 15.71 m/s; check against the belt’s rated speed and power. Wrap 166° sets the traction limit.

Belt length

1,277.5 mm

Ratio

2 : 1

Wrap

166°

Recommendations

•Wrap angle is acceptable.
•Choose the nearest standard pitch length, then set C to match.
•Allow take-up (adjustment) in the centre distance.
•Keep C between ~2× and ~5× the large diameter.
•For >5:1, use a staged or different drive.

Educational Content

Introduction

Belt drives are everywhere because they are cheap, quiet and absorb shock. This calculator gives the exact open-belt pitch length from the pulley diameters and centre distance — or the reverse — plus the speed ratio, wrap angle and belt speed you need to choose a real belt.

Concept Explanation

Open-belt length L = 2C + π(D+d)/2 + (D−d)²/(4C). The first term is the two straight spans, the second the arcs, the third the size-difference correction. Invert it to get C from a chosen L by solving the quadratic 8C² + (2π(D+d)−4L)C + (D−d)² = 0. Wrap on the small pulley is θ_s = 180° − 2·asin((D−d)/(2C)); belt speed v = π·D·n/60.

Applications

▸Industrial conveyors

▸HVAC and compressor drives

▸Agricultural machinery

▸Workshop equipment

▸Replacement belt sizing

▸Centre-distance layout

Benefits

•Exact open-belt length
•Reverse mode (C from L)
•Wrap angle & speed
•SI/imperial units
•Clear span breakdown

Limitations

•Open belts only
•Ignores belt thickness
•No take-up allowance
•No power rating
•Ideal (no sag/stretch)

Best Practices

•Keep wrap ≥120° on small pulley
•Pick standard pitch length
•Set C from the chosen belt
•Allow adjustment/take-up
•Match C to 2–5× large dia

Common Misconceptions

Myth: L is just 2C + πD.

Truth: Both diameters and the size correction matter.

Myth: Pulleys equal length = 2C+πD.

Truth: True only when D=d (then correction=0).

Myth: Any centre works.

Truth: Centre sets wrap and grip.

Myth: Length = catalogue length.

Truth: Catalogue is pitch length; add take-up.

Practical Tips

•Belt 1,277 mm, ratio 2:1.
•Wrap 166° on small pulley.
•Pick nearest standard pitch length, then set C.
•Bigger centre distance → more wrap.
•Use V-belt calculator for section/speed detail.

Common Mistakes

Wrong mode input

Length mode needs C; centre mode needs L.

Low wrap

Increase C or reduce D−d.

Forgetting take-up

Add supplier allowance to centre.

Mixed units

Keep all lengths in mm or in.

Using catalogue length as L

Catalogue = pitch length; matches this formula.

Assumptions

This calculator makes the following assumptions to provide estimates:

Open belt: Same-direction rotation.

Pitch length: Geometric, no take-up.

One unit: mm or in consistently.

Negligible sag: Ideal straight spans.

No thickness: Thin belt assumption.

Limitations

Be aware of these limitations when using this calculator:

No power rating: Geometry only.

No take-up: Add installation allowance.

Open only: Crossed belts differ.

No slip: Ideal traction.

Frequently Asked Questions

Answers to common questions about this calculator.

What is an open belt drive?

An open belt connects two pulleys so they rotate in the same direction; the belt runs straight between them with the length set by pulley diameters and centre distance.

What is the belt length formula?

For an open belt: L = 2C + π(D+d)/2 + (D−d)²/(4C), where C is centre distance and D, d the pulley diameters.

Why the (D−d)²/(4C) term?

It corrects for the belt slack/extra length caused by the different pulley sizes; it vanishes when D = d and grows as the pulleys differ.

How do I get centre distance from belt length?

Solve the implicit formula for C: 8C² + (2π(D+d) − 4L)C + (D−d)² = 0 and keep the positive root.

What is the belt speed?

v = π·D·n/60 (m/s with D in m), where n is the pulley speed in rpm. Both pulleys share the same belt speed.

What is the speed ratio?

i = D/d (or n_small/n_large) for an open belt — the larger pulley turns slower.

What is the wrap (contact) angle?

On the small pulley: θ_s = 180° − 2·asin((D−d)/(2C)); more wrap means more grip. Keep it well above the minimum for the belt type.

What is a crossed belt?

A crossed belt makes the pulleys rotate in opposite directions and has a slightly different (longer) length formula; this calculator is for open belts.

What units can I use?

Millimetres (SI) or inches (imperial); belt speed is m/s or ft/min. The formula is unit-agnostic as long as all lengths share the unit.

How accurate is the formula?

It is the standard exact open-belt expression; results are accurate to < 0.1% for normal C/D ratios. Very short centres relative to diameter need care.

What is a typical centre distance?

Usually 2–5× the large pulley diameter for good wrap and tension; too short reduces wrap, too long needs a tensioner.

When do I need a tensioner?

Long centres, pulsating loads, or when the belt cannot be tightened by moving pulleys; a tensioner keeps the right sag/tension.

What is belt sag?

The natural dip between spans; too much sag slips, too little over-tensions. Belt type sets the target sag/tension.

What is the minimum pulley diameter?

Set by belt section and supplier data; too small bends the belt sharply and cuts life.

How does pulley size affect length?

Larger diameters increase π(D+d)/2 directly and slightly change the correction term; length scales roughly with the average diameter.

What is the difference between belt length and pitch length?

Pitch length is measured at the belt’s neutral (pitch) line; the catalogue length is pitch length, which is what the formula gives.

Can I use this for V-belts?

The geometry is the same; V-belts just add a wedge grip. Use the V-belt calculator for wrap/speed detail.

Can I use this for timing belts?

Timing belts use a pitch-based tooth count; use the timing-belt calculator for those.

What if the pulleys are equal?

Then L = 2C + πD and wrap is exactly 180° on both — the correction term is zero.

Why does belt length matter?

Belts are made to standard pitch lengths; you pick the catalogue belt whose pitch length matches (or set C from the chosen belt).

How do I set centre distance in practice?

Compute L, choose the nearest standard belt, then solve C from that L so the belt fits with adjustment.

What is belt tension?

The force in the belt; too low slips, too high wears bearings. Tension comes from power, speed and the arc of contact.

What about belt efficiency?

Open belts are ~94–98% efficient; see the gear/chain efficiency tools for comparisons.

What is slip?

A flat/V belt can slip under overload; timing belts do not (they are positive drive).

How do I convert mm to inches?

1 inch = 25.4 mm; the unit toggle handles it automatically.

What is the max speed ratio?

Open belts comfortably handle 3:1 to 5:1; beyond that use multiple stages or a different drive.

Does the calculator include stretch?

No — it gives geometric pitch length; add the supplier’s take-up allowance for installation.

What standards apply?

ISO 4184 / RMA (IP-20/22) for belt lengths and pulley dimensions.

Can I size a belt from power here?

This tool sizes geometry (length/centre). Power rating needs belt section and speed data.

What if I get no result?

Enter positive diameters and either a centre distance (length mode) or a belt length (centre mode); ensure the quadratic has a real root.

How do I verify the answer?

Recompute with the other mode: set C from L then check L matches, or vice versa.

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Related Guides

Deepen your understanding with these educational resources.

ISO 4184 — Belt lengths

Standard belt lengths.

Gates — Belt drive design

Drive selection guide.

Glossary

Technical terms used in mortgage calculations explained in plain language.

Belt Length (L): Pitch length of the belt.
Centre Distance (C): Distance between pulley axes.
Wrap Angle: Contact arc on a pulley.
Pitch Length: Length at the belt neutral line.
Speed Ratio: D/d of the pulleys.
Belt Speed: π·D·n/60 (m/s).

Authoritative References

Trusted sources and standards referenced by this calculator.

ISO 4184 — Belt drives (lengths) Gates — Belt drive design MIT OpenCourseWare — Mechanical design NIBL / PSG — Design data Belt drive reference (Engineering Toolbox)

Applicable Standards

ISO 4184RMA IP-20/22ISO 5290 (V-belt)DIN 2218

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Page Information

Last Updated:

August 2026

Version:

2.1.0

References:

License:

Free to use for educational and professional purposes.