August 2026 13 min read

Timing Belt Calculator

Free timing belt calculator. Compute synchronous belt pitch length, the nearest whole number of belt teeth, pulley pitch diameters (D = p·z/π), speed ratio, belt speed and wrap angle for MXL/XL/L/H/T5/T10/AT-series belts.

Timing Belt Calculator

Timing Belt Inputs

Unit System

SI — mm Imperial — in

Belt Pitch / Series

Sets tooth pitch

Teeth z₁ (driver)

Small pulley

Teeth z₂ (driven)

Large pulley

Centre Distance C (mm)

Axis-to-axis

Driver Speed n (rpm)

Auto-calculate instantly

Belt Length

685.80mm

72 teeth @ 9.525 mm pitch

Wrap is good (≥120°).

Belt Teeth N

Pulley D (z₁)

60.64mm

Pulley d (z₂)

121.28mm

Speed Ratio

2:1

Belt Speed

3.18m/s

Wrap (small)

162.6°

Belt Teeth N

Whole teeth

Pulley D (z₁)

60.64mm

p·z₁/π

Pulley d (z₂)

121.28mm

p·z₂/π

Speed Ratio

2:1

z₂/z₁

Belt Speed

3.18m/s

π·D·n/60

Wrap (small)

162.6°

Load sharing

Result Summary

Pitch	9.525 mm
Teeth z₁ / z₂	20 / 40
Pulley D	60.64 mm
Pulley d	121.28 mm
Centre C	200 mm
Belt Length	685.80 mm
Belt Teeth N	72
Speed Ratio	2 : 1
Belt Speed	3.18 m/s
Wrap (small)	162.6°

Estimated Result — Uses D = p·z/π for pulley pitch diameters and the open-belt length L = 2C + π(D+d)/2 + (d−D)²/(4C), then rounds to the integer tooth count N = round(L/p) with L = N·p. Speed ratio i = z₂/z₁, belt speed v = π·D·n/60, and small-pulley wrap θ_s = 180° − 2·asin((d−D)/(2C)). For the width/torque rating, consult the manufacturer capacity tables.

Interactive Diagram

Synchronous teeth mesh with the pulleys for an exact, slip-free ratio.

Visualizations

Belt Length Breakdown

400mm2C

285.8mmπ(D+d)/2

4.6mm(d−D)²/4C

Small-Pulley Wrap

θ_s163°

Formula

A timing (synchronous) belt has teeth that mesh with matching pulley grooves, giving a fixed, slip-free ratio. Each pulley’s pitch diameter is set by the tooth count and pitch: D = p·z/π. The belt length is the open-belt geometric length, but a real belt must have an integer number of teeth, so we round L/p to the nearest whole tooth count and multiply back.

D = p·z₁/π , L = round( (2C + π(D+d)/2 + (d−D)²/(4C)) / p ) · p

Alternative Form

i = z₂/z₁ , v = π·D·n/60 , θ_s = 180° − 2·asin((d−D)/(2C))

Variables

Symbol	Name	Unit	Description
p	Pitch	mm	Tooth spacing
z₁, z₂	Teeth		Per pulley
D, d	Pitch dia	mm	p·z/π
C	Centre	mm	Axis-to-axis
N	Belt teeth		Whole number
i	Ratio	:1	z₂/z₁
v	Belt speed	m/s	π·D·n/60

Explanation

Because teeth lock, the ratio is exactly z₂/z₁ with no slip. Pulley diameters follow from the pitch and tooth count; the belt length is rounded to the nearest integer tooth count (standard belts come in fixed tooth numbers). Belt speed comes from the driver pulley; wrap on the small pulley governs how many teeth share the load — keep it high for even wear.

Derivation

D = p·z₁/π, d = p·z₂/π. L_geo = 2C + π(D+d)/2 + (d−D)²/(4C). N = round(L_geo/p), L = N·p. i = z₂/z₁ = d/D. v = π·D·n/60 (m/s). θ_s = 180° − 2·asin((d−D)/(2C)). Tooth engagement: belt speed v = pitch·N·n/(60·z₁) matches π·D·n/60.

Step-by-Step Calculation

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

Step 1

Pitch diameters.

D = p·z₁/π , d = p·z₂/π

p:9.525

z₁:20

z₂:40

Intermediate: D = 9.525·20/π = 60.64; d = 9.525·40/π = 121.3

Result: D=60.64, d=121.28 mm

Step 2

Geometric belt length then nearest tooth count.

L = 2C + π(D+d)/2 + (d−D)²/(4C); N = round(L/p)

Intermediate: L_geo=690.3, N≈72, L=N·p

Result: 685.80 mm

Step 3

Speed ratio.

i = z₂/z₁

Intermediate: i = 40/20

Result: 2 : 1

Step 4

Belt speed & wrap.

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

n:1000 rpm

Intermediate: v=3.18 m/s; θ_s=162.6°

Result: v=3.18 m/s

Final Answer

685.80 mm (72 teeth)

Worked Examples

See how the calculator works with different scenarios.

Scenario

L pitch, z₁=20, z₂=40, C=200, n=1000.

Inputs

pitch:L

z1:20

z2:40

C:200

n:1000

Calculation

D=9.525·20/π=60.66; d=9.525·40/π=121.31; L_geo=400+π·181/2+60.65²/800=400+284.2+4.6=689 mm; N=round(689/9.525)=72; v=π·60.66·1000/60000=3.18 m/s

Result

L≈689 mm, 72 teeth

Interpretation

2:1 ratio drive.

Understanding Your Result

Your Result: 685.80 mm

Typical range: Keep small-pulley wrap ≥120° (yours 163°) and belt speed within the series rating. Standard belts come in fixed tooth counts — pick the nearest N (72).

What This Means

A L timing belt with z₁=20, z₂=40, C=200 mm gives D=60.6 mm, d=121.3 mm, a 72-tooth belt (L=685.8 mm), 2:1 ratio, 3.2 m/s, 163° wrap.

Why It Matters

Timing belts give exact, slip-free motion for indexing, conveyors and engine drives. Choosing the right number of teeth and keeping good wrap avoids tooth jump and uneven wear; the geometry must be exact because the belt length is fixed to a tooth count.

Professional Interpretation

Select a standard L belt with N = 72 teeth (or the nearest catalogued value), choose width for the torque from the maker’s rating, and verify ≥6 teeth in mesh. Keep C ≈ 1.5–3× d and add an idler on the slack side if needed.

Belt length

685.8 mm

Belt teeth

Ratio

2 : 1

Recommendations

•Wrap is acceptable.
•Pick the nearest standard belt tooth count.
•Choose width from the torque rating table.
•Keep ≥6 teeth in mesh on the small pulley.
•Confirm ratio is exactly z₂/z₁ (no slip).

Educational Content

Introduction

A timing belt (synchronous belt) transmits motion without slip because its teeth mesh with matching pulley grooves. This calculator returns the pulley diameters, the exact belt length rounded to a whole number of teeth, the exact speed ratio, belt speed and wrap angle for any standard pitch (MXL, XL, L, H, T5, T10, AT, …).

Concept Explanation

Pitch diameter follows from the tooth count: D = p·z/π. Belt length uses the open-belt formula, but a real belt has an integer tooth count, so N = round(L/p) and L = N·p. The speed ratio is exactly z₂/z₁. Belt speed v = π·D·n/60, and the small-pulley wrap θ_s = 180° − 2·asin((d−D)/(2C)) sets how many teeth share load.

Applications

▸CNC and 3D printers

▸Automotive cam drives

▸Conveyors

▸Robotics and automation

▸Packaging machinery

▸Indexing tables

Benefits

•Exact ratio (no slip)
•Whole-tooth length
•Pulley sizing
•Many standards
•SI/imperial units

Limitations

•Geometry only
•No width rating
•No torque rating
•No tension model
•Open belt only

Best Practices

•Keep wrap ≥120°
•≥6 teeth in mesh
•Use nearest standard tooth count
•Size width from torque table
•Idler on slack side

Common Misconceptions

Myth: Timing belts slip.

Truth: They are synchronous; no slip (unless teeth jump under overload).

Myth: Any length works.

Truth: Length must be a whole tooth count.

Myth: Ratio = diameter only.

Truth: Exact ratio z₂/z₁.

Myth: Same as V-belt.

Truth: Toothed, slip-free, needs no high tension.

Practical Tips

•Belt 686 mm, 72 teeth.
•Ratio 2:1
•Pick the nearest standard tooth count.
•Keep wrap ≥120° on small pulley.
•Size width from torque rating.

Common Mistakes

Non-integer teeth

Round L/p to whole N.

Low wrap

Increase C or change teeth.

Width guess

Use torque rating table.

Wrong pitch

Match belt series.

Teeth jump

Wider belt / more wrap / tension.

Assumptions

This calculator makes the following assumptions to provide estimates:

Open belt: Same direction.

Pitch length: Geometric.

Whole teeth: Rounded count.

No slip: Synchronous.

One unit: mm or in.

Limitations

Be aware of these limitations when using this calculator:

Geometry only: No torque rating.

No tension: Ideal.

Open only: No crossed.

Single stage: No compound.

Frequently Asked Questions

Answers to common questions about this calculator.

What is a timing belt?

A synchronous belt with moulded teeth that mesh with matching pulley grooves, giving a fixed, slip-free speed ratio. Used where timing must be exact (engines, CNC, conveyors).

What does this calculator give?

Pulley pitch diameters, belt pitch length, the nearest whole number of belt teeth, speed ratio, belt speed and wrap angle — for a chosen tooth pitch and tooth counts.

What is pitch?

The centre-to-centre distance between adjacent teeth (mm or inch). It defines the belt series (MXL, XL, L, H, T5, T10, etc.).

How is pulley diameter related to teeth?

D = p·z/π, where p is pitch and z the tooth count. Circumference = pitch length over the teeth = π·D, so D = z·p/π.

What is the belt length formula?

Geometric (open belt): L = 2C + π(D+d)/2 + (d−D)²/(4C). Then round L/p to the nearest integer number of teeth: N = round(L/p), and L = N·p.

Why round the tooth count?

A real timing belt has an integer number of teeth, so length must be a whole multiple of pitch. Use the nearest standard belt tooth count.

What is the speed ratio?

i = z2/z1 (or d/D). The driven pulley turns slower by that factor; positive (non-slip) because teeth lock.

What is belt speed?

v = π·D·n/60 (m/s) using the driver pulley D and rpm n. Tooth engagement speed = v.

What is the wrap angle?

θ_s = 180° − 2·asin((d−D)/(2C)) on the small pulley; high wrap (≥120°) is good for load sharing across teeth.

What is backlash?

Small clearance between tooth flanks; allows assembly and thermal growth but permits tiny positional error under reversing loads.

What standards exist?

ISO 5296 (metric MXL/XL/L/H), ISO 9011 (T-series), RMA/MPTA IP-25/26, DIN 7721 (AT).

How do I choose centre distance?

Typically 1.5–3× the larger pulley; enough for wrap and to tension, but not so long the belt whips. Many designs use an adjustable/tensioning idler.

What is belt width vs torque?

Wider belts (more ribs) carry more torque/more teeth in contact; width must match the pulley face and the load.

What is the minimum tooth engagement?

Keep ≥6 teeth in mesh on the smaller pulley for even load distribution; low wrap reduces this.

Glass-fibre vs steel cord?

Steel offers higher stiffness/lower stretch and better positional accuracy; fibre is lighter/cheaper for general use.

What about an idler?

A spring or fixed idler keeps tension and improves wrap; place it on the slack side, never in the teeth-mesh span if avoidable.

Can I compute centre from a known belt?

Yes: N = known belt teeth, solve 8C² + (2π(D+d)−4Np)C + (d−D)² = 0 for the positive root.

What is the max speed?

Well-made timing belts run 30–60 m/s+ for light loads; follow the maker’s rating for the width and pitch.

What is the difference from a V-belt?

Timing belts do not slip (toothed), so ratio is exact; V-belts can slip and need tension/wrap management.

What is the tension?

Set per the catalogue (deflection method). Too loose jumps teeth; too tight overloads bearings. Auto-tensioners help.

What is the tooth profile?

Trapezoidal (MXL/XL/L/H/T) or curvilinear (HTD/STD) which carries higher loads with less stress concentration.

What causes tooth shear/jump?

Overload, shock, or slack causing the belt to ride up teeth; fix with wider belt, more wrap, or tension.

What is pitch line clearance?

The pitch line sits a fixed distance from the belt back; pulley root diameter and clearance follow the standard.

How accurate is the ratio?

Exact to the tooth ratio (no slip), making timing belts ideal for indexing and sync applications.

What maintenance?

Inspect for cracked/ missing teeth and glazing, check tension, keep pulleys aligned and clean; replace as a unit.

When do I use timing vs chain?

Timing belt for quiet, low-maintenance, lube-free sync; chain for very high torque/rough service.

What is the belt weight effect?

At high speed, centrifugal tension reduces capacity; the catalogue rating accounts for it.

How do I convert to inches?

Toggle Imperial; pitches shown in inch equivalents (e.g., L = 0.375").

What is the result text for?

Copy the plain-text block for reports or to paste the calculation into records.

Is this for design or sizing?

It sizes geometry (length, teeth, ratio, speed). For the width/torque rating, consult the manufacturer’s capacity tables.

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Related Guides

Deepen your understanding with these educational resources.

ISO 5296 — Synchronous belts

Dimensions.

Gates — Timing belt manual

Design.

Glossary

Technical terms used in mortgage calculations explained in plain language.

Timing Belt: Synchronous toothed belt.
Pitch p: Tooth spacing.
Teeth z: Per pulley.
Belt Teeth N: Whole number.
Ratio i: z2/z1.
Belt Speed: π·D·n/60.

Authoritative References

Trusted sources and standards referenced by this calculator.

ISO 5296 — Synchronous belt dimensions Gates — Timing belt design manual ContiTech / Synchroflex manuals MPTA — Belt drive standards MIT OpenCourseWare — Mechanical design

Applicable Standards

ISO 5296ISO 9011DIN 7721RMA/MPTA IP-25/26

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Page Information

Last Updated:

August 2026

Version:

2.1.0

References:

License:

Free to use for educational and professional purposes.