August 2026 12 min read

Chain Length Calculator

Free chain length calculator. Compute roller-chain length (in pitches and mm/in) from sprocket teeth and centre distance, or solve for centre distance from a chosen whole number of pitches. Includes the exact wrap-angle check.

Chain Length Calculator

Chain Length Inputs

Unit System

SI — mm Imperial — in

Mode

Length from centre Centre from length

Chain Pitch / Series

Sets link spacing

Teeth N₁ (driver)

Teeth N₂ (driven)

Centre Distance C (mm)

Axis-to-axis

Auto-calculate instantly

Chain Length

1,549.6mm

81.3 pitches

Wrap is good (≥120°).

Pitches Lp

81.3

Pitch p

19.050mm

Pitch Dia d₁

115.74mm

Pitch Dia d₂

230.69mm

Wrap (small)

166.8°

Pitches Lp

81.3

Whole preferred

Pitch p

19.050mm

Link spacing

Pitch Dia d₁

115.74mm

p/sin(π/N₁)

Pitch Dia d₂

230.69mm

p/sin(π/N₂)

Wrap (small)

166.8°

Load sharing

Result Summary

Mode	Length from centre
Pitch	19.050 mm
Teeth N₁ / N₂	19 / 38
Pitches Lp	81.3
Centre C	500 mm
Wrap (small)	166.8°

Estimated Result — Uses the standard roller-chain length formula in pitches Lp = 2C/p + (N₁+N₂)/2 + ((N₂−N₁)/(2π))²·(p/C) with L = Lp·p, and the inverse centre-distance solution C = (p/4)[(2Lp−N₁−N₂)+√((2Lp−N₁−N₂)²−8((N₂−N₁)/(2π))²)]. For layout, round Lp to the nearest even whole number; small-sprocket wrap θ₁ = 180° − 2·asin((d₂−d₁)/(2C)), d = p/sin(π/N).

Interactive Diagram

The chain wraps both sprockets; its length is a whole number of pitches.

Visualizations

Chain Length Breakdown

1,000mm2C

542.9mm(N₁+N₂)p/2

6.6mmCorrection

Small-Sprocket Wrap

θ₁167°

Formula

A roller chain has a fixed pitch, so its length must be a whole number of pitches. From the centre distance C, the pitch count is Lp = 2C/p + (N₁+N₂)/2 + ((N₂−N₁)/(2π))²·(p/C); length is then L = Lp·p. Conversely, if you choose a whole pitch count Lp (preferably even), the required centre distance is the positive root of the rearranged quadratic.

Lp = 2C/p + (N₁+N₂)/2 + ((N₂−N₁)/(2π))²·(p/C) , L = Lp·p

Alternative Form

C = (p/4)[(2Lp−N₁−N₂)+√((2Lp−N₁−N₂)²−8((N₂−N₁)/(2π))²)]

Variables

Symbol	Name	Unit	Description
p	Pitch	mm	Link spacing
N₁, N₂	Teeth		Driver / driven
C	Centre	mm	Axis-to-axis
Lp	Pitches		Whole number
L	Length	mm	Lp·p
θ₁	Wrap	°	Small sprocket

Explanation

The two straight spans contribute 2C, the wrapped arcs contribute (N₁+N₂)/2 pitches, and the unequal-sprocket term corrects for the offset. For design use the length mode and round Lp to an even whole number; for maintenance use the centre mode to find the adjustable centre you must set. Always check the small-sprocket wrap stays ≥120°.

Derivation

Lp = 2C/p + (N₁+N₂)/2 + ((N₂−N₁)/(2π))²·(p/C). Inverted: C = (p/4)[(2Lp−N₁−N₂)+√((2Lp−N₁−N₂)²−8((N₂−N₁)/(2π))²)]. Wrap θ₁ = 180° − 2·asin((d₂−d₁)/(2C)), d = p/sin(π/N). For N₁=N₂: Lp = 2C/p + N, L = 2C + N·p.

Step-by-Step Calculation

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

Step 1

Pitch diameters.

d = p/sin(π/N)

Intermediate: d₁=115.7, d₂=230.7

Result: d₁=115.74, d₂=230.69 mm

Step 2

Length in pitches.

Lp = 2C/p + (N₁+N₂)/2 + ((N₂−N₁)/(2π))²·(p/C)

C:500

Intermediate: Lp = 81.34

Result: 81.34 pitches

Step 3

Chain length.

L = Lp·p

Intermediate: L = 81.34·19.05

Result: 1,549.6 mm

Step 4

Wrap angle.

θ₁ = 180 − 2·asin((d₂−d₁)/(2C))

Intermediate: θ₁ = 166.8°

Result: 166.8°

Final Answer

1,549.6 mm

Worked Examples

See how the calculator works with different scenarios.

Scenario

ISO 12A, N₁=19, N₂=38, C=500 (length mode).

Inputs

pitch:60

N1:19

N2:38

C:500

Calculation

Lp=1000/19.05+28.5+1=81.0; L=1543 mm

Result

L≈1543 mm (81 pitches)

Interpretation

Round to 80 or 82 even.

Understanding Your Result

Your Result: 1,549.6 mm

Typical range: Wrap should be ≥120° (yours 167°). Prefer an even pitch count near 81.

What This Means

With N₁=19, N₂=38 and C=500 mm, the chain is 81 pitches long (L=1,550 mm); round to an even count near this value, giving wrap θ₁=167°.

Why It Matters

Chain length must be exact to the pitch; too short and it will not fit, too long and it needs excessive tension or an idler. This tool removes the guesswork for both new designs (length from C) and service (C from a given chain).

Professional Interpretation

Round Lp to an even whole number and set C accordingly; verify the small-sprocket wrap and allow ~1.5–2% take-up for tension/wear. Confirm sprocket and chain series match (p).

Pitches

Length

1,550 mm

Recommendations

•Wrap is acceptable.
•Use an even number of pitches.
•Allow ~1.5–2% take-up for tension.
•Match chain series to sprocket pitch.
•Check sprocket wear before reuse.

Educational Content

Introduction

Because a roller chain is built from discrete pitches, its length must be an exact whole number of links. This calculator finds that count and the resulting chain length from two sprockets and a centre distance, or works backwards to the centre distance for a chain you already have — with a wrap-angle check.

Concept Explanation

Length in pitches: Lp = 2C/p + (N₁+N₂)/2 + ((N₂−N₁)/(2π))²·(p/C); L = Lp·p. Inverse for centre: C = (p/4)[(2Lp−N₁−N₂)+√((2Lp−N₁−N₂)²−8((N₂−N₁)/(2π))²)]. Choose an even Lp so a standard connecting link joins the chain without an offset link. Wrap on the small sprocket: θ₁ = 180° − 2·asin((d₂−d₁)/(2C)), d = p/sin(π/N).

Applications

▸New drive design

▸Chain replacement

▸Centre adjustment

▸Sprocket selection

▸Maintenance planning

▸Conveyor layout

Benefits

•Exact pitch count
•Centre solve
•Wrap check
•Even-count aid
•SI/imperial units

Limitations

•Geometry only
•No rating
•Ideal tension
•Open layout
•One stage

Best Practices

•Round to even Lp
•Keep wrap ≥120°
•Allow take-up
•Match series
•Verify sprockets

Common Misconceptions

Myth: Any length fits.

Truth: Must be whole pitches; even preferred.

Myth: Length is continuous.

Truth: It is discrete like belt is continuous.

Myth: Wrap never matters.

Truth: Low wrap overloads few teeth.

Myth: C from C is exact.

Truth: Use the positive root only.

Practical Tips

•Chain 81 pitches.
•Round Lp to an even whole number.
•Wrap 167°
•Allow ~1.5–2% take-up.
•Match chain series to sprockets.

Common Mistakes

Odd pitch count

Use even; avoid offset link.

Low wrap

Increase C or change teeth.

Wrong C root

Take the positive (physical) root.

Series mismatch

Match p to sprockets.

No take-up

Allow 1.5–2% adjustment.

Assumptions

This calculator makes the following assumptions to provide estimates:

Roller chain: Standard pitch.

Whole pitches: Rounded count.

Open drive: Same direction.

Ideal geometry: No wear.

One unit: mm or in.

Limitations

Be aware of these limitations when using this calculator:

Geometry only: No rating.

No wear: As-new.

Open only: No crossed.

Single stage: No compound.

Frequently Asked Questions

Answers to common questions about this calculator.

What is the chain length calculator for?

It computes the required roller-chain length (in pitches and in length units) for two sprockets at a given centre distance, or the centre distance for a chosen whole number of pitches.

What is the chain length formula?

In pitches: Lp = 2C/p + (N₁+N₂)/2 + ((N₂−N₁)/(2π))²·(p/C). Length L = Lp·p.

What is Lp?

The chain length expressed as a number of pitches (links). A real chain must have a whole number, preferably even, of pitches.

Can I compute centre distance from length?

Yes. For a chosen whole-pitch count Lp: C = (p/4)[(2Lp − N₁ − N₂) + √((2Lp − N₁ − N₂)² − 8((N₂−N₁)/(2π))²)].

Why prefer an even number of pitches?

An even count lets the chain run in the same orientation each lap and join with a standard connecting link; odd counts need a cranked (offset) link.

What is pitch p?

The centre-to-centre distance between adjacent rollers; it defines the chain series (40=12.7 mm, 50=15.875, 60=19.05, 80=25.4, 100=31.75).

How does pitch diameter relate to teeth?

d = p/sin(π/N). The chain length formula uses teeth and pitch directly, so diameters are not needed.

What is the correction term?

((N₂−N₁)/(2π))²·(p/C) accounts for unequal sprockets; it vanishes when N₁ = N₂.

What centre distance is typical?

Often 30–50× the pitch; short centres need an idler or tensioner, very long spans may need support.

What is chain elongation?

Roller chains grow by bushing/pin wear; replace at ~1.5–3% over nominal length per the maker’s limit.

How much slack/adjustment?

Design C to allow ~1.5–2% take-up; over-tension overloads shafts and wears plates.

What is the wrap angle?

On the small sprocket θ₁ = 180° − 2·asin((d₂−d₁)/(2C)); keep ≥120° for load sharing. d = p/sin(π/N).

What standards apply?

ISO 606 (roller chains), ANSI/ASME B29.1, DIN 8187/8188; preferred length tables appear in catalogues.

What is a master/connecting link?

The link that closes the loop; offset links are used for odd pitches and are weaker.

Can I shorten an existing chain?

Yes — remove an even number of pitches with a chain breaker and rejoin with a master link.

What is the difference from belt length?

Chain length is discrete (whole pitches); belt length is continuous. Both share the 2C + arcs + correction structure.

Why two modes?

Layout (known C → L) is the design case; maintenance (known L → C) finds the adjustable centre you must set.

What about triplex chains?

Length is the same per strand; capacity multiplies with derating. Count pitches per strand.

How do I read the result?

Use the nearest whole (even) pitch count in the length; for centre mode, set C to the positive root shown.

What is the maximum ratio?

Keep single-stage tooth ratios modest (typically ≤4–5:1) for reasonable wrap; beyond that consider compound drives.

Does speed matter for length?

No — length is geometric; speed affects wear and rating, not the required pitch count.

What if my sprockets are equal?

Lp = 2C/p + N (since N₁=N₂=N) and wrap = 180°; simplest case.

What is the torque effect?

Length does not change with torque; but higher torque needs a stronger (or multi-strand) chain, not a longer one.

How do I verify the formula?

Set N₁=N₂=N: Lp = 2C/p + N. Then L = 2C + N·p — exactly two straight spans plus N pitches of arc. Correct.

What lubrication affects length?

Only wear over time; fresh length is geometric. Lubrication extends life, not the as-new length.

Can I use inches?

Yes — toggle Imperial; pitch shown in inch equivalents (40≈0.5", 50≈0.625", 60≈0.75").

What is a broken/chipped link count?

For replacement, count the existing pitches (even preferred) rather than measuring worn length.

What if C is adjustable?

Use the length mode to get Lp, round to even, then the centre mode gives the exact adjustable C.

How accurate is this?

Exact for ideal geometry; real life adds a couple of pitches for tensioning and wear take-up.

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Related Guides

Deepen your understanding with these educational resources.

ISO 606 — Roller chains

Dimensions.

SKF — Chain design

Selection.

Glossary

Technical terms used in mortgage calculations explained in plain language.

Lp: Length in pitches.
Pitch p: Link spacing.
Teeth N: Per sprocket.
Centre C: Axis-to-axis.
Wrap θ₁: Small-sprocket contact.

Authoritative References

Trusted sources and standards referenced by this calculator.

ISO 606 — Roller chains ASME B29.1 — Roller chain SKF / Renold chain manuals Engineering Toolbox — Chain length

Applicable Standards

ISO 606ANSI/ASME B29.1DIN 8187/8188

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Page Information

Last Updated:

August 2026

Version:

2.1.0

References:

License:

Free to use for educational and professional purposes.