August 2026 13 min read

Chain Drive Calculator

Free chain drive calculator. Compute sprocket pitch diameters (d = p/sin(π/N)), speed ratio, driven speed, chain speed, chain length in pitches, wrap angle and tensile chain force for a given power. Real roller-chain geometry.

Chain Drive Calculator

Chain Drive Inputs

Unit System

SI — mm Imperial — in

Chain Pitch / Series

Sets link spacing

Teeth N₁ (driver)

Small sprocket

Teeth N₂ (driven)

Large sprocket

Centre Distance C (mm)

Axis-to-axis

Driver Speed n₁ (rpm)

Power (kW)

Power Unit

kW hp

Auto-calculate instantly

Chain Length

1,549.6mm

81.3 pitches

Wrap is good (≥120°).

Speed Ratio

2:1

Driven Speed

500rpm

Chain Speed

6.03m/s

Pitch Dia d₁

115.74mm

Pitch Dia d₂

230.69mm

Wrap (small)

166.8°

Chain Force

825N

Chain Tension

0.83kN

Speed Ratio

2:1

N₂/N₁

Driven Speed

500rpm

n₁/ratio

Chain Speed

6.03m/s

N₁·p·n₁/60000

Pitch Dia d₁

115.74mm

p/sin(π/N₁)

Pitch Dia d₂

230.69mm

p/sin(π/N₂)

Wrap (small)

166.8°

Load sharing

Chain Force

825N

2·T/d₁

Chain Tension

0.83kN

From power

Result Summary

Pitch	19.050 mm
Teeth N₁ / N₂	19 / 38
Centre C	500 mm
Driver n₁	1000 rpm
Pitch Dia d₁	115.74 mm
Pitch Dia d₂	230.69 mm
Chain Length	1,549.6 mm
Speed Ratio	2 : 1
Chain Speed	6.03 m/s
Power	5 kW
Chain Tensile F	825 N

Estimated Result — Uses exact roller-chain geometry: pitch diameter d = p/sin(π/N), speed ratio i = N₂/N₁ (no slip), chain speed v = N₁·p·n₁/(60·1000), length in pitches Lp = 2C/p + (N₁+N₂)/2 + ((N₂−N₁)/(2π))²·(p/C) with L = Lp·p, and small-sprocket wrap θ₁ = 180° − 2·asin((d₂−d₁)/(2C)). Tensile force F = 2·T₁/d₁ with T₁ = 9549·P/n₁. Efficiency ≈96–98%; confirm rating against the chain maker’s tables.

Interactive Diagram

The chain meshes positively with both sprockets — exact ratio, no slip.

Visualizations

Chain Length Breakdown

1,000mm2C

542.9mm(N₁+N₂)p/2

6.6mmCorrection

Small-Sprocket Wrap

θ₁167°

Formula

A roller chain drives two sprockets positively. Each sprocket’s pitch diameter follows from the pitch and tooth count: d = p/sin(π/N). The speed ratio is exactly the tooth ratio (no slip). Chain length is found in pitches from the centre distance, then multiplied by pitch; the small-sprocket wrap governs how many teeth share the load. The tensile force comes from the driver torque and pitch diameter.

d = p/sin(π/N) , Lp = 2C/p + (N₁+N₂)/2 + ((N₂−N₁)/(2π))²·(p/C)

Alternative Form

i = N₂/N₁ , v = N₁·p·n₁/(60·1000) , F = 2·T₁/d₁

Variables

Symbol	Name	Unit	Description
p	Pitch	mm	Link spacing
N₁, N₂	Teeth		Driver / driven
d₁, d₂	Pitch dia	mm	p/sin(π/N)
C	Centre	mm	Axis-to-axis
n₁	Driver speed	rpm	Input
i	Ratio	:1	N₂/N₁
v	Chain speed	m/s	N₁·p·n₁/60000
F	Chain force	N	2·T₁/d₁

Explanation

Because the chain engages teeth, the ratio is exact and there is no slip. Pitch diameters set the geometry; chain speed is set by the driver. The wrap angle on the small sprocket should stay high (≥120°) so load is shared; chain tensile force follows from power and pitch diameter and is the basis for selecting an appropriately rated chain.

Derivation

d = p/sin(π/N). i = N₂/N₁, n₂ = n₁/i. v = N₁·p·n₁/(60·1000) (m/s). Lp = 2C/p + (N₁+N₂)/2 + ((N₂−N₁)/(2π))²·(p/C); L = Lp·p. θ₁ = 180° − 2·asin((d₂−d₁)/(2C)). T₁ = 9549·P/n₁ (N·m, P kW); F = 2·T₁/d₁ (N, d₁ m).

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)

p:19.050

N₁:19

N₂:38

Intermediate: d₁=115.7; d₂=230.7

Result: d₁=115.74, d₂=230.69 mm

Step 2

Speed ratio and driven speed.

i = N₂/N₁ ; n₂ = n₁/i

n₁:1000

Intermediate: i=2; n₂=500

Result: 2 : 1

Step 3

Chain speed.

v = N₁·p·n₁/(60·1000)

Intermediate: v = 19·19.05·1000/60000

Result: 6.03 m/s

Step 4

Chain length in pitches then length.

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

Intermediate: Lp=81.34; L=1,550

Result: 1,549.6 mm

Step 5

Chain tensile force from power.

T₁ = 9549·P/n₁ ; F = 2·T₁/d₁

P:5 kW

Intermediate: T₁=47.7 N·m; F=825 N

Result: 825 N

Final Answer

1,549.6 mm (81.3 pitches)

Worked Examples

See how the calculator works with different scenarios.

Scenario

ISO 12A, N₁=19, N₂=38, C=500, n₁=1000, P=5 kW.

Inputs

pitch:60

N1:19

N2:38

C:500

n1:1000

P:5

Calculation

d₁=19.05/sin(π/19)=121.2; d₂=19.05/sin(π/38)=242.4; i=2; n₂=500; v=19·19.05·1000/60000=6.03 m/s; Lp=1000/19.05+28.5+1=81.0; L=1543 mm; T₁=47.7; F=787 N

Result

L≈1543 mm, i=2

Interpretation

2:1 reduction, 6 m/s chain.

Understanding Your Result

Your Result: 1,549.6 mm

Typical range: Keep small-sprocket wrap ≥120° (yours 167°) and chain speed within the series rating. Choose an even pitch count near 81. Driver force 825 N.

What This Means

A ANSI chain with N₁=19, N₂=38, C=500 mm gives d₁=115.7 mm, d₂=230.7 mm, a 81-pitch chain (L=1,550 mm), 2:1 ratio, 6.0 m/s, 167° wrap, and 825 N tensile force at 5 kW.

Why It Matters

Chain drives move real power with no slip. Correct length and wrap prevent jumping and uneven wear; the tensile force tells you whether the chain is rated for the load. The geometry must be exact because the chain has a fixed pitch count.

Professional Interpretation

Select a chain whose rated working load exceeds 825 N with a service factor (typically 1.2–1.5). Use an even pitch count near 81, keep driver ≥17 teeth, and verify lubrication/speed limits from the maker’s catalogue.

Chain length

1,550 mm

Pitches

Tensile F

825 N

Recommendations

•Wrap is acceptable.
•Use a whole (preferably even) number of pitches.
•Confirm chain rating vs tensile force + service factor.
•Keep driver sprocket ≥17 teeth for life.
•Set slack-side sag ~2–3% of span.

Educational Content

Introduction

A chain drive transmits power between two sprockets through a roller chain. This calculator returns the exact pitch diameters, the no-slip speed ratio, chain speed, chain length (in pitches and length), the small-sprocket wrap angle and the tensile chain force for your power — the full picture for a chain drive design.

Concept Explanation

Pitch diameter is set by tooth count: d = p/sin(π/N). The ratio is exactly N₂/N₁. Chain length uses the pitch formula Lp = 2C/p + (N₁+N₂)/2 + ((N₂−N₁)/(2π))²·(p/C), then L = Lp·p. Chain speed v = N₁·p·n₁/(60·1000). The small-sprocket wrap θ₁ = 180° − 2·asin((d₂−d₁)/(2C)) sets load sharing. Tensile force F = 2·T₁/d₁ with T₁ = 9549·P/n₁.

Applications

▸Motorcycles & bicycles

▸Industrial conveyors

▸Agriculture machinery

▸Automotive timing

▸Lifting equipment

▸Power transmission

Benefits

•Exact ratio (no slip)
•High load capacity
•Long centre distances
•Durable & efficient
•SI/imperial units

Limitations

•Geometry only
•No rating table
•No wear model
•Ideal tension
•Open layout only

Best Practices

•Keep wrap ≥120°
•Even pitch count
•Driver ≥17 teeth
•Rate vs force + SF
•Proper lubrication

Common Misconceptions

Myth: Chains slip.

Truth: Positive engagement — no slip (unless jumping teeth).

Myth: Any length works.

Truth: Length is a whole number of pitches.

Myth: d = p·N/π always.

Truth: Exact is p/sin(π/N); the ratio is an approximation.

Myth: Force is small.

Truth: It scales with torque and shrinks with diameter.

Practical Tips

•Chain 1,550 mm, 81 pitches.
•Ratio 2:1, 6.0 m/s
•Use an even number of pitches.
•Keep wrap ≥120° on small sprocket.
•Rate chain vs tensile force + service factor.

Common Mistakes

Non-integer pitches

Round Lp to nearest whole (even) count.

Low wrap

Increase C or change teeth.

Wrong diameter

Use d = p/sin(π/N), not p·N/π for few teeth.

Underrated chain

Compare force to rated working load + SF.

Over-tension

Allow ~2–3% slack-side sag.

Assumptions

This calculator makes the following assumptions to provide estimates:

Roller chain: Standard pitch geometry.

Open drive: Same direction.

Whole pitches: Rounded count.

Ideal tension: No slack loss.

One unit: mm or in.

Limitations

Be aware of these limitations when using this calculator:

Geometry only: No rating.

No wear: Ideal.

Open only: No crossed.

Single stage: No compound.

Frequently Asked Questions

Answers to common questions about this calculator.

What is a chain drive?

A chain drive transmits power between two sprockets through a roller or bush chain. It is positive (no slip), efficient, and handles high loads and long centre distances.

What does this calculator give?

Sprocket pitch diameters, speed ratio, driven speed, chain speed, chain length (in pitches and length), wrap angle on the small sprocket, and the tensile chain force for a given power.

How is pitch diameter found from teeth?

d = p / sin(π/N), where p is pitch and N the tooth count. For many teeth this is close to d ≈ p·N/π.

What is the speed ratio?

i = N2/N1 = n1/n2. The driven sprocket turns slower by the tooth ratio; it is exact (no slip).

How is chain speed calculated?

v = N1·p·n1 / (60·1000) m/s — the chain advances one pitch per tooth engaged, times teeth and rpm.

What is the chain length formula?

In pitches: Lp = 2C/p + (N1+N2)/2 + ((N2−N1)/(2π))²·(p/C). Multiply by pitch for length: L = Lp·p.

Why the correction term?

((N2−N1)/(2π))²·(p/C) corrects length for unequal sprockets; it is zero for equal sprockets.

What is the wrap angle?

On the small sprocket θ₁ = 180° − 2·asin((d2−d1)/(2C)). More wrap (toward 180°) shares load over more teeth.

What is the chain tensile force?

F = 2·T1/d1, where T1 is the driver torque and d1 the driver pitch diameter. It is the main tensile load in the chain.

How do I get torque?

T1 = 9549·P/n1 (N·m), with P in kW and n1 in rpm.

What efficiency should I assume?

Well-lubricated roller chains are about 96–98% per stage; allow ~2–4% loss in power-transmission estimates.

What is centre distance?

The span C between sprocket axes; it sets chain length and wrap. Typical C ≈ 30–50× pitch, up to ~80× for fixed centres.

How do I choose the number of pitches?

Use an even whole number of pitches; the preferred (even) count lets the chain run in the same orientation each time.

What is the minimum sprocket size?

Smaller sprockets increase tooth load and wear; keep the driver ≥ 17 teeth (≥19–21 for smooth, long life).

What is the maximum speed?

Chains run up to ~20–30 m/s for quality drives; high speed needs precision chains and good lubrication.

What causes chain failure?

Wear (elongation), fatigue of plates/rollers, shock overload, poor lubrication, and misalignment. Inspect regularly.

What is chain stretch?

Roller chains elongate by bushing/pin wear, not elastic stretch; replace at ~1.5–3% elongation per the maker.

When do I use chain vs belt?

Chain for no-slip, high torque, long life, dirty/rough service; belts for quiet, shock-absorbing, low-maintenance, precise-speed-not-critical.

What about an idler?

A slack-side idler maintains tension and improves wrap; never put it on the tight side or in the loaded span.

What standards cover chains?

ISO 606 (roller chains), ANSI/ASME B29.1 (roller), ISO 1275 (leaf), DIN 8187/8188.

How do I set tension?

Allow a small sag (~2–3% of span) on the slack side; over-tension overloads shafts and wears faster.

What is the preferred length?

An even number of pitches so you can join the chain without an offset link; odd counts need a cranked link.

What is a duplex/triplex chain?

Multiple strands side-by-side multiply capacity; they need accurate alignment.

How does load share across strands?

Imperfectly; derating applies (≈1.7× for duplex, ≈2.5× for triplex of single-strand capacity).

What lubrication is needed?

Manual, drip, bath or forced oil depending on speed; proper lube is the single biggest life factor.

What is the silent/leaf chain?

Leaf chains for lifting/hauling; silent (inverted-tooth) chains for smooth, high-speed, low-noise drives.

Can I shorten a chain?

Yes by removing an even number of pitches with a chain breaker and rejoining with a master link.

What is the safety factor?

Choose working load well below rated; typical design factors 5–10× for shock/peak loads.

How accurate are these results?

Geometry and kinematics are exact; the tensile force is a first estimate — confirm rating against the chain maker’s tables.

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Related Guides

Deepen your understanding with these educational resources.

ISO 606 — Roller chains

Dimensions.

SKF — Chain drive design

Selection.

Glossary

Technical terms used in mortgage calculations explained in plain language.

Pitch p: Link-to-link spacing.
Teeth N: Per sprocket.
Pitch Dia d: p/sin(π/N).
Lp: Length in pitches.
Wrap θ₁: Small-sprocket contact.
Chain Force F: 2·T/d.

Authoritative References

Trusted sources and standards referenced by this calculator.

ISO 606 — Roller chains ASME B29.1 — Roller chain Renold / SKF chain manuals MIT OpenCourseWare — Mechanical design Engineering Toolbox — Chain drives

Applicable Standards

ISO 606ANSI/ASME B29.1ISO 1275DIN 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.