Fareed Mohmed · Engineering
Chain Drive Layout Calculator
Sprockets · Length · Sag · Load · Wear
Once you have a chain size, lay the drive out: sprocket diameters, the chain length in links, the true centre distance, the wrap angle, the sag, the chain tension, the load on the shafts and the safety factor. Then measure a chain in service and see how much wear is left.
This tool does the geometry and the loads for a two-sprocket roller chain drive. It does not choose the chain size or check its power rating: use the Chain and Sprocket Selector for that. The design limits are common practice, not catalogue limits, so confirm the layout with your chain maker.
Start Here: Laying Out a Chain Drive
Once you know the chain size, a chain drive still has to be laid out: how big the sprockets are, how long the chain is, how far apart the shafts sit, how much slack the chain needs, what load it puts on the shafts, and when it is worn out. This tool does those steps. It does not choose the chain size: use the Chain and Sprocket Selector for that.
Pick the chain and the sprockets
Choose the chain size, the number of teeth on each sprocket and the speed. The tool gives the pitch, outside and root diameters, the chain speed and the chordal speed variation.
Fill section 01 →Fix the centre distance and the chain length
Enter the centre distance, or the number of links you have. You get an even number of links, the true centre distance, the wrap angle and the teeth in mesh.
See section 02 →Check the tension and the shaft load
Set the service factor, the drive angle and the sag. The tool gives the chain tension, the safety factor and the radial load on the shafts.
See section 03 →Measure wear on a chain in service
Measure a run of pitches with the chain tight. The tool gives the elongation and the limit for your sprockets.
See section 04 →Read the drive check
A table of common design rules tells you what to look at again: tooth counts, ratio, centre distance, wrap and lubrication.
See section 05 →Rate the chain and confirm
This page does the geometry. The chain’s power rating and service factor are in the Chain and Sprocket Selector. Confirm sprocket dimensions with the maker.
Common mistakes
Chain and Sprockets
Choose the chain and the sprockets. The chain data (roller diameter, width, breaking load and mass per metre) come from the Diamond catalogue for the ANSI sizes and the Rexnord catalogue for the ISO B sizes. The speed and power also feed the tension and load results in section 03.
Worked example
A gearbox output delivers 2.2 kW at 200 rpm and drives a conveyor head shaft at 100 rpm. It uses ISO 12B chain (19.05 mm pitch) on a 19-tooth and a 38-tooth sprocket, with 600 mm between the shafts, a service factor of 1.5 and 2 % sag. The chain speed is 1.21 m/s and the pull is 1,818 N. After some months the chain is measured at 384.5 mm over 20 pitches (nominal 381 mm, which is 0.92 % elongation). The button fills all of the sections below.
Don’t know the teeth? Calculate from the speeds
Enter the small sprocket teeth and the two speeds you want. The large sprocket needs z1 × n1 ÷ n2 teeth, rounded to a whole number. The button sends the result to the fields above.
Centre Distance and Chain Length
The chain length in links follows from the centre distance and the two tooth counts. The links must be a whole, even number, so the true centre distance is slightly different from the one you started with. Or work backwards: enter the number of links you have and find the centre distance.
Sag, Tension and Shaft Load
The chain pulls on the shafts with its working pull and also with the tension from its own weight and speed. The slack side needs a little free movement (sag): too little overloads the bearings, too much lets the chain slap and jump. The safety factor compares the peak tension with the chain’s breaking load.
Wear and Replacement
As the pins and bushes wear, each pitch grows longer and the chain gets longer. Measure the chain, tight, over a number of pitches. The chain is worn out when it has stretched by 3 %, or sooner on a drive with a big sprocket: the limit is the lower of 3 % and 200 ÷ the teeth on the large sprocket.
Drive Check
The result of each check against the common design rules for roller chain drives. Anything marked warn or bad is worth looking at again.
Reference Tables
The formulas used, the common design limits, and the chain data loaded.
Formulas
| Quantity | Formula |
|---|---|
| Pitch diameter | D = p ÷ sin(180° ÷ z) |
| Maximum outside diameter | Do = p × (0.6 + cot(180° ÷ z)) |
| Root diameter | Dr = D − d1, where d1 is the roller diameter |
| Caliper over rollers, odd teeth | D × cos(90° ÷ z) − d1 |
| Chain speed | v (m/s) = z × p (mm) × n (rpm) ÷ 60,000 |
| Chordal speed variation | (1 − cos(180° ÷ z)) × 100 % |
| Chain length (pitches) | L = 2C ÷ p + (z1 + z2) ÷ 2 + ((z2 − z1) ÷ 2π)² × p ÷ C |
| Centre distance from links | C = p ÷ 4 × [A + √(A² − 8 × ((z2 − z1) ÷ 2π)²)], with A = L − (z1 + z2) ÷ 2 |
| Wrap angle, small sprocket | 180° − 2 × asin((D2 − D1) ÷ 2C) |
| Working pull | F = P (W) ÷ v |
| Centrifugal tension | Fc = q × v², q in kg/m, v in m/s |
| Slack-side tension | T2 = q × g × C² × cosα ÷ (8 × sag), all in metres |
| Elongation | (measured length ÷ (N × p) − 1) × 100 % |
Common design limits
| Item | Common limit |
|---|---|
| Teeth on the small sprocket | 17 or more; 12 to 16 only at low speed |
| Teeth on the large sprocket | 114 or fewer |
| Speed ratio | 7 : 1 or less on one stage |
| Centre distance | 30 to 50 pitches; not under 20 or over 80 |
| Wrap on the small sprocket | 120° or more; never fewer than 3 teeth in mesh |
| Free movement on the slack side | About 2 % of the centre distance for a horizontal drive |
| Safety factor on breaking load | 8 or more for a smooth drive; below 6 is too low |
| Wear limit | 3 %, or 200 ÷ teeth on the large sprocket if that is lower |
| Links | Even number; avoid an offset link |
Chain data loaded (one strand)
| Chain | Pitch (mm) | Roller dia. (mm) | Inner width (mm) | Breaking load (kN) | Mass (kg/m) |
|---|---|---|---|---|---|
| ANSI 25 | 6.35 | 3.302 | 3.175 | 3.892 | 0.125 |
| ANSI 35 | 9.525 | 5.08 | 4.775 | 9.341 | 0.313 |
| ANSI 40 | 12.7 | 7.925 | 7.95 | 17.793 | 0.61 |
| ANSI 50 | 15.875 | 10.16 | 9.525 | 29.358 | 1.012 |
| ANSI 60 | 19.05 | 11.913 | 12.7 | 37.81 | 1.473 |
| ANSI 80 | 25.4 | 15.875 | 15.875 | 64.499 | 2.575 |
| ANSI 100 | 31.75 | 19.05 | 19.05 | 106.757 | 3.735 |
| ANSI 120 | 38.1 | 22.225 | 25.4 | 151.239 | 5.491 |
| ANSI 140 | 44.45 | 25.4 | 25.4 | 204.617 | 7.441 |
| ANSI 160 | 50.8 | 28.575 | 31.75 | 257.996 | 9.718 |
| ANSI 180 | 57.15 | 35.712 | 35.712 | 338.063 | 13.483 |
| ANSI 200 | 63.5 | 39.675 | 38.1 | 422.579 | 15.849 |
| ANSI 240 | 76.2 | 47.625 | 47.625 | 701.036 | 25.344 |
| ISO 06B | 9.525 | 6.35 | 5.72 | 9.0 | 0.41 |
| ISO 08B | 12.7 | 8.51 | 7.75 | 18.0 | 0.7 |
| ISO 10B | 15.875 | 10.16 | 9.65 | 22.4 | 0.9 |
| ISO 12B | 19.05 | 12.07 | 11.68 | 29.0 | 1.15 |
| ISO 16B | 25.4 | 15.88 | 17.02 | 60.0 | 2.6 |
| ISO 20B | 31.75 | 19.05 | 19.56 | 95.0 | 3.7 |
| ISO 24B | 38.1 | 25.4 | 25.4 | 160.0 | 6.9 |
| ISO 28B | 44.45 | 27.94 | 30.99 | 200.0 | 8.6 |
| ISO 32B | 50.8 | 29.21 | 30.99 | 250.0 | 9.5 |
| ISO 40B | 63.5 | 39.37 | 38.1 | 355.0 | 15.1 |
| ISO 48B | 76.2 | 48.26 | 45.72 | 560.0 | 24.5 |
Explanatory Notes
What this tool is for
The Chain and Sprocket Selector sizes the chain from power, speed and service. This tool takes the chain you chose and works out the geometry, the slack, the load on the shafts and the wear. Use them together.
Sprocket diameters
The pitch, outside and root diameters follow from the pitch and the tooth count. The outside diameter shown is the largest one the standard allows. Sprocket makers cut the tooth form slightly differently, so take the actual outside and bore dimensions from their catalogue.
Chordal action
A chain wraps a sprocket as a polygon, so the chain speed rises and falls once for every tooth. The speed variation is (1 − cos(180°/z)) and the chain rises and falls by the same fraction of the radius. A sprocket with more teeth gives a smoother drive.
Chain length
The length uses the standard approximate formula, which is accurate for the usual ratios and centre distances. The chain length is rounded up to an even number. The centre distance is then worked out again from the whole number of links, and every later result uses that distance.
Sag and tension
The slack-side tension from the chain weight is the parabolic (small sag) approximation. It is a good estimate for sags of a few per cent of the centre distance. The chain’s tension on a vertical drive from its weight is not included, and the centrifugal tension is added to the peak tension but not to the shaft load, because it is balanced around each sprocket.
Shaft load
The load is the vector sum of the two strand tensions on the sprocket, using the strand angle from the sprocket diameters and the centre distance. It is the load from the chain only. Add the weight of the sprocket and any other loads on the shaft.
Safety factor
The factor is the breaking load of the chain (times the strand factor for several strands) divided by the peak tension. The limits used (8 and 6) are common practice for smooth, slow drives, not a catalogue rule. The chain’s fatigue and wear ratings in the Chain and Sprocket Selector matter more at speed, and they give the real size limit.
Wear limit
3 % elongation is the usual replacement limit. On a drive with a large sprocket the chain rides further out on the teeth as it stretches, so the limit is lower: 200 ÷ the teeth on the large sprocket, in per cent. Both are common practice. Check the maker’s own limit.
Chain data
The ANSI sizes (25 to 240, standard series) are from the Diamond catalogue and the ISO B series (06B to 48B) from the Rexnord catalogue, as loaded in the Chain and Sprocket Selector. Masses are for one strand and include the standard pins and bushes. Heavy series, double-pitch, stainless and other chains are not loaded.
Not covered
Silent (inverted-tooth) chain, double-pitch and conveyor chain, idler and tensioner sprocket positions, three-sprocket and multi-shaft layouts, sprocket bore and hub sizes, and sprocket materials and hardening. A drive with more than two sprockets needs its own layout.
Sources
The geometry is standard roller-chain practice. The chain dimensions were read from the catalogues named below. The design limits in the drive check are common industry practice, not read from one catalogue for this page. Confirm all of them with your chain and sprocket maker before you order.
Standards
ISO 606 (short-pitch transmission roller chains and sprockets) and ANSI B29.1 (precision power transmission roller chains, attachments and sprockets) define the chain dimensions and the tooth form.
Chain data
Diamond Chain Company roller chain catalogue (ANSI standard series) and Rexnord Quality Chains catalogue (ISO B series): pitch, roller diameter, inner width, breaking load and mass per metre.
Rules of thumb
Teeth counts, ratio, centre distance, wrap, sag and the wear limit follow the common guidance in chain makers’ drive handbooks. They are general rules and the maker’s own figures take priority.