Chain Speed and Chain Drive Calculator

Find the chain speed, the sprocket pitch diameters, the output speed, the chain length and the pull for a roller chain drive.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Each tooth moves the chain one pitch, so the chain speed is the number of teeth times the pitch times the sprocket speed. The pitch diameter of a sprocket is the pitch divided by the sine of 180 degrees over the number of teeth. The speed ratio is the teeth on the driven sprocket over the teeth on the driving sprocket.

Add the centre distance for the chain length in pitches, rounded up to an even number so no offset link is needed, and the power for the pull in the chain.

Formulas used

  • v = \dfrac{z\,p\,N}{60\,000}
  • D = \dfrac{p}{\sin(180^\circ/z)}
  • L_p = \dfrac{2C}{p} + \dfrac{z_1+z_2}{2} + \left(\dfrac{z_2-z_1}{2\pi}\right)^2\dfrac{p}{C}

Worked example

With the default numbers in the calculator above:

  1. Pitch diameter of the driving sprocket: 115.74 mm
  2. Pitch diameter of the driven sprocket: 230.69 mm
  3. Chain speed: 1.858 m/s
  4. Chain speed by the pitch diameter (the textbook form): 1.8665 m/s
  5. Speed ratio: 2 : 1
  6. Speed of the driven sprocket: 154 rpm
  7. Chain length before rounding: 91.782 pitches
  8. Chain length to use (an even number of pitches, to avoid an offset link): 92 pitches (1752.6 mm)
  9. Centre distance with that chain: 602.08 mm
  10. Wrap of the chain on the smaller sprocket: 169.01°
  11. Pull in the chain at this power: 1076.4 N

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

Which diameter do I use for the speed?

The pitch diameter, which is the circle through the chain pins. It is not the outside diameter of the sprocket.

Why an even number of pitches?

An odd number needs an offset link, which is weaker. An even number joins with a normal connecting link.

Is this enough to choose a chain?

No. The chain size, strands, service factor and lubrication come from the chain maker's rating tables.

Related calculators

Further reading: Roller chain maker's selection catalogues and standard machine design texts (chain drive geometry).

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