Chain Sag Calculator - Calculator Academy

Reviewed By: Patrick Myers (BSME)

Enter the weight per unit length (lb/in), the length of the span (in), and the total tension (lb) into the Chain Sag Calculator. The calculator will evaluate the Chain Sag.

Chain Sag Formula

The following formula is used to calculate the Chain Sag.

S = w*l^2 / (8*T)

Variables:

S is the Chain Sag (in)
w is the weight per unit length (lb/in)
l is the length of the span (in)
T is the total tension (lb)

To calculate the chain sag, square the length of the span, multiply by the weight per unit length, then divide by the product of 8 times the total tension.

How to Calculate Chain Sag?

The following steps outline how to calculate the Chain Sag.

First, determine the weight per unit length (lb/in).
Next, determine the length of the span (in).
Next, determine the total tension (lb).
Next, gather the formula from above = S = w*l^2 / (8*T).
Finally, calculate the Chain Sag.
After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge.

weight per unit length (lb/in) = 40

length of the span (in) = 5

total tension (lb) = 30

S = w*l^2 / (8*T) = ?

Follow-Up Calculations

If your chain is set to about 30 mm of slack and your bike runs a 15/45 sprocket setup, the final-drive ratio is 3.0:1, so 6,000 engine rpm becomes roughly 2,000 rpm at the rear wheel before tire size is considered. You can estimate your rear-wheel speed from sprocket teeth and engine rpm to see how gearing changes cruising speed and acceleration.

If your chain sag is around 25-35 mm, the drivetrain is usually loose enough to move freely but tight enough to avoid lash, which matters when you’re estimating how much push reaches the pavement. After the chain is adjusted correctly, you can see the force at the tire by combining engine torque, gearing, and tire radius; that number is what actually accelerates the bike.

If a 180 kg rider and 15 kg of luggage bring a 160 kg bike close to its limit, the rear suspension can compress enough that a chain that measured 30 mm of sag in the garage may become much tighter on the road. You can check your safe payload range first so you know whether you should recheck chain slack with the bike loaded.