How do I calculate timing belt length from pulley diameters and center distance?

Question

Accepted Answer

Short answer: For two equal pulleys, belt length is about 2C + 3.14 x D, where C is the center distance and D is the pitch diameter. For unequal pulleys, use L = 2C + 1.57(D1 + D2) + (D2 - D1)^2 / 4C. Then round the result to the nearest available whole-tooth length, because timing belts are made in pitch multiples.

The formulas

Drive	Formula	Use it when
Two equal pulleys	L = 2C + 3.14 x D	Mirrored drives and idler layouts where both pitch diameters match
Two different pulleys	L = 2C + 1.57(D1 + D2) + (D2 - D1)^2 / 4C	The general case for most two-pulley drives
Three or more pulleys, idlers	Approximation only	Wrap angles change the picture; ask us to calculate from the full layout

Worked example: an HTD 8M drive with two 20-tooth pulleys (160 mm pitch diameter) and a 500 mm center distance gives L = 2 x 500 + 3.14 x 160 = 1502.4 mm. The nearest whole-tooth 8M belt is 1504 mm (188 teeth), about 1.6 mm longer than calculated, which the center distance adjustment or a tensioner absorbs.

Operator machining a timing belt pulley on a lathe — Pulley geometry is the input: pitch diameter and tooth count decide the belt before any tape measure comes out.

From calculated length to a real belt

Round to whole teeth: the final belt length is always the tooth count times the pitch.
Check center distance adjustment: the drive needs extra travel to fit the belt and to set tension, commonly a few millimetres each way depending on size.
Use pitch diameter, not outside diameter: the outside diameter is larger by roughly twice the tooth depth, and mixing them up shifts the result by several teeth.
For drives with three or more pulleys or small wrap angles, let us calculate the exact length from your layout sketch, because the simple formula drifts as angles change.

The formula gives a theoretical length. Real belts carry pitch-length tolerances, and the drive has to tolerate the rounding. When in doubt, send the pulley tooth counts and the center distance and we will verify the belt length before quoting.

Technician checking pulley alignment and belt tracking with a straightedge — Center distance and tension are checked on the machine after the calculated length is chosen.

Timing belt running between two pulleys — A correctly calculated length runs with even tooth engagement and steady tracking.

Want us to verify your belt length?

Send the pulley tooth counts, diameters and center distance, or a photo of the drive. We will confirm the pitch, length and width and quote the belt.

Verify My Belt Length