Engine timing (cam) belts and multi-pulley toothed belt drives: belt length and tooth count around any number of pulleys, idlers and tensioners, crank-to-cam ratio, how far the valve timing moves per belt tooth, teeth in mesh and wrap on every pulley. Drag the pulleys to change the layout.
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Leave “Belt teeth” empty to use the nearest whole number of teeth. Enter the tooth count printed on the belt to see how far the tensioner has to take up the difference.
In belt order around the loop. Role “crank” and “cam” set the timing ratio. Inside = belt teeth on the pulley; Back = smooth idler or tensioner pressing on the back of the belt. Coordinates from the crank centre, y up.
| Name | Role | Teeth / Ø | Side | x mm | y mm | Pitch Ø | Wrap | Teeth in mesh | rpm |
|---|
The belt runs on its pitch line, which lies inside the tension cords. On a toothed pulley the pitch line radius is z·p / 2π. On a smooth idler running on the back of the belt it is the idler radius plus the distance from the belt back to the pitch line. Between two pulleys the belt follows the common tangent, so the length is the sum of the straight spans plus the arcs wrapped on each pulley.
Belt data (pitch p, pitch line offset u, thickness t, tooth height h): HTD 8M 8 / 0.686 / 5.6 / 3.4 mm; STD S8M 8 / 0.686 / 5.3 / 3.05 mm; HTD 5M 5 / 0.572 / 3.6 / 2.06 mm; GT2 5 mm 5 / 0.572 / 3.8 / 1.91 mm (Gates design manuals). Automotive cam belts are usually 8 mm curvilinear or STD profiles; check the belt maker’s data for your engine. The tensioner travel shown is the length change the tensioner must absorb; actual arm movement depends on its geometry.
This calculator works out the timing belt for an engine or any toothed belt drive with more than two pulleys. Pick a layout (SOHC or DOHC inline-four, V6 with four cams, or a simple two-pulley drive), choose the belt profile, and drag the crank, cam, water pump, idler and tensioner pulleys to where they sit on your engine. It returns the belt length on the pitch line and the tooth count, how much the tensioner must take up for the belt you fit, the crank-to-cam ratio, how many degrees the valve timing moves if the belt is put on one tooth out, the wrap and teeth in mesh on every pulley, pulley speeds and the belt speed.
The layout needs a 143-tooth HTD 8M belt; the tensioner absorbs the last 1.1 mm. If the belt is fitted one tooth out on a cam, the valve timing for that cam is off by about 16° of crank rotation, enough to cost power or, on an interference engine, let valves hit the pistons.
Add up the straight spans and the arcs around each pulley, all measured on the belt's pitch line. For each pair of neighbouring pulleys the span is √(d² − (r1 − r2)²), where d is the distance between centres and r the pitch radii; each pulley adds r × its wrap angle in radians. Divide by the pitch to get the number of teeth, which must be a whole number.
In a four-stroke engine each cylinder fires once every two crank revolutions, and each valve opens once in that cycle, so the camshaft must turn at exactly half crank speed. With a toothed belt that means the cam pulley needs exactly twice as many teeth as the crank pulley.
One belt tooth moves the cam by 360° divided by the number of teeth on the cam pulley, which is twice that at the crank. With a 44-tooth cam pulley one tooth is 8.2° of camshaft or 16.4° of crankshaft, enough to lose power, make the engine run badly and, on an interference engine, risk valves hitting the pistons.
Belt makers recommend at least six teeth in mesh on pulleys that carry load, such as the crank and the camshafts. With fewer, the belt can ratchet over the teeth under load. Lightly loaded accessories like a water pump can work with three or four. Idlers and the tensioner are used to increase the wrap where it is too small.
A belt has a whole number of teeth, so its length rarely matches the pulley layout exactly. The tensioner takes up the difference and keeps the belt at the right tension as it stretches and warms up. Its travel must cover the small length difference plus the belt's stretch over its life.
Belts are quieter, lighter and cheaper and need no oil, but must be replaced at intervals, typically 60 000 to 160 000 km, and a broken belt can wreck an interference engine. Chains last much longer but are heavier, noisier and can stretch. Many BMW engines, including the M30 in the E23 7 Series, use chains, while many 1980s–2000s four-cylinders use belts.
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