Belt & Pulley Drive Calculator — Tension, Wrap Angle & Belt Selection (ISO 4184 / DIN 7753)

The fundamental relationship between tight-side tension T₁ and slack-side tension T₂ in a friction drive is the Euler–Eytelwein capstan equation. It shows that the maximum transmitted force before slip depends exponentially on the product of the friction coefficient and the wrap angle — so increasing either the grip (choose a grippy belt or groove geometry) or the contact arc (add an idler) raises the power capacity. For a V-belt the grooved sheave amplifies the effective friction coefficient: µ_eff = µ / sin(β/2), where β is the included groove angle (≈ 34° for standard V-belts), making a V-belt drive significantly more slip-resistant than a flat belt at the same friction and tension.

The design power is the nominal power multiplied by the service factor (Ks ≥ 1.0 for steady loads, higher for shock or reversing duty). The required effective pull Fe is then computed from the design power and belt velocity, and T₁ and T₂ follow from the Euler ratio.

For an open belt drive the wrap angle on the small pulley is α₁ = π − 2 arcsin((D₂ − D₁)/(2C)), and the belt pitch length follows from the standard two-pulley geometry. A crossed belt drive gives equal, larger wrap on both pulleys (both rotate the same direction reversal), while a tensioner idler adds an additional increment Δθ to the effective wrap. The calculator evaluates all three configurations; a warning is raised when the small-pulley wrap angle falls below 120°, the commonly accepted minimum for reliable V-belt power transmission.

A synchronous (timing) belt transmits load by tooth engagement rather than friction, so its capacity is governed by the shear strength of the belt teeth rather than the slip margin. The number of teeth in mesh (TIM) is calculated as TIM = floor(z₁ × α₁ / (2π)), where z₁ is the number of teeth on the small sprocket and α₁ is the wrap angle in radians. Only fully engaged teeth are counted (floored), consistent with Gates and ContiTech synchronous drive design manuals. The tangential force is distributed equally across all teeth in mesh, and the resulting shear stress in each tooth is compared against the material allowable — higher shear allowables are available from polyurethane-reinforced construction versus rubber.