V-Belt & Pulley Calculator: RPM, Length, Wrap and Power

For two parallel shafts with an open belt, the diameter ratio is $i=d_2/d_1$. Ideal driven speed is $n_2=n_1/i$; the optional entered speed-loss fraction multiplies this by $(1-s)$. The ideal driven diameter for a target speed follows the same relation.

With all lengths on the same datum/pitch basis, use

This is Gates' Formula D13 open-drive approximation (attached manual p.287, printed D19), using full $\pi/2$ instead of rounded 1.57. Automatic mode selects the nearest feasible Optibelt SK SPB product length; equal differences choose the shorter belt. Entered-length mode accepts another supplier's datum length.

Put $A=L-\pi(d_1+d_2)/2$. The larger quadratic root gives $C=(A+\sqrt{A^2-2(d_2-d_1)^2})/4$. Catalogue filtering and custom-length validation use the exact tangent-and-arc length at $C_{touch}=(d_1+d_2)/2$ as the minimum. Reject any selected length at or below this contact length; the approximate quadratic alone cannot establish physical feasibility. With $\alpha=\arcsin[(d_2-d_1)/(2C)]$, the small-pulley wrap is $180^\circ-2|\alpha|$. The exact tangent-and-arc length is also calculated to expose the approximation error; the centre distance is the inverse of the approximate formula.

Belt speed is $v=d_1\omega_1/2$. From the selected manufacturer's manual enter nominal power per belt (including any speed-ratio addition), wrap factor and length factor. Then $P_b=P_N K_{wrap}K_L$, $P_d=P K_s$ and $z=\lceil P_d/P_b\rceil$. Optibelt's worked example uses 21.87 kW, 1.00, 1.02 and a service factor of 1.3 (printed pp.85–87 in the linked edition). These inputs do not update automatically when geometry changes.

Entered stopped-drive pretension $T_0$ gives static pull on each shaft $F_s=2zT_0\cos\alpha$. This is the vector sum of equal strand tensions, equivalent to Optibelt's $2zT_0\sin(\beta/2)$. Effective tangential pull is $P/v$; it is a different quantity.

For the same fan, density and system, $r=(d_{1,new}/d_{2,new})/(d_1/d_2)$. Speed and flow multiply by $r$, pressure by $r^2$, and absorbed power by $r^3$ (Greenheck, attached p.5). Transfer replacement dimensions and power to the main inputs for a new belt design.

• Open two-pulley drive, parallel shafts, fixed circular datum/pitch diameters and no idlers.
• Belt lengths and diameters use one consistent manufacturer's datum/pitch basis. Outside, inside and effective-length designations are not interchangeable.
• Matched belts share power equally. The calculated count is the minimum integer at the entered catalogue rating.
• Ratings, correction factors, service factor and pretension are supplied by the user. Defaults are a published Optibelt SK SPB fan example, not a general SPB rating.
• Static shaft pull uses the calculated belt count and the entered stopped-drive tension in each strand. No inference of pretension from power is made.
• Animation shows ideal belt geometry and no-slip angular ratio in slow motion. Playback stops after one belt circuit; reset the slider to replay. It is not a speed or slip measurement.
• Fan comparison holds motor speed and estimated slip fixed and assumes similar operating points on an unchanged system curve.

The centre-distance result inverts an approximate length equation. The exact geometric-length residual is shown under How it's calculated; unequal pulleys at short centres need supplier confirmation. The minimum-length check uses exact tangent-and-arc geometry at datum-circle contact, independently of the centre-distance approximation. Datum-circle clearance alone does not ensure outside-diameter or guard clearance. Automatic selection uses the attached manufacturer's product-length list, not a comprehensive catalogue or a claim of current stock.

Always reselect nominal power, wrap and length factors when pulley size, speed, section, maker or length changes. Do not apply the example rating to another drive. Confirm the section's minimum pulley diameter, maximum belt speed, flex rate, fitting allowance, tensioning travel and pulley balance with the manufacturer. The 120° wrap and 30 m/s speed warnings are screening prompts, not universal approval limits.

Static pull excludes pulley weight, centrifugal effects, running tight/slack tension, transients and shaft/bearing geometry. It is not the dynamic bearing reaction. Fan-law estimates exclude density changes, stall, changed dampers and efficiency changes; check motor capacity and the fan's permitted RPM. A changed-pulley comparison does not resize the main drive.

Installation work belongs to a qualified person, with isolation, alignment, guarding and supplier tensioning procedures.