V-Belt Length & Pulley Calculator
Belt pitch length for two pulleys from diameters and centre distance — or centre distance from a standard belt — speed ratio, belt speed, wrap angle and standard A/B/C belt numbers with the equivalent metric SPZ/SPA/SPB length.
How it works
L = 2C + (π/2)(d₁ + d₂) + (d₂ − d₁)² ÷ (4C); C = [b + √(b² − 2(d₂ − d₁)²)] ÷ 4 with b = L − (π/2)(d₁ + d₂); wrap = 180° − 2 asin((D − d)/(2C)); belt speed = π d₁ n₁ ÷ 60
A belt wrapping two pulleys travels two straight spans plus roughly half the circumference of each pulley, with a small correction because unequal pulleys tilt the spans — hence the classic length formula, exact enough for all practical purposes. Belts are made in standard lengths, so designers usually pick the nearest belt and solve back for the centre distance, then build in adjustment for installation and tensioning. The speed ratio follows from the diameters, belt speed from the drive pulley, and the wrap angle on the smaller pulley must stay above about 120° or the belt slips under load. Classical V-belts are numbered by inside length in inches with a section letter; metric wedge belts (SPZ, SPA…) are labelled by pitch length in millimetres.
Worked example
100 mm and 250 mm pulleys at 450 mm centres: L = 900 + 549.8 + 12.5 = 1,462 mm — an A56 classical belt (pitch ≈ 1,455 mm) or SPA 1460; ratio 2.5:1 giving 580 rpm, belt speed 7.6 m/s, wrap 161°.
Frequently asked questions
Pitch, outside or inside length?
Formulas use pitch (effective) length at the belt’s neutral line. Classical belts are numbered by inside length (add ~1.3″ for A, 1.8″ for B); metric wedge belts are numbered by pitch length.
How tight should the belt be?
Deflect the span midpoint by 1/64 of the span length (about 16 mm per metre) under the force given in the belt maker’s table; too loose slips and burns, too tight overloads bearings.
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This calculator is for educational purposes. Double-check important results before acting on them.