Belt Drive Calculator

Formula

• Design power: P_design = P × Ks (power mode).
• Driven diameter: D2 = D1 × (N1/N2) × (1 − slip/100) (power mode).
• Open length (approx): L ≈ 2C + π(D+d)/2 + (D−d)²/(4C).
• Open length (exact): α = arcsin((D−d)/(2C)); L = π(D+d)/2 + (D−d)·α + 2√(C²−((D−d)/2)²).
• Crossed length (approx): L ≈ 2C + π(D+d)/2 + (D+d)²/(4C).
• Wrap (open, small): 180° − 2·arcsin(|D−d|/(2C)); target ≥ 120°.
• Belt speed: v = π·D1·N1/60000 (m/s).
• Power per belt ≈ Pr × kθ × kl; required belts = ceil(P_design / P_belt).
• Center from length (open approx inverse): C = (b + √(b² − 2(D−d)²))/4 with b = L − π(D+d)/2.

How it works

Three modes: power sizing across classical V, narrow V, cogged, flat, timing, and poly-V sections with service factor; open or crossed belt length (exact and engineering approximation); or center distance from a known belt length. Wrap under 120° and min pulley diameter trigger warnings. Manufacturer catalogs still own final section ratings.

Pick Input mode: Power sizing (default), Belt length, or Center distance from length. In power mode choose Belt type (classical V, narrow V, cogged, flat, timing, poly-V), then section and Ks. Timing locks slip at 0%. Geometry modes use open/crossed arrangement. CALCULATE updates Results and the live sketch: front (tangents + wrap) and top plan (Ø along C, face = thickness; open band or crossed X). Play/Pause available. Editing clears Results. RESET restores classical B · 5 kW · C=500.

Exact length vs the Fenner-style approximation

Mode 1 open preset: L ≈ 3710.6 mm; wrap on the small pulley ≈ 174.3°.

Order the nearest standard pitch length, then fine-tune take-up from Mode 2 if you already have a belt code.

Open wrap, crossed wrap, and the 120° floor

Power path: Ks, Pr screen, and how many belts

Default CALCULATE path: 6.5 kW design power, three B-section belts after kθ·kl correction.

If status flips Unsafe, fix min pulley or wrap before trusting the belt count.

What this pad is not

Worked example

Default Power sizing: V-belt B, 5 kW, 1450→500 rpm, D1=150 mm, C=500 mm, slip 2%, Ks=1.3. Reproduce on CALCULATE.

1. Leave Quick preset on Power · B · 5 kW · 1450→500 (or enter the same values). Mode = Power sizing.
2. CALCULATE → design power 6.5 kW; D2=426.3 mm; L≈1943 mm; wrap≈147.9°.
3. Belt speed ≈ 11.39 m/s; power per belt ≈ 3.01 kW; required belts = 3; status Safe.
4. Length example: switch to Belt length with 150/300 mm, C=1500 mm, open → L≈3710.6 mm.
5. C-from-L example: Mode Center distance from length with L=3711 mm → C≈1500.2 mm.
6. Min-pulley check: set D1=100 mm on B-section → min pulley warning and Unsafe status.

Result: Default: 3 belts, L≈1943 mm, wrap≈147.9°, Safe. Geometry modes match open length ≈3710.6 mm.

When to use

• Estimating open or crossed belt pitch length before ordering
• First-pass V-belt count from power, rpm, and section
• Checking wrap angle before freezing shaft spacing
• Solving center distance from a known belt length
• Flagging undersized driver pulleys against section min PD

Limitations

• Pr rows are approximate screening values, not current manufacturer ratings at your rpm.
• Power mode uses open-belt geometry only; switch to Mode 1 for crossed length.
• Timing rows are capacity screens, not full toothed-module width design.
• Does not compute installation tension, shaft loads, or multi-pulley serpentine paths.
• Does not design guards, take-up hardware, or LOTO procedures.
• OEM selectors remain the authority for product selection.
• Retail belt ordering tools are out of scope.

FAQ

How many belts do I need?

In Power sizing, required belts is ceil(design power ÷ corrected power per belt). The default B-section case needs 3 belts at 6.5 kW design power. Always confirm catalog kW per belt at your small-pulley diameter and rpm.

Open or crossed belt length?

Open belts keep the same rotation sense and use (D−d)²/(4C) in the approx length. Crossed belts reverse rotation, use (D+d)²/(4C), and raise wrap above 180°, with more wear at the crossing. Pick the arrangement in Mode 1 or 2.

Why show approx and exact length?

Catalogs and Fenner-style worksheets use the engineering approximation. The exact geometric form is the true tangent-and-arc length. For typical industrial C they agree closely; large diameter ratios at short C are where they diverge.

What wrap angle should I target?

Keep open-belt wrap on the smaller pulley at or above 120°. Below that, capacity drops and slip risk rises. Increase C, reduce ratio, or add an idler. Crossed layouts naturally sit above 180°.

What does belt status mean?

Safe means driver pulley is at or above section min PD, belt speed is within the section max, wrap is at least 120°, and the center distance fits the pulley pair. Caution usually means wrap or speed is marginal. Unsafe means min pulley failed, geometry is impossible, or more than one hard limit is broken.

Why does center distance fail for some inputs?

Open belts need C greater than |D1-D2|/2 so the tangent geometry exists. Crossed belts need C greater than (D1+D2)/2. Mode 2 also fails when the entered belt length is too short to close around the pulleys.

Why add a service factor?

Shock, starts, and duty cycle make motor nameplate power optimistic. Ks scales design power. Presets cover uniform (1.1), light shock (1.3), and heavy shock (1.5).

Which belt types can I choose?

Power mode offers classical V (Z–E), narrow V (3V/5V/8V and VX), cogged/raw-edge (AX–DX), flat widths, timing/synchronous (MXL–XXH), and poly-V/ribbed (PJ–PM). Timing locks slip at 0%. Section power ratings are screening values; confirm with the manufacturer catalog.