Belt Length Calculator
Calculate belt length for two-pulley systems with exact and engineering approximation formulas
Calculate Belt Length
Belt Length Results
Primary result: Exact formula
Difference: 0.000 m(NaN%)
Formula used: L = (π/2)(D_L + D_S) + (D_L - D_S)arcsin((D_L - D_S)/(2L)) + 2√(L² - 0.25(D_L - D_S)²)
Example Calculation
V-Belt Factory Example
Problem: Calculate belt length for factory machinery
Large pulley diameter: 30 cm
Small pulley diameter: 15 cm
Center distance: 1.5 m = 150 cm
Calculation Steps
1. Using exact formula:
2. D_L = 30 cm, D_S = 15 cm, L = 150 cm
3. Belt length = (π/2)(30+15) + (30-15)×arcsin((30-15)/(2×150)) + 2√(150² - 0.25×(30-15)²)
4. Belt length = 70.69 + 15×arcsin(0.05) + 2√(22444)
5. Belt length ≈ 371 cm
Common Belt Types
V-Belt
Wedge-shaped cross-section
High power transmission
Flat Belt
Rectangular cross-section
Simple and versatile
Timing Belt
Toothed for synchronization
Precise positioning
Belt Design Tips
Use exact formula for critical applications
Engineering approximation works for similar-sized pulleys
Ensure adequate center distance for proper belt wrap
Consider belt stretch and manufacturing tolerances
Understanding Belt Length Calculations
What is Belt Length Calculation?
Belt length calculation determines the required length of a belt to connect two pulleys in a power transmission system. This is crucial for machinery design, conveyor systems, and mechanical drives where precise belt sizing ensures optimal performance.
Why Two Different Formulas?
- •Exact Formula: Mathematically precise for all configurations
- •Engineering Approximation: Simpler calculation for practical use
- •Approximation works well when pulleys are similar size or far apart
- •Use exact formula for critical applications or dissimilar pulleys
Formula Components
Exact:
L = (π/2)(D_L + D_S) + (D_L - D_S)arcsin((D_L - D_S)/(2L)) + 2√(L² - 0.25(D_L - D_S)²)
Approximation:
L = (π/2)(D_L + D_S) + 2L + (D_L - D_S)²/(4L)
- D_L: Large pulley diameter
- D_S: Small pulley diameter
- L: Center-to-center distance
- π/2(D_L + D_S): Arc lengths around pulleys
- 2L (approx): Straight sections of belt
Note: The exact formula accounts for the wrap angle around pulleys, while the approximation simplifies this with straight-line geometry.