ONE FORMULA, ONE ANSWER
Exact open belt length calculator
Compute an uncrossed belt’s pitch-line length using tangent and circular-arc geometry. Choose input units and calculate one value within the stated conditions.
Inputs
Calculations run in this browser. Scientific notation such as 1.2e-3 is supported. Do not group thousands.
Result
Belt pitch-line length L
Enter values and select Calculate.
q = |D₁ − D₂|/(2C); L = 2C√(1 − q²) + π(D₁ + D₂)/2 + |D₁ − D₂| asin(q)
Assumptions
Required: parallel pulley axes, coplanar pitch circles, pitch diameters rather than outside diameters, and C > (D₁ + D₂)/2. The geometric pitch-line result excludes belt thickness, elastic stretch, take-up allowance, standard sizes, and integer tooth-count selection.
Displayed values are floating-point approximations. Design safety factors and unprovided error contributions are not calculated.
Formula references and credits
NaNa Lab created the code, descriptions, icons and preview images. Text, figures and code from the linked references have not been reproduced.
Physical constants: NIST / CODATA 2022. The values of μ₀ and ε₀ are measured recommendations, not exact defining constants. Values and precision notes are in the source record.
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