Belt Length Calculator
The length of a belt wrapped around two pulleys isn't just the straight-line distance doubled — it also has to account for the curve around each pulley, more so when the two pulleys are different sizes.
Inputs
Result
1,873.2 mm
73.75 inches
How the belt length calculator works
L = 2C + (π/2)(D1 + D2) + (D2 − D1)² ÷ (4C), where C is the centre distance and D1, D2 are the two pulley diameters.
The first term is the two straight belt runs; the second approximates the wrap around both pulleys; the third corrects for the extra length needed when the pulleys are different sizes.
Worked example: pulleys 120 mm and 300 mm, 600 mm centre distance
- 2C term: 2 × 600 = 1,200.
- Wrap term: (π/2)(120+300) = 1.5708 × 420 ≈ 659.7.
- Correction term: (300−120)² ÷ (4×600) = 32,400 ÷ 2,400 = 13.5.
- Total L ≈ 1,200 + 659.7 + 13.5 = 1,873.2 mm (about 73.75 inches).
Common mistakes to avoid
Using this formula for a chain-and-sprocket system instead of a belt
Chain length calculations use a related but distinct formula based on the number of teeth per sprocket rather than continuous diameters — mixing the two gives an inexact result for a chain drive.
Forgetting the centre distance is measured between pulley axles, not edges
C is the distance between the two pulleys' rotational centres, not the gap between their outer edges — using edge-to-edge distance understates the true centre distance and skews the result.
Frequently asked questions
Why does the formula get more complex when pulleys are different sizes?
With equal-sized pulleys, the belt wraps each one by exactly the same amount and the geometry simplifies; unequal pulleys create an asymmetric wrap angle on each pulley, which the correction term accounts for.
How much slack should I allow beyond this calculated length?
Real belts typically need a small amount of adjustable slack for tensioning — check the belt manufacturer's tensioning guidance rather than cutting to the exact calculated length.
Does this work for a crossed-belt configuration (figure-8 layout)?
No, this formula assumes an open (non-crossed) belt configuration — a crossed belt uses a different geometry entirely.
What if the two pulleys are the same diameter?
The correction term becomes zero (D2−D1 = 0), and the formula simplifies to L = 2C + πD — the classic 'two straight runs plus one full circle' approximation.
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