Belt Length Calculator
The open belt's tape measure: tangent runs, the two half-wraps and the correction term, plus the wrap-angle check that guards the grip.
Belt Length Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Open two-pulley belt; no crossed or idler drives
- Pitch geometry — not inside V-sections
In short: Two 100 mm and 200 mm pulleys set 500 mm apart on shaft centres wear an open belt of 1,476.238898 mm — 2 × 500 of tangent run, π/2 × 300 of half-wraps, and a 5.000000 mm correction for the diameter mismatch. The small pulley still sees 168.522 degrees of wrap, comfortably past the 120-degree floor where grip begins to starve — the belt is the transmission's cheapest part and the first thing a bad centre distance ruins.
Formula
L = 2C + π/2·(D₁+D₂) + (D₂−D₁)²/4C ··· θ = 180° − 2·asin(ΔD/2C)
The belt is two straight tangents and two arcs, and the classic formula folds the arcs into a half-sum with a correction term that prices the diameter mismatch — zero when the pulleys match, growing as they diverge. Accurate to about half a percent for ordinary spacing, which is tighter than any belt's tension window.
Worked Example
- Enter both pulley diameters.
- Enter the centre distance between shafts.
- Read the belt length and its three parts.
- Check the small pulley's wrap angle holds grip.
Defaults: 100 and 200 mm at C 500 → 1,476.238898 mm, wrap 168.522° on the small pulley. The equal-pulley check: D₂ = D₁ → the correction term vanishes and L = 2C + πD exactly. Pull the pulleys close together and the wrap door speaks before the geometry does.
Strengths & Limits Of This Model
Where this engine is strong
- Three-part breakdown, not just a total
- Wrap-angle grip check built in
Where it stops
- No tension or take-up model
- No standard belt-section rounding
Practical Use Cases
Drive layout
belt stock before the frame exists
Retrofit checks
will the shelf stock fit
Teaching
geometry you can tension
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Belt Length Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why is the formula an approximation?
Because it folds two unequal arcs into a half-sum plus a correction term — exact when the pulleys match, within about half a percent for ordinary centre distances. Belt tensions swing several percent through their life, and centres are usually adjustable by a slot, so the approximation is tighter than the things it measures. Precision beyond that belongs to a cad model, not a tape.
What is the correction term doing?
It prices the diameter mismatch: two pulleys of equal size need exactly 2C of tangent and πD of wrap, and every millimetre of difference makes one tangent longer and one arc shorter in a way the (D₂−D₁)²/4C term captures. It grows as the square of the mismatch and shrinks with the centre distance — far-apart pulleys barely notice a size difference; close-coupled ones feel it in the tape.
Why does wrap angle matter more than length?
Because grip lives in the arc of contact: the belt transmits torque by friction over the arc, and below roughly 120 degrees on the small pulley the capacity falls faster than any length correction can rescue. A belt of perfect length wrapping a starved pulley is a conveyor for smoke. The check card exists because length problems announce themselves at installation; wrap problems announce themselves under load.
Does this work for crossed or quarter-turn drives?
No — the open-belt tape assumes parallel shafts with the belt running plain figure of eight-less. Crossed belts add wrap on both pulleys and a mid-cross clearance problem; quarter-turn drives need guides and their own geometry. The formula prices the layout nine tenths of drives actually use; the exotic arrangements earn their own page.
Which pulley is 'small' in the wrap check?
The one with less arc — always the smaller diameter in an open drive, since the larger pulley's wrap exceeds 180 degrees by exactly what the smaller loses. That is why capacity tables key on the small pulley: it is the grip bottleneck of the whole drive. The check card computes the small pulley's angle so the bottleneck is inspected, not guessed.
How much tension take-up should the frame allow?
Belt length itself is stable, but tension windows and wear stretch the practical requirement: frames typically allow several percent of centre adjustment both directions — in to tension, out to fit a worn belt. A belt ordered at 1,476.238898 mm wants a frame that can argue with it. The tape is the middle of the negotiation, not its end.
Why do the tangents contribute exactly 2C together?
Because in an equal-pulley drive the two straight runs are the tangent segments of a belt around a double circle — each run's horizontal projection is C and the arcs contribute πD. With unequal pulleys the tangents tilt, and the tilt is precisely what the correction term pays for. The geometry is a wrapped trapezoid wearing a belt.
Can I just measure the old belt?
You can, and it lies politely: a worn belt has crept, cracked and stretched past its installed length, and the top width tells you nothing of the pitch line inside the V. Compute the tape from the geometry, then sanity-check the stock room's nearest standard section against it. The old belt is evidence of wear, not of length.