Conveyor belt sag calculator
Mid-span sag between idlers from belt-plus-material mass, idler spacing and belt tension, with the sag ratio in percent.
Result
How it works
Too much sag between carrying idlers makes the belt flex and spill, increases resistance and wears covers and idlers. Sag depends on the weight carried per metre, the idler spacing and the belt tension at that point.
For a horizontal, uniformly loaded span, the small-sag parabola gives the mid-span sag directly. Compare the sag ratio (sag ÷ spacing) with the limit approved for your plant or design standard.
Formula
y = q × g × a² / (8 × H) Sag ratio = y / a × 100 % g = 9.81 m/s²; H in N (kN × 1000)
| Symbol | Meaning | Unit |
|---|---|---|
| y | Mid-span sag | m (shown in mm) |
| q | Belt mass + material mass per metre of belt | kg/m |
| a | Idler spacing | m |
| H | Horizontal belt tension at the span | kN |
| g | Gravitational acceleration | 9.81 m/s² |
Worked example
Inputs: Combined belt + material mass q = 50 kg/m; Idler spacing a = 1.2 m; Horizontal belt tension H = 10 kN.
- y = 50 × 9.81 × 1.2² / (8 × 10,000) = 706.3 / 80,000 = 0.00883 m
- Sag = 8.83 mm
- Sag ratio = 0.00883 / 1.2 × 100 = 0.736 %
Assumptions and limits
- Horizontal, uniformly loaded span; small-sag parabolic approximation. Inclined spans and transient (start/stop) tension are not solved.
- Use the tension at the location you are checking. Tension varies along the conveyor; on head-driven conveyors it is often lowest near the tail on the carrying side.
- Compare the sag ratio with the allowable sag in your design standard or site specification. This tool does not set the limit.
- Above about 2 % sag, review both the allowable sag and whether the small-sag approximation is still adequate.
Screening estimate, not a design approval. Verify measured inputs, current standards, manufacturer limits and site procedures before purchasing, cutting or installation. Isolate and lock out equipment before any hands-on measurement.
Questions
How do I reduce belt sag?
Increase belt tension at that point (usually via the take-up) or reduce idler spacing. Both change other parts of the design, so check the full tension profile first.
What is q?
The mass per metre of belt plus the mass per metre of material on it. Material mass per metre = capacity [t/h] / (3.6 × belt speed [m/s]).
Source notes
- Small-sag statics as presented in IS 11592:2000, clause 8.5.4.4. Check the current edition before relying on it.
Related calculators
More: Belt roll length · Conveyor belt length · Pulley speed (rpm) · Te & belt tensions · Belt tensile rating · Belt cover wear · Cover grade checklist · Spare reorder point
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