Belt Tension and Shaft Load Calculator

How tight, measured the way you can actually measure it — deflect the span by a sixty-fourth of its length and read the force — and then the part every other belt-tension page leaves out: the resultant shaft load, in magnitude and direction, and what it does to the bearing’s rating life. The capstan relation with the groove angle done properly, the centrifugal term on both sides where it belongs, and ISO 281’s exponent to turn an over-tension into a number.

From power to the bearing, in one line of vectors

Belt sections, and what the groove buys

The force-deflection method, and the makers’ own rules

What each extra turn on the adjuster costs — the default drive, tension by tension

Every relation this page uses, and where it comes from

The tension is the easy half. The bearing is the other half

Every belt-tensioning page stops at the tension. The bearing does not. Tensioning a belt correctly is the easy half: measure the span, deflect it by a sixty-fourth of its length at mid-point with the drive stopped, and read the force. The hard half is that the tension you set does not go into the belt and stay there. It goes into the shaft, and from the shaft into two bearings, as a resultant that is the vector sum of the tight and slack side tensions — on the default drive here, 1.8 times the tension that is actually doing the work. And bearing life does not go with load; it goes with load cubed. That is why over-tensioning is the commonest cause of premature bearing failure on a belt drive, and why this page does not end at the tension.

The number nobody prints. The two belt spans are tangent to both pulleys, so they are symmetric about the line of centres and each leans away from it by α, where sin α = (D − d)/2C. The pulley therefore feels T₁ along one span and T₂ along the other, and the resultant is √(T₁² + T₂² + 2T₁T₂·cos 2α) — which collapses neatly to T₁ + T₂ when the pulleys are the same size, which is the form everybody quotes. It also has a direction, a few degrees off the line of centres toward the tight side, and that direction is what tells you which way to orient a self-aligning housing. None of the belt-drive material consulted in this batch printed either the magnitude or the direction. It is elementary statics; it is also the whole reason for this page, so it was derived here and then checked three independent ways over 500 random geometries — the closed form, a component sum, and an explicit construction that finds the tangent points on the two circles numerically and adds the vectors.

Why a V-belt essentially never slips, and why that is a problem. The capstan relation for a flat belt is (T₁ − T_c)/(T₂ − T_c) = e^(μθ). Put the belt in a groove and the wedging action multiplies the effective friction by 1/sin(γ/2), γ being the full included groove angle: 3.42 at 34°, 3.24 at 36°, 3.07 at 38°. So a modest μ of 0.30 behaves like 1.03, and over 166° of wrap the belt can hold a tension ratio of about 20 — against about 2.4 for the same belt running flat. The consequence is that slip is almost never the binding constraint on a V-belt drive, which is exactly why makers publish a deflection-force table rather than asking you to compute a slip limit, and exactly why over-tensioning is so easy to do: there is no audible feedback. A belt that is 60% too tight sounds better than one that is 10% too loose.

The centrifugal tension belongs on both sides, and it does no work. T_c = m·v², and it adds equally to the tight and the slack side, so it must be subtracted from both before the friction relation is applied — the Cambridge engineering notes go so far as to call ρv² “often conveniently if erroneously referred to as the centrifugal tension”, because it is a tension in the belt that transmits nothing. Below about 5 m/s you can ignore it. At 25 m/s it is often the largest single term, and Khurmi’s condition for maximum power transmission says the useful limit is reached when it hits one third of the total: past that, running faster transmits LESS power. The page prints its share of the tight-side tension so you can see where you are.

What a new belt needs, and what this page will not do. A new belt is set tighter and loses it fast: TB Wood’s put the initial tension at twice their tabulated minimum, say it falls “rapidly during the first few hours”, and ask for a recheck inside 24 hours, with retensioning between the minimum and 1.5 times it — Gates define a new belt as one that has run less than about 24 hours. Where your maker publishes a deflection force for your section, sheave diameter and speed, use theirs: their table is indexed by four things this page does not ask about, and it is sized for the belt’s RATED power rather than the power you are transmitting, which is why a tabulated figure is usually higher than the one computed here for a lightly loaded drive. And this page will not compute a belt length or a centre distance for a given belt — that is a different calculation and the site already answers it elsewhere. What it will do is take the span, which is what the deflection is measured over, and carry the tension all the way to the bearing. The service factor that starts it off comes from the drive service factor calculator; the same shaft-load question on a chain drive is a different shape, because a chain has no slack-side tension to speak of — see the roller chain selection calculator and the chain length and centre distance calculator.

Frequently asked questions

Related calculators

References

1. TB Wood’s (Altra Industrial Motion). Tensioning Drives, catalogue section BEV-1, P-1686-TBW. “The deflection height (h) is always 1/64″ per inch of span length (t)”, with the span itself “t = √(C² – ((D–d)/2)²)”; the force applied “perpendicular to any ONE of the belts at the mid point of the span”; initial tension at twice the tabulated minimum, falling “rapidly during the first few hours”, with retensioning between the minimum and 1.5 times it; and, on an older drive, excessive tension leading to “excessive bearing load or excessive shaft deflection”.
2. Gates Corporation. Design Flex force/deflection tensioning (Gates Belts, Hoses and Applications). Confirms the same “1/64 of an inch per inch of span length”, and adds two rules this page uses: on a multiple-belt drive “you must multiply the deflection force by the number of strands that you will be deflecting”, and “any belt that has not been run more than about 24 hours is considered a new belt”.
3. R.S. Khurmi and J.K. Gupta, A Textbook of Machine Design, chapter 21 Chain Drives and chapter 20 V-Belt and Rope Drives (the chapters as distributed by Al-Mustansiriyah University and Al-Mustaqbal University). Source for Table 21.2, factor of safety for bush roller chain against the smaller sprocket’s speed; for the service factor as K1 × K2 × K3 (load, lubrication, hours); for the recommended teeth on the smaller sprocket against velocity ratio; for the V-belt tension ratio 2.3 log(T1/T2) = μθ cosec β with β the groove HALF angle and a groove angle of 32° to 38°; for the centrifugal tension Tc = mv²; and for the maximum-power condition Tc = T/3.
4. University of Cambridge, Department of Engineering. DANotes: V-belt drives — Kinetics and fatigue. Gives the tension ratio with the centrifugal term separated, “(Fmax − ρv²)/(Fmin − ρv²) ≤ e^(fθ)min”, and the effective friction coefficient “f ≡ μ∗cosec β” with β the groove half angle. It also calls ρv² “often conveniently if erroneously referred to as the centrifugal tension”, which is why this page subtracts it from both sides rather than adding it to the load.
5. ISO 281:2007, Rolling bearings — Dynamic load ratings and rating life. Cited by number for the life exponent only: basic rating life goes as (C/P) raised to 3 for a ball bearing and 10/3 for a roller bearing. That exponent is what turns a 30% over-tension into a bearing-life figure on this page, and it is the only thing taken from the standard.
6. BestORQ. V-Belt Quick Selection Guide. The V-belt service factor table used here: four driven-machine groups with their named examples, driving Group 1 (normal-torque AC, shunt-wound DC, multiple-cylinder engines) against Group 2 (high-torque and single-phase AC, series and compound-wound DC, single-cylinder engines), and three service bands — intermittent 3–5 hours, normal 6–16 hours, continuous 16–24 hours or a start above 200% of rated load. Also the idler additions: inside slack side 0.0, outside slack side 0.1, inside tight side 0.1, outside tight side 0.2.