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engineering · rotating-equipment-drives · belt-drives

Belt Pulley Drive Performance Calculator

Rates an open-belt drive from its pitch diameters: ideal and actual speed ratio under an entered driven-speed loss, belt speed, approximate belt length and smaller-pulley wrap angle from external-tangent geometry, and delivered power, shaft torques and input-side effective belt pull at an entered overall efficiency. It is a drive-performance screen, not a belt selection or tension design.

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Calculator overview

Inputs and outputs

This summary comes from the calculator's published input and output contract.

Inputs

BD Input Power
About this input

Nonnegative mechanical power entering the driver shaft. Zero is accepted as a checked no-load boundary.

Unit kW Default 6.37 Range At least 0
BD Driver Speed
About this input

Positive steady rotational speed of the driver pulley.

Unit rpm Default 1463 Range At least 0
BD Unit System
About this input

Select SI metric or US customary entry/display units; both paths use the same SI base equations.

Default SI metric Allowed SI metric, US customary
BD Overall Drive Efficiency
About this input

User-entered delivered-to-input shaft power ratio from 0 through 1; the calculator does not estimate it.

Unit fraction Default 0.873 Range 0 to 1
BD Driven Pitch Diameter
About this input

Positive effective pitch diameter of the driven pulley.

Unit mm Default 389 Range At least 0
BD Center Distance
About this input

Positive shaft-center distance. Open-belt external-tangent geometry additionally requires C > abs(D-d)/2.

Unit mm Default 827 Range At least 0
BD Driver Pitch Diameter
About this input

Positive effective pitch diameter of the driving pulley; not an outside-diameter or catalog designation.

Unit mm Default 137 Range At least 0
BD Driven Speed Loss Percent
About this input

Aggregate percentage reduction from ideal no-slip driven speed. A value of 100 percent is schema-valid but makes output speed and torque undefined and returns NOT VALID.

Unit percent Default 1.37 Range 0 to 100

Outputs

BD Output Power
About this output

Input shaft power multiplied by the user-entered overall drive efficiency.

Unit kW
BD Input Shaft Torque
About this output

Input power divided by driver angular speed.

Unit N*m
BD Input Effective Belt Pull
About this output

Input power divided by driver pitch-line belt speed, representing tight-side minus slack-side tension at the driver; not either individual span tension.

Unit N
Model Status
About this output

Returns actionable NOT VALID or CHECK text. OK means the stated kinematic and power identities closed; it is not a belt selection, safety, or design approval.

No unit declared
BD Smaller Pulley Wrap Angle
About this output

Open-belt contact angle on the smaller pulley from external-tangent geometry; it is not an arc-of-contact rating factor.

Unit deg
BD Output Shaft Torque
About this output

Delivered shaft power divided by actual driven angular speed.

Unit N*m
BD Ideal Speed Ratio
About this output

Driven pitch diameter divided by driver pitch diameter; equivalently driver rpm divided by ideal driven rpm.

Unit ratio
BD Approximate Belt Length
About this output

Two-pulley external-tangent approximation; not a selected catalog pitch length or installation allowance.

Unit mm
BD Actual Speed Ratio
About this output

Driver rpm divided by driven rpm after the entered speed loss.

Unit ratio
BD Actual Driven Speed
About this output

Ideal driven speed multiplied by one minus the entered driven-speed-loss fraction.

Unit rpm
BD Ideal Driven Speed
About this output

Driven rotational speed from pitch-diameter kinematics before the entered speed loss.

Unit rpm
BD Drive Relationship
About this output

Classifies actual driven speed as reduction, increase, or one-to-one relative to driver speed.

No unit declared
BD Belt Speed
About this output

Linear belt speed at the driver pitch diameter; local creep or slip speed is not separately modeled.

Unit m/s

What it is

The Belt and Pulley Drive Performance Calculator rates an open-belt drive from its two pitch diameters, its centre distance and its driver speed. It reports the ideal speed ratio, the ideal no-slip driven speed and the driven speed after an entered loss, the actual ratio, the pitch-line belt speed, an approximate belt length and the wrap angle on the smaller pulley, then the delivered shaft power, the input and delivered shaft torques and the effective belt pull at the driver.

Two of the numbers that move the answer most are yours rather than the calculator's. The overall drive efficiency is entered, not estimated, and so is the aggregate driven-speed loss that stands in for creep and slip. The workbook holds no friction law and no creep correlation from which either could be derived.

It accepts SI metric or US customary entry, and both paths run the same SI base equations, so the same physical drive entered either way returns the same ratios and the same wrap angle with correctly converted dimensional results.

It is a drive-performance screen, not a belt selection and not a tension design. No service factor, no arc-of-contact correction, no belt-length correction and no manufacturer power rating is embedded. The wrap angle it reports is geometry rather than a rating factor, and the belt length it reports is not a catalogue pitch length. Take the selection itself from the belt manufacturer's published design procedure.

Methodology

Purpose and model boundary

This model estimates speed, power, torque, belt speed, effective pull and open-belt geometry for two coplanar pulleys connected by one open belt. It separates the entered driven-speed loss from the entered overall power efficiency. It is a performance-screening calculation, not a belt, pulley, shaft or guarding design.

The spreadsheet remains the calculation authority. The page submits the named inputs through the calculation service and displays the workbook's returned results, chart and status; the browser does not reimplement the drive equations.

Inputs and units

Input group Values used by the model
Unit basis SI metric or US customary. The workbook converts length and power to SI internally and converts displayed results back.
Pulley geometry Driver pitch diameter d, driven pitch diameter D, and centre distance C. These are effective pitch dimensions.
Operating point Driver speed n1 and input mechanical power P1.
Performance assumptions Overall drive efficiency η from 0 to 1 and driven-speed loss s from 0% to 100%.

The speed-loss fraction and efficiency are independent aggregate inputs. The workbook does not allocate them among slip, creep, bending, bearings or windage.

Governing relationships

The workbook evaluates the no-slip ratio Rideal = D/d, ideal driven speed n2,ideal = n1/Rideal, loss-adjusted driven speed n2 = n2,ideal(1 − s/100), output power P2 = ηP1, and pitch-line belt speed v = πdn1/60 after converting d to metres.

With angular speed ω = 2πn/60, shaft torque follows T = P/ω. Input effective belt pull is Fe = P1/v; it is the tension difference implied by the input power, not either individual span tension. Open-belt geometry uses

L ≈ 2C + π(D + d)/2 + (D − d)²/(4C)

and smaller-pulley wrap

θ = π − 2 asin(|D − d|/(2C)).

The actual speed ratio is n1/n2. The workbook labels the relationship as speed reduction, speed increase, or 1:1 shaft speed.

Calculation sequence

  1. Validate the unit selection, positive pulley geometry and centre distance, positive driver speed, nonnegative power, efficiency in [0,1], and speed loss in [0,100].
  2. Convert the selected units to the workbook's SI calculation basis.
  3. Check that |D − d|/(2C) < 1, which is required by the open-belt tangent geometry.
  4. Calculate ideal and loss-adjusted speeds, belt speed, open-belt length and wrap angle.
  5. Apply efficiency to power and use P = Tω and P = Fv for torque and effective pull.
  6. Confirm that derived and converted public values are finite and physically consistent, then return the chart and ordered status.

Outputs and interpretation

Primary results are output power, ideal and actual driven speed, ideal speed ratio and belt speed. Detail outputs expose input and output torque, effective belt pull, approximate belt length, smaller-pulley wrap, actual speed ratio and relationship label. The speed chart compares the driver, ideal driven and actual driven states.

Approximate length is not a selected catalogue pitch length. Effective pull is not tight-side or slack-side tension. Results describe the entered steady operating point and assumptions only.

Validation and status logic

The workbook applies these states in order:

Condition Returned status
A selection or basic numeric input is outside the authored domain NOT VALID: choose a listed unit system and correct diameter, center-distance, speed, power, efficiency, or speed-loss inputs
|D − d|/(2C) ≥ 1 NOT VALID: center distance must exceed half the pitch-diameter difference for an open belt
Driven-speed loss is 100% NOT VALID: 100 percent driven-speed loss makes output speed and torque undefined
A required derived or displayed value is not finite or is outside the supported numeric range NOT VALID: derived result exceeds the supported calculation range
Input power is zero CHECK: zero input power; speed and geometry results remain available
Entered efficiency is zero CHECK: zero entered efficiency gives zero delivered shaft power
None of the preceding conditions applies OK

Assumptions and limitations

  • The pulleys are circular and coplanar, the driver speed is steady, and one open belt follows effective pitch diameters.
  • The standard two-pulley length expression is an approximation. It omits belt thickness, pulley deflection, tensioning travel, idlers, crossed-belt geometry and installation allowance.
  • No belt type, groove, pitch, width, number of belts, pretension, service factor, catalogue length or allowable rating is selected.
  • No friction law, individual span tension, centrifugal tension, creep correlation, manufacturer correction or proprietary rating table is embedded.
  • Shaft, bearing, key, hub, alignment, fatigue, thermal, overspeed, guarding and personnel-safety checks are outside scope.

Restrictions and non-computing states

Pitch diameters, centre distance and driver speed must be positive. The tangent geometry must be feasible, and 100% speed loss is non-computing because output angular speed and torque become undefined. A NOT VALID state supersedes any displayed formula residue. Zero power and zero efficiency are intentionally computing boundary states with CHECK messages.

Errors and warnings

A rejected entry means the submitted values did not satisfy the published input rules. NOT VALID means the workbook refused the state; CHECK means a defined boundary was calculated but needs interpretation. Calculation-service failures are availability errors, not drive conclusions, and should not be interpreted from stale values.

References

No belt catalogue, rated-power table, service-factor table or arc-of-contact correction chart is reproduced, and none is embedded. The calculator holds no belt data at all: the pitch diameters, the centre distance, the overall drive efficiency and the driven-speed loss are entirely user-entered, and the shipped values are synthetic demonstration numbers describing no real drive. The workbook implements the ordinary textbook form of open-belt geometry, kinematics, power, torque and force, plus exact public unit definitions, rather than any one publication's treatment. Its cited sources are below.

Naming these organisations identifies the source only; no endorsement or approval is implied.

Service factors, rated power per belt, arc-of-contact and belt-length corrections, span tensions, installation tension and belt life are not supplied here. Take them from the belt manufacturer's design procedure for the cross-section you intend to use.

Additional source notes migrated from Methodology

Project-specific equipment data, manufacturer limits and qualified mechanical review govern real belt-drive design.

Frequently asked questions

Can I select a belt from the delivered power on this page?
No, and doing so will under-select the drive. A real selection multiplies the transmitted power by a service factor for the driver, the driven machine and the duty, corrects for arc of contact below 180 degrees of wrap and for belt length, and compares the result with a rated power per belt. None of that exists here and no rating or correction table is embedded. The wrap angle reported is geometry, and the contract states explicitly that it is not an arc-of-contact rating factor.
Is the effective belt pull the load on my shaft and bearings?
No, and this is the mistake most likely to cause damage. The effective belt pull is the tight-side tension minus the slack-side tension, the net pull that transmits power. The shaft and bearings carry the two tensions added together, which is always larger. This calculator cannot say how much larger: it holds no friction law, no wrap-dependent tension ratio and no centrifugal-tension model. Take the individual tensions from the belt manufacturer's tensioning procedure.
Why did the delivered power not change when I increased the speed loss?
Because the speed loss does not touch the power path. It lowers the driven speed, and the delivered power stays where the efficiency put it. On the shipped defaults, moving the loss from 0 to 1.37 percent leaves the delivered power at 5.561 kilowatts and raises the delivered torque from 103.065 to 104.496 newton metres, because the same power now arrives at a lower speed. Real belt slip dissipates power as heat; here no loss is allocated between the two assertions you make.
Where does the drive efficiency actually apply?
To exactly two outputs: the delivered shaft power and the delivered shaft torque. The input shaft torque and the effective belt pull come from the input power and are unaffected by it. Set the efficiency to zero on the shipped defaults and the input torque still reads 41.578 newton metres and the belt pull 606.98 newtons, while both delivered figures read zero. A badly wrong efficiency leaves half the page correct, with no inconsistency and no status message to warn you.
What does the driven-speed loss represent, and what should I enter?
It is a single aggregate percentage standing in for elastic creep, slip and anything else keeping the driven shaft below its ideal no-slip speed. The calculator does not derive it from tension, wrap, load or belt construction. A toothed synchronous belt has no creep by construction; a friction belt has some, and that figure is yours to establish. The shipped 1.37 percent is synthetic. Exactly 100 percent is inside the bound but returns NOT VALID.
Why did the model reject my centre distance?
Open-belt external-tangent geometry requires the centre distance to exceed half the difference between the two pitch diameters. At exactly that value the wrap on the smaller pulley collapses to zero and the belt can transmit nothing, so the model returns NOT VALID rather than a meaningless number. If a real layout is near that limit the wrap will be small, and a real selection would apply an arc-of-contact penalty that this calculator does not.
Can I order a belt to the length it reports?
No. It is the standard two-pulley external-tangent approximation, carrying no belt thickness, no pulley deflection, no tensioning travel, no idler and no installation allowance. Real belts come in discrete catalogue pitch lengths, and the centre distance is then adjusted to suit the nearest one, with movement left to tension the drive. Use the reported length to find the catalogue size, not as the size.
Why is every number on the page zero?
Because the model refused the inputs. Negatives, blanks, nulls, an efficiency above one and a speed loss above 100 percent are rejected before the model runs. Zero is accepted by the bound and then judged by the model, and a zero pitch diameter, centre distance or driver speed returns NOT VALID, which zeroes the whole block and sets the drive relationship to NOT AVAILABLE. Zero input power and zero efficiency are different: they return CHECK and the geometry and speed results stay live.
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This page is provided by LogicCommons for informational purposes only. Results are analysis outputs computed from the inputs you supply and are not engineering advice, a design, or a substitute for review by a licensed professional under the codes adopted where the work is built. Verify all inputs and results independently.

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