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August 2026 13 min read

Coupling Calculator

Free online coupling calculator for mechanical engineering. Compute bolt shear stress, bearing stress, required bolt diameter, and torque capacity for bolted flange couplings with standard coupling selection reference.

Coupling Calculator

Flange Coupling Details

Unit System
SI (mm, Nm, MPa) Imperial (in, lb-ft, psi)
Torque (N·m)
N·m

Torque transmitted through the coupling

Bolt Circle Diameter D_p (mm)
mm

Diameter through the bolt centres

Number of Bolts

Typically 4–12 for flange couplings

Bolt Diameter d_b (mm)
mm

Nominal bolt shank diameter

Flange Thickness t (mm)
mm

Thickness of each flange half at the bolt circle

Allowable Shear Stress (MPa)
MPa

Bolt allowable shear (before service factor)

Allowable Bearing Stress (MPa)
MPa

Flange allowable bearing/crushing stress

Decimal Precision
Auto-calculate instantly

Rated Torque Capacity

7,238N·m

Lesser of the bolt-shear limit (7,238) and the bearing limit (17,280).

Capacity exceeds applied torque
Bolt Shear Stress

22.1MPa

Bearing Stress

13.89MPa

Service Factor

3.619×

Required Bolt Dia (Shear)

5.947mm

Required Bolt Dia (Bearing)

1.852mm

Flange Shear Stress

5.659MPa

SF — Shear

3.619×

SF — Bearing

8.64×

Bolt Shear Stress

22.1MPa

τ_b = 2T/(n·A_b·D_p)

Bearing Stress

13.89MPa

σ_b = T/(n·t·d_b·D_p/2)

Service Factor

3.619×

Capacity / applied torque

Required Bolt Dia (Shear)

5.947mm

For target shear allowable

Required Bolt Dia (Bearing)

1.852mm

For target bearing allowable

Flange Shear Stress

5.659MPa

At the hub-flange junction

SF — Shear

3.619×

τ_allow / τ_b

SF — Bearing

8.64×

σ_allow / σ_b

Result Summary

Bolt Circle Diameter150.00 mm
Number of Bolts6
Bolt Diameter16.00 mm
Flange Thickness20.00 mm
Bolt Shear Stress22.10 MPa
Bearing Stress13.89 MPa
Torque Capacity7,238 N·m
VerdictAdequate (SF 3.619×)
Estimated Result — Results use classical bolted-joint shear and bearing theory with equal bolt sharing and elastic material behaviour. Real couplings must also satisfy hub, key and shaft capacity, fatigue limits, balance quality and alignment tolerances per the governing standard. Verify final designs with a qualified engineer.

Interactive Diagram

Bolts on pitch circle Bolt circle D_p Torque / adequate Under-capacity

Diagram updates live with your inputs — the bolt circle, bolt count, and status indicator reflect the current flange coupling.

Visualizations

Torque — Capacity vs Applied (N·m)

7,238N·mShear Capacity
17,280N·mBearing Capacity
7,238N·mRated Capacity
2,000N·mApplied Torque

Utilization (Applied / Capacity)

T / T_max28%

Formula

Bolt shear stress is the transmitted torque shared equally across the bolt circle and resisted by the bolt areas at the pitch radius. Bearing stress is the compression of the bolt against the flange hole wall over the projected bearing area.

τ_b = 2T / (n · A_b · D_p) ; σ_b = T / (n · t · d_b · D_p / 2)

Alternative Form

T_shear = n · A_b · D_p · τ_allow / 2 ; T_bearing = n · t · d_b · D_p · σ_allow / 2

Variables

SymbolNameUnitDescription
TApplied torqueN·mTorque transmitted through the coupling
nNumber of bolts-Bolts sharing the torque equally
A_bBolt areamm²A_b = π·d_b²/4, shear cross-section of one bolt
D_pBolt circle diametermmDiameter through the bolt centres
tFlange thicknessmmThickness of each flange half at the bolt circle
d_bBolt diametermmNominal bolt shank diameter
τBolt shear stressMPaAverage shear in each bolt
σBearing stressMPaCrushing stress of bolt against flange

Explanation

The bolts lie on a circle of diameter D_p, so the tangential force per bolt is F = T/(n·D_p/2) = 2T/(n·D_p). Dividing by the bolt area A_b gives the shear stress τ_b. The bearing (crushing) stress on the flange hole wall is the same tangential force spread over the projected area n·t·d_b, giving σ_b = T/(n·t·d_b·D_p/2). Each mode has its own allowable, and the rated capacity is the smaller of the two torque limits.

Derivation

Torque equilibrium about the shaft axis: T = n · F_b · (D_p/2), where F_b is the tangential force resisted by each bolt. Shear stress τ_b = F_b / A_b = (2T/(n·D_p))/A_b = 2T/(n·A_b·D_p). Bearing stress σ_b = F_b·n / (n·t·d_b) = F_b/(t·d_b) = 2T/(n·D_p·t·d_b) = T/(n·t·d_b·D_p/2). Multiplying by the respective allowable and dividing by 2 yields the torque limits T_shear and T_bearing.

Step-by-Step Calculation

Follow each step to understand how the result is calculated from your inputs.

Step 1

Compute the bolt cross-sectional area from its diameter.

A_b = π·d_b² / 4
Bolt diameter d_b:16.00 mm
Intermediate: A_b = 201.06 mm²
Result: Bolt shear area established
Step 2

Compute bolt shear stress at the flange interface.

τ_b = 2T / (n · A_b · D_p)
T:2000.00 N·m
n:6
Dp:150.00 mm
Intermediate: τ_b = 2000·2000.00 / (6·201.06·150.00)
Result: τ_b = 22.10 MPa
Step 3

Compute bearing (crushing) stress between bolt and flange hole.

σ_b = T / (n · t · d_b · D_p / 2)
t:20.00 mm
d_b:16.00 mm
Intermediate: σ_b = 2000·2000.00 / (6·20.00·16.00·150.00)
Result: σ_b = 13.89 MPa
Step 4

Determine torque capacity from both failure limits.

T_shear = n·A_b·D_p·τ_all/2 ; T_bearing = n·t·d_b·D_p·σ_all/2
Intermediate: Shear limit 7,238 N·m, Bearing limit 17,280 N·m
Result: T_max = min = 7,238 N·m
Step 5

Compare rated capacity against the applied torque to get the service factor and verdict.

SF = T_max / T
Intermediate: SF = 7,238 / 2000.00
Result: SF = 3.619 × → ADEQUATE
Step 6

Verify the flange hub shear at the hub-flange junction.

τ_flange = 2000·T / (π·D_p·t·D_p/2)
Intermediate: Projected hub area π·D_p·t/2
Result: τ_flange = 5.66 MPa
Final Answer
7,238 N·m

Worked Examples

See how the calculator works with different scenarios.

Scenario

A small rigid flange coupling transmits a modest torque between two close-coupled pump shafts.

Inputs

Torque:2000 Nm
Bolt circle D_p:150 mm
Bolts:6
Bolt dia d_b:16 mm
Flange t:20 mm
Allowable shear:80 MPa
Allowable bearing:120 MPa

Calculation

A_b = π·16²/4 = 201.06 mm²; τ_b = 2000·2000/(6·201.06·150) = 22.1 MPa; σ_b = 2000·2000/(6·20·16·150) = 27.8 MPa

Result

T_max ≈ 9066 Nm, SF ≈ 4.5× — comfortably adequate

Interpretation

The coupling has large reserve; a smaller bolt or fewer bolts would still be safe.

Understanding Your Result

Your Result: 7,238 N·m

Typical range: Healthy designs use a service factor of 1.5–3.0×. Yours: 3.619× at 27.63% utilization.

What This Means

Your flange coupling experiences a bolt shear stress of 22.10 MPa and a bearing stress of 13.89 MPa. Its rated torque capacity is 7,238 N·m, giving a service factor of 3.619× against the applied 2000.00 N·m.

Why It Matters

A flange coupling fails by bolt shear or flange crushing — both are sudden and catastrophic. Confirming the rated capacity exceeds the duty torque (with margin for shock) is the core of safe coupling and power-transmission design.

Professional Interpretation

The coupling is adequate with reserve. If the SF is very high, a smaller bolt, fewer bolts, or a tighter bolt circle would be more economical.

Governing Limit

Bolt shear is the limiting failure mode (capacity set by T_shear).

Required Bolt Size

For the target allowables a bolt of 5.95 mm (shear) or 1.85 mm (bearing) would be needed.

Status

Capacity 7,238 N·m ≥ applied 2000.00 N·m — adequate.

Recommendations

  • •Always compare both the bolt-shear and bearing limits; the smaller governs the rated capacity.
  • •If bolt shear governs, increase d_b or D_p first — both raise capacity strongly.
  • •If bearing governs, increase flange thickness t or bolt diameter d_b.
  • •Apply a duty-based service factor of 1.5–3.0× for starting and shock loads.
  • •Confirm hub, key and shaft capacity separately — they may govern before the bolts.

Educational Content

Introduction

Couplings connect rotating shafts to transmit torque, accommodate misalignment and absorb shock. The bolted flange coupling is the simplest rigid type: two flanges bolted face-to-face, where the bolts resist the transmitted torque by shear at the interface and the flanges resist crushing of the bolt holes. A coupling calculator turns classical bolted-joint theory into instant checks of stress, capacity and safety margin.

Concept Explanation

Torque applied to the coupling creates a tangential force in each bolt equal to F = 2T/(n·D_p). Shear stress in the bolt is that force divided by the bolt area A_b. The same tangential force presses each bolt against its hole wall, producing a bearing (crushing) stress over the projected area n·t·d_b. Each mode has an allowable stress; the rated torque capacity is the smaller of the two limits. The service factor compares that capacity to the duty torque.

Applications

▸Close-coupled pumps, compressors and gearboxes
▸Rolling mills, crushers and heavy conveyors (high torque)
▸Power-transmission shaft lines in process plants
▸Marine propulsion and generator set drives
▸Any rigid, precisely-aligned shaft connection
▸Teaching aid for bolted-joint shear and bearing design

Benefits

  • •Instant shear and bearing stress without manual derivation
  • •Both failure modes checked; governing capacity identified automatically
  • •Required bolt diameter feedback for design sizing
  • •Service factor verdict for adequacy under load
  • •Live diagram visualising the bolt circle and torque path

Limitations

  • •Rigid flange couplings only — no flexible-element types
  • •Excludes hub, key and shaft capacity checks
  • •No fatigue, impact or thermal effects
  • •Assumes equal bolt sharing and uniform preload
  • •Not a substitute for code/standard verification

Best Practices

  • •Use an even bolt count on a symmetric pitch circle
  • •Torque bolts in a star pattern to the specified preload
  • •Apply a duty-based service factor (1.5–3.0×) for shock loads
  • •Keep flange thickness proportionate to bolt diameter
  • •Align shafts precisely — rigid couplings tolerate no misalignment

Common Misconceptions

Myth: Only the bolt shear stress matters.
Truth: Bearing (crushing) of the flange hole can govern first, especially with thin flanges or large bolts — always check both.
Myth: More bolts always means more capacity.
Truth: Capacity also depends on bolt circle diameter and bolt area; adding bolts helps but D_p and d_b often dominate.
Myth: A rigid flange coupling handles misalignment.
Truth: Flange couplings are rigid and require precise alignment; misalignment overloads bolts and connected bearings.
Myth: The steady torque is all that matters.
Truth: Starting, braking and shock peaks can far exceed steady torque; size with a service factor, not the nominal value.

Practical Tips

  • •Current service factor is 3.619×. Aim for 1.5–3.0× when the coupling must absorb starting and shock loads.
  • •Bolt shear stress scales with 1/D_p — increasing the bolt circle diameter is the most effective way to raise torque capacity without changing bolt size.
  • •Bearing stress is governed by flange thickness and bolt diameter; thin flanges crush before bolts shear. Keep t reasonably large relative to d_b.
  • •Use an even number of bolts and a balanced bolt circle to avoid eccentric loading and vibration.
  • •Verify both failure modes: the governing (lower) limit sets the rated capacity, not just the bolt shear check.

Common Mistakes

Checking only bolt shear
Always take the minimum of the shear and bearing limits — a thin flange may crush first even when bolts are safe.
Forgetting unit conversion
This tool works in Nm with mm and MPa (or lb-ft with in and psi). Mixing systems silently changes results by large factors.
Ignoring service factor
Duty torque includes starting and shock peaks; divide allowable by a duty-based SF rather than using the steady torque directly.
Over-tightening / uneven bolt pattern
Torque bolts in a star pattern to spec; uneven preload causes local crushing and fatigue at the flange interface.
Assuming flexible behaviour
A flange coupling is rigid; it requires precise shaft alignment or it will overload the bolts and connected bearings.

Assumptions

This calculator makes the following assumptions to provide estimates:

Equal bolt sharing: All bolts carry the torque equally; the bolt circle is symmetric and preload is uniform.
Pure shear at interface: Bolts see direct shear at the flange face; bending and preload effects are neglected.
Rigid flange faces: Flange deformation under load is small; the interface stays planar and transmits shear uniformly.
Static elastic loading: Stresses stay below yield; fatigue, impact and thermal effects are excluded.

Limitations

Be aware of these limitations when using this calculator:

No hub or key check: Shaft, key and hub crushing capacity must be verified separately against the transmitted torque.
Bolt shear only: Bolt tension from preload, fatigue and combined loading are not modelled.
Rigid coupling only: This analysis applies to bolted flange (rigid) couplings, not gear, disc, grid or elastomeric types.
No misalignment loads: Flexible-coupling misalignment forces and damping behaviour are outside this scope.
Single load case: One steady torque is analysed; cyclic, shock and transient spectra need fatigue evaluation.

Frequently Asked Questions

Answers to common questions about this calculator.

What is a coupling?
A coupling is a mechanical device that connects two shafts together to transmit torque while accommodating misalignment, absorbing shock loads, and allowing for thermal expansion. Couplings are essential in rotating machinery including pumps, motors, generators, and gearboxes.
What types of couplings exist?
Common coupling types include: rigid couplings (flange, sleeve), flexible couplings (gear, grid, disc, diaphragm), elastomeric couplings (jaw, tire, donut), fluid couplings, and specialty couplings (universal joints, Oldham, Schmidt). Each type has distinct torque, misalignment, and damping characteristics.
What is a flange coupling?
A flange coupling consists of two flanges, each keyed to a shaft end, bolted together face-to-face. The flanges have hubs that fit over the shafts and a bolt circle for the connecting bolts. Flange couplings are rigid, requiring precise shaft alignment, and transmit high torques.
How is bolt shear stress calculated in a flange coupling?
Bolt shear stress in a flange coupling is τ_b = 2T/(n·A_b·D_p), where T is torque, n is number of bolts, A_b is bolt cross-sectional area, and D_p is bolt circle diameter. The bolts are assumed to share the torque equally, and shear acts at the flange interface.
How is bearing stress calculated in a coupling?
Bearing (crushing) stress between the bolt and flange hole is σ_b = T/(n·t·d_b·D_p/2), where t is flange thickness and d_b is bolt diameter. The bearing area is the projected area of the bolt shank against the flange hole wall.
What is a flexible coupling?
A flexible coupling accommodates misalignment between connected shafts while transmitting torque. It contains a flexible element (elastomeric, metallic disc, or grid spring) that deforms elastically to absorb angular, parallel, and axial misalignment without overloading connected equipment.
What is a gear coupling?
A gear coupling uses crowned external gear teeth on the hubs that mesh with internal gear teeth on a floating sleeve. The gear teeth allow angular misalignment while transmitting high torque. Gear couplings are used in heavy industrial applications like rolling mills and crushers.
What is a disc coupling?
A disc coupling uses thin metallic diaphragms or disc packs bolted alternately to the driving and driven hubs. The discs flex to accommodate misalignment while maintaining torsional stiffness. Disc couplings are maintenance-free, handle high speeds, and require no lubrication.
What is a jaw coupling?
A jaw coupling has two metal hubs with projections (jaws) that interlock with a flexible elastomeric spider. The spider compresses under load, absorbing shock and vibration while accommodating misalignment. Jaw couplings are common in small to medium power applications.
How do I select a coupling?
Coupling selection involves: torque and speed requirements, shaft diameters, misalignment type and magnitude, space constraints, operating temperature, environmental conditions (moisture, chemicals), service factor, and cost. The coupling torque rating must exceed the maximum expected torque including starting and shock loads.
What is the service factor in coupling selection?
The service factor (SF) multiplies the nominal torque to account for load variations, starting torque, and shock loads. Typical SF: 1.0-1.5 for uniform loads (fans, pumps), 1.5-2.0 for moderate shock (compressors, conveyors), 2.0-3.0 for heavy shock (crushers, mills).
What is coupling misalignment?
Coupling misalignment occurs when the rotational axes of the two connected shafts are not collinear. Three types: angular misalignment (shaft axes at an angle), parallel misalignment (axes parallel but offset), and axial misalignment (end-to-end gap variation). Flexible couplings accommodate these to varying degrees.
How does coupling balance affect performance?
Coupling imbalance causes vibration, noise, and accelerated wear of bearings and seals. High-speed couplings require precision balancing to ISO 1940 grades G6.3 (general) or G2.5 (precision). Balanced couplings have correction planes for adding balance weights.
What is coupling torsional stiffness?
Torsional stiffness is the torque required per unit angular deflection (Nm/rad). A stiff coupling (disc, diaphragm) provides precise angular transmission. A soft coupling (elastomeric, grid) provides torsional damping to reduce shock loads and vibration at the expense of positional accuracy.
What is the bolt circle diameter?
The bolt circle diameter (D_p or D_bc) is the diameter of the circle passing through the centers of the coupling bolts. It is a critical dimension in flange coupling design because the torque capacity is proportional to D_p — larger bolt circle provides higher torque capacity for the same bolt size.
How many bolts are used in a flange coupling?
Standard flange couplings use 4-12 bolts depending on size and torque requirements. Small couplings (25-50 mm shaft) use 4 bolts. Medium (50-100 mm) use 6-8 bolts. Large (>100 mm) use 8-12 or more. The number is typically even for balanced force distribution.
What is the flange thickness?
Flange thickness (t_f) is the thickness of each flange half at the bolt circle. It must be sufficient to prevent bending under bolt preload and to provide adequate bearing area for the bolts. Typical thickness ranges from 10-50 mm depending on coupling size and torque.
What materials are used for couplings?
Coupling materials: ductile iron (most common, good strength/cost), cast steel (high strength), forged steel (critical applications), aluminum (light weight), stainless steel (corrosion resistance), and engineered plastics (low cost, light duty). Material selection depends on strength, weight, and environmental requirements.
What is coupling lubrication?
Gear and grid couplings require periodic lubrication with extreme pressure (EP) grease to prevent wear of the gear teeth or grid spring. Disc and diaphragm couplings are maintenance-free (no lubrication needed). Elastomeric couplings require no lubrication but the spider may need periodic replacement.
What is coupling failure?
Coupling failure modes: bolt shear (overload or fatigue), key failure (shear or crushing), flexible element fatigue (elastomeric cracking, disc fatigue), gear tooth wear (lubrication failure), corrosion, fretting (micro-motion wear), and misalignment-induced accelerated wear.
How do I calculate coupling torque capacity?
Coupling torque capacity is calculated from bolt shear and bearing limits: T_shear = n·A_b·D_p·τ_all/2, T_bearing = n·t·d_b·D_p·σ_all/2. The rated torque is the minimum of these limits, derated by the service factor. The coupling must also be checked for hub key and shaft capacity.
What is the difference between rigid and flexible couplings?
Rigid couplings (flange, sleeve) require precise shaft alignment and transmit torque without compliance. They are used where shafts are already well-aligned (close-coupled pumps, gearboxes). Flexible couplings accommodate misalignment and provide vibration damping but may introduce backlash.
What is a grid coupling?
A grid coupling uses a serpentine steel grid spring that fits into slots on both hubs. The grid deflects under load, providing torsional flexibility and damping. Grid couplings handle high torque, accommodate misalignment, and are used in heavy industrial applications like conveyors and mills.
What is a diaphragm coupling?
A diaphragm coupling uses thin metal diaphragms welded or bolted between hubs. The diaphragms flex axially and angularly while maintaining torsional stiffness. Diaphragm couplings are used in high-speed, high-temperature applications like gas turbines and turbomachinery.
How does temperature affect coupling selection?
Temperature affects: elastomeric elements (soften above 80°C, harden below -20°C), lubricant viscosity, metal dimensions (thermal expansion), and material strength (reduction at high temperature). High-temperature couplings use metal discs or diaphragms with appropriate coatings.
What is a universal joint (U-joint)?
A universal joint connects two shafts at an angle (up to 30-45°). It uses a cross-shaped trunnion with needle bearings at each arm. U-joints are used in automotive driveshafts, industrial PTO shafts, and steering columns. A single U-joint creates velocity fluctuation; constant-velocity joints eliminate this.
What is an Oldham coupling?
An Oldham coupling consists of three discs: two hubs keyed to the shafts and a floating center disc with perpendicular slots. The center disc slides in the hub slots to accommodate parallel misalignment. Oldham couplings transmit moderate torque with zero backlash and are used in servo applications.
What is a Schmidt coupling?
A Schmidt coupling is a type of flexible coupling that accommodates large parallel misalignment (up to several shaft diameters) using multiple linked discs. It maintains constant angular velocity and is used where precise positioning is needed despite misalignment.
How do I install a coupling?
Coupling installation: 1) Clean shafts and coupling bores. 2) Apply anti-seize to prevent fretting. 3) Using a coupling installer or press, mount hubs on shafts (avoid hammering). 4) For rigid couplings, align shafts precisely (0.05mm TIR). 5) Torque bolts to specification using a pattern. 6) Check runout.
What is the maximum speed of a coupling?
Maximum coupling speed is limited by centrifugal stresses in rotating elements and balance quality. Elastomeric couplings are limited to 5000-8000 RPM. Disc/diaphragm can reach 30000+ RPM. Gear couplings are limited by lubrication method to 6000-20000 RPM.
How do I align shafts for a coupling?
Shaft alignment uses dial indicators or laser systems to measure and correct: angular misalignment (gap variation at 0°/180°/90°/270°) and parallel misalignment (offset at top/bottom and sides). Typical tolerances: 0.05mm for rigid couplings, 0.1-0.5mm for flexible couplings.
What is a fluid coupling?
A fluid coupling (fluid drive) uses hydraulic fluid to transmit torque between an impeller (input) and runner (output). It provides smooth torque transmission, vibration damping, and overload protection. Fluid couplings allow the motor to start under load and limit starting torque.
What is coupling torsional vibration?
Torsional vibration is oscillatory angular motion superimposed on steady rotation, caused by engine firing pulses, gear meshing, or load variations. Couplings can mitigate torsional vibration through damping (elastomeric) or by tuning system natural frequencies (stiffness selection).
How does coupling weight affect system dynamics?
Coupling weight affects: bearing loads, critical speeds (heavy coupling lowers natural frequency), starting torque (higher inertia requires more starting torque), and overall system dynamics. Lightweight couplings (aluminum, composite) are preferred for high-speed applications.
Can I use this calculator for grid coupling design?
This calculator focuses on bolted flange coupling analysis (bolt shear, bearing, required diameter). For grid, gear, disc, or elastomeric couplings, use manufacturer selection software that accounts for the specific design geometry and material properties of each type.
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Glossary

Technical terms used in mortgage calculations explained in plain language.

Bolt Circle Diameter (D_p)
The diameter of the circle through the centres of the coupling bolts. Torque capacity is directly proportional to D_p, so a larger pitch circle yields higher capacity for the same bolt size.
Bolt Shear Stress (τ_b)
Average shear stress carried by each bolt at the flange interface, τ_b = 2T/(n·A_b·D_p). It must stay below the allowable shear stress of the bolt material.
Bearing (Crushing) Stress (σ_b)
Compressive stress between the bolt shank and the flange hole wall over the projected bearing area n·t·d_b·D_p/2. Limits flange crushing.
Torque Capacity (T_max)
The lesser of the bolt-shear limit and the bearing limit. The selected coupling must carry at least the maximum expected applied torque.
Service Factor (SF)
Ratio of rated torque capacity to the applied torque. A value above 1.0 indicates adequate margin; multiply nominal duty torque by a duty-based SF when sizing.
Flange Thickness (t)
Thickness of each flange half at the bolt circle. Provides the bearing area resisting bolt crushing and resists bending under bolt preload.
Bolt Area (A_b)
Tensile/shear cross-sectional area of one bolt, A_b = π·d_b²/4. Governs both the shear and bearing limits.

Authoritative References

Trusted sources and standards referenced by this calculator.

Applicable Standards

AGMA 9000ISO 14691DIN 740

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Page Information

Last Updated:

August 2026

Version:

2.1.0

License:

Free to use for educational and professional purposes.