Shaft Key Shear & Bearing Stress Calculator — Required Key Length
Check a rectangular shaft key from torque or power and speed, or size the required effective key length from allowable shear and bearing stresses with an optional design/load factor and available-length check.
Enter the known values and review the calculated result
Input parameters
Use consistent values and select the intended engineering units.
Calculation mode
Load input
Power input
Key & shaft geometry
Design factor (optional)
Allowable stresses
Results
Calculation tools Save, export and manage your results
Save your calculation, export available results, or store a finalized engineering artifact in your account.
Method, application and limitations
Review the calculation method, intended application and engineering assumptions before using the result in a design decision.
Formula and calculation method
Shaft key shear, bearing and required-length formulas
The calculator models torque transfer through a rectangular shaft key. The transmitted torque is converted into a tangential force acting at the shaft radius, and the key is then evaluated for average shear stress and nominal bearing stress.
1. Design torque
When torque is entered directly:
Td = Kd · T
When transmitted power and rotational speed are entered:
ω = 2 · π · n / 60
T = P / ω
Td = Kd · T
where:
- T — nominal transmitted torque [N·m]
- Td — design torque after application of the design/load factor [N·m]
- Kd — design/load factor [-], with Kd ≥ 1
- P — transmitted power [W]
- n — rotational speed [rpm]
- ω — angular speed [rad/s]
If Kd is not entered, the calculator uses Kd = 1.
2. Tangential force at the shaft surface
F = 2 · Td / d
where d is the shaft diameter [m] and F is the transmitted tangential force [N].
3. Key shear stress
The nominal shear area is:
Aτ = b · l
Therefore:
τ = F / (b · l)
or, after substituting the tangential-force expression:
τ = 2 · Td / (d · b · l)
where:
- τ — nominal key shear stress [Pa]
- b — key width [m]
- l — effective key length [m]
4. Key bearing stress
The simplified bearing model uses one-half of the key height:
heff = h / 2
The projected bearing area is:
Ac = (h / 2) · l
Therefore:
σc = F / ((h / 2) · l)
or:
σc = 4 · Td / (d · h · l)
where h is the total key height [m] and σc is the nominal bearing stress [Pa].
5. Stress utilization
When allowable stresses are supplied, the calculator evaluates:
ητ = τ / τallow
ηc = σc / σc,allow
ηmax = max(ητ, ηc)
A utilization of 1.0 corresponds to the entered allowable value. The larger available utilization identifies the governing checked criterion.
6. Required effective key length
Required length from the shear criterion:
lreq,τ = F / (τallow · b)
Required length from the bearing criterion:
lreq,c = F / (σc,allow · (h / 2))
The governing required length is:
lreq = max(lreq,τ, lreq,c)
Both allowable stresses are required in the dedicated required-length modes.
7. Nominal torque and power capacity
In stress-check modes, when the corresponding allowable stresses are entered, the calculator can invert the stress equations to determine nominal torque capacity.
Tcap,τ = τallow · b · l · d / (2 · Kd)
Tcap,c = σc,allow · (h / 2) · l · d / (2 · Kd)
Tcap = min(Tcap,τ, Tcap,c)
In power-and-speed stress-check mode:
Pcap = Tcap · ω
8. Available-length check
In required-length mode, an optional available effective key length can be compared with the calculated requirement:
Δl = lavail - lreq
Rl = lavail / lreq
The calculator also monitors the ratio l/d or lreq/d. A value greater than 1.5 produces an engineering warning in the implemented screening logic.
When to use this calculator
When to use this calculator
Use this calculator to perform a simplified strength check or preliminary sizing of a rectangular shaft key transmitting torque between a shaft and a hub such as a gear, pulley, sprocket or coupling.
Stress check from torque
Use Stress check — from torque when the nominal transmitted torque is already known. Enter the shaft diameter, key width, key height and effective key length. The calculator determines the design torque, tangential force, nominal key shear stress and nominal bearing stress.
Stress check from power and speed
Use Stress check — from power & speed when transmitted power and shaft speed are known instead of torque. The calculator first converts power and rotational speed into torque and then performs the same shear and bearing checks.
Required key length from torque
Use Required length — from torque when the shaft diameter and key cross-section are known and the objective is to determine the effective key length required to satisfy entered allowable shear and bearing stresses.
Required key length from power and speed
Use Required length — from power & speed when the design load is defined by transmitted power and rotational speed. Both allowable stresses are required to determine the governing key length.
Allowable-stress verification
In stress-check modes, allowable shear and bearing stresses are optional. Without them, the calculator still determines nominal stresses but does not perform a complete two-criterion allowable-stress verification. When both limits are entered, it also reports utilization, the governing criterion, required length and nominal torque capacity.
Design/load factor
Use Kd when the nominal transmitted torque must be multiplied by a chosen design or load factor before the key is evaluated. The factor must be at least 1.0. Avoid applying the same service, shock or safety allowance twice if it has already been included in the entered torque or allowable stresses.
When this calculator is not sufficient
This calculator does not select a standard key width, height, keyseat depth or tolerance from DIN, ISO, ANSI or another dimensional standard. Those dimensions must be supplied separately.
It also does not calculate shaft stress concentration caused by the keyway, detailed keyway flank contact pressure, fatigue life, fretting, wear, fit effects, multiple-key load sharing, spline behavior or local finite-element stresses. These effects may require separate verification for final design.
How to interpret the result
How to interpret the results
Nominal key shear stress, τ
τ is the average shear stress calculated over the effective shear area b·l. For unchanged geometry, it increases directly with design torque. Increasing key width or effective key length reduces the calculated shear stress.
Nominal bearing stress, σc
σc is the nominal compressive bearing stress calculated using a projected bearing height of h/2. Increasing key height or effective key length reduces this value, while increasing design torque raises it.
Tangential force, F
F represents the tangential load transferred at the shaft surface. It increases with design torque and decreases as shaft diameter increases.
Shear and bearing utilization
ητ compares key shear stress with the entered allowable shear stress. ηc compares nominal bearing stress with the entered allowable bearing stress.
- Utilization < 1.0: the evaluated nominal stress remains below its entered allowable.
- Utilization = 1.0: the calculated nominal stress equals the entered allowable.
- Utilization > 1.0: the evaluated nominal stress exceeds its entered allowable.
The larger available utilization is reported as the governing checked criterion.
Required effective key length
lreq,τ is the minimum effective length produced by the shear criterion, while lreq,c is the corresponding length from the bearing criterion. The calculator uses the larger value as lreq.
In the dedicated design modes, an optional available effective length can be entered. A negative length margin means that the available length is below the calculated requirement.
Nominal torque capacity
Tcap is the lower of the shear-based and bearing-based nominal torque capacities calculated from the entered allowable values, geometry and Kd. In power mode, the corresponding power capacity is evaluated at the entered rotational speed.
Engineering status — stress-check modes
- Safe: both allowable stresses are available, neither checked utilization exceeds 1.0, and l/d does not exceed 1.5.
- Unsafe: at least one checked utilization exceeds 1.0.
- Warning: only one allowable stress is available, or the effective key length exceeds 1.5 shaft diameters without an allowable-stress exceedance.
- Info: nominal stresses were calculated without allowable-stress verification and the long-key warning is not active.
Engineering status — required-length modes
- Safe: the entered available effective length is at least the calculated requirement and lreq/d does not exceed 1.5.
- Unsafe: the entered available effective length is below lreq.
- Warning: the required effective length exceeds 1.5 shaft diameters.
- Info: the required length was calculated but no available effective length was supplied for comparison.
A favorable result means only that the nominal shear and/or bearing criteria evaluated by this calculator satisfy the entered limits. It does not establish complete safety of the shaft-key-hub connection or verify other relevant failure modes.
Calculation example
Worked example — shaft key stress check from torque
A rectangular shaft key must transmit a nominal torque of 500 N·m. The shaft diameter is 50 mm, the key is 14 mm wide, 9 mm high and has an effective length of 60 mm. A design/load factor of 1.25 is applied.
The entered allowable shear stress is 70 MPa and the entered allowable bearing stress is 140 MPa.
Input data
- T = 500 N·m
- Kd = 1.25
- d = 50 mm = 0.050 m
- b = 14 mm = 0.014 m
- h = 9 mm = 0.009 m
- l = 60 mm = 0.060 m
- τallow = 70 MPa
- σc,allow = 140 MPa
Step 1 — design torque
Td = Kd · T
Td = 1.25 · 500 = 625 N·m
Step 2 — tangential force
F = 2 · Td / d
F = (2 · 625) / 0.050 = 25,000 N
Step 3 — key shear stress
τ = F / (b · l)
τ = 25,000 / (0.014 · 0.060)
τ = 29.76 MPa
Step 4 — bearing stress
The effective bearing height used by the calculator is:
h / 2 = 0.009 / 2 = 0.0045 m
σc = F / ((h / 2) · l)
σc = 25,000 / (0.0045 · 0.060)
σc = 92.59 MPa
Step 5 — utilization
ητ = 29.76 / 70 = 0.425
ηc = 92.59 / 140 = 0.661
Bearing is the governing checked criterion because its utilization is higher.
Step 6 — required effective key length
From shear:
lreq,τ = 25,000 / (70 · 106 · 0.014)
lreq,τ = 25.51 mm
From bearing:
lreq,c = 25,000 / (140 · 106 · 0.0045)
lreq,c = 39.68 mm
Therefore:
lreq = 39.68 mm
Step 7 — nominal torque capacity
The shear-based nominal torque capacity is 1176 N·m and the bearing-based nominal torque capacity is 756 N·m.
The governing capacity is therefore:
Tcap = 756 N·m
Interpretation
Both calculated nominal stresses are below the entered allowable values. Bearing governs the check with a utilization of approximately 0.661. The entered effective length of 60 mm also gives l/d = 1.20, which remains below the calculator's 1.5 warning threshold.
This result verifies only the simplified key shear and bearing criteria represented by the calculator. Shaft keyway stress concentration, fatigue, fit, tolerances, local contact effects and other relevant connection failure modes still require separate consideration where applicable.
Assumptions and limitations
Assumptions and limitations
- The calculation represents a simplified rectangular shaft key transmitting torque between a shaft and hub.
- Torque is converted into a tangential force acting at the shaft radius using F = 2Td/d.
- The load is treated as uniformly distributed over the effective key length for the nominal stress calculation.
- The shear area is modeled as b·l.
- The bearing calculation assumes an effective projected bearing height equal to h/2. Actual keyseat depths and asymmetric shaft/hub engagement are not modeled.
- The entered length represents effective load-carrying key length. It may differ from the physical overall length where end geometry does not carry load uniformly.
- Kd is a user-selected design/load multiplier. The calculator does not determine an appropriate service, shock or duty factor automatically.
- Allowable shear and bearing stresses are user inputs. The calculator does not derive them from material grade, yield strength, hardness or a specific design standard.
- The calculator does not automatically select standard key width, height, keyseat depth, tolerance or fit from DIN, ISO, ANSI or another key standard.
- The l/d > 1.5 condition is an implemented engineering warning. It is not a standard-compliance assessment and does not by itself establish failure.
- The model does not calculate local stress concentration in the shaft caused by the keyway.
- Shaft and hub strength outside the simplified bearing criterion are not verified.
- Fatigue, alternating or reversing torque, fretting, wear, plastic deformation, local contact-pressure distribution, backlash and manufacturing imperfections are not explicitly modeled.
- Multiple keys and non-uniform load sharing between keys are outside the calculation.
- Splines, tapered keys, Woodruff keys and other connection geometries may require different design models.
- Temperature effects and environmental degradation are included only indirectly if they have already been reflected in the entered allowable stresses or design load.
- Final design should also consider the applicable dimensional and strength standards, shaft fatigue and stress concentration, hub geometry, fits and tolerances, manufacturing requirements and any other relevant failure modes.