CTR K

Shaft Keys Calculator — Shear, Bearing & Key Length (DIN 6885 / ISO 3912)

Governing standard: DIN 6885· DIN 6885:1968 Part 1 (parallel keys & keyways) · ISO 3912 · Woodruff keys DIN 6888 · Spline strength ISO 4156 / ANSI B92.1

How DIN 6885 works — the method explained

The MechanixCalc shaft key calculator sizes and verifies parallel keys to DIN 6885 / ISO 3912 — the governing standards for rectangular shaft-hub keyway connections. Enter the shaft diameter, key geometry, torque, application factor and materials, and the tool returns the shear stress, bearing (surface) pressure, minimum key length and safety factors for both failure modes in a single pass.

Built for drivetrain, gearbox and general power-transmission engineers, the calculator also covers Woodruff keys to DIN 6888 with automatic key selection from the standard table, spline strength analysis to ISO 4156 / ANSI B92.1, and multi-key load sharing for two- or three-key arrangements — all backed by a standards-cited PDF engineering report.

What this calculator does

  • DIN 6885 / ISO 3912 parallel key shear and bearing safety factors with application factor Ka
  • Minimum key length calculation and DIN 6885 auto-size lookup from the standard table
  • Woodruff key analysis to DIN 6888 with automatic key selection for shaft diameter
  • Spline strength analysis per ISO 4156 / ANSI B92.1 — contact pressure and shear
  • Multi-key load sharing comparison for 1, 2 or 3 keys with fit-tolerance k_s factor
  • Key and hub material library (C45, 42CrMo4, cast iron, S235, S355) with custom override
  • Branded PDF engineering report with the full method and standard reference shown

Method & formulas

Shear strength (DIN 6885)

The key is loaded in shear across the plane at the shaft-hub interface. The tangential force is derived from the design torque (nominal torque amplified by the application factor Ka), and the shear stress is distributed over the shear area, which is the key width b multiplied by the effective engaged length L. For multiple keys, DIN 6885 / Roloff-Matek applies a load-sharing factor k_s (0.75 for two keys, 0.67 for three) because tolerance stack-up prevents perfect equal distribution.

Shear stress
τ = (T_d × 2000) / (d × b × L_eff × n_k_eff)

where τ = shear stress (MPa); T_d = T × Ka = design torque (N·m); d = shaft diameter (mm); b = key width (mm); L_eff = effective key length (mm); n_k_eff = n_keys × k_s = effective number of keys

Shear safety factor
SF_shear = τ_allow / τ

where τ_allow = allowable shear stress of the key material, reduced by the fit-tolerance factor Kt (Normal fit: Kt = 1.0; Close fit: Kt = 0.9; Loose fit: Kt = 1.15)

Bearing (surface) pressure — DIN 6885

The bearing failure mode is compressive crushing of the hub keyway flank. The bearing force is the same tangential force, but the contact area is the hub engagement height (h − t1) multiplied by the effective length. DIN 6885 uses the asymmetric keyway geometry, where t1 is the shaft slot depth and h is the total key height, giving the true hub-flank contact height h − t1 rather than the simplified h/2 approximation. The allowable bearing pressure depends on the hub material and surface hardness.

Bearing pressure
p = (2 × T_d × 1000) / (d × (h − t1) × L_eff × n_k_eff)

where p = bearing pressure (MPa); T_d = design torque (N·m); d = shaft diameter (mm); h = key height (mm); t1 = shaft keyway depth (mm); h − t1 = hub engagement height (mm); L_eff = effective key length (mm); n_k_eff = effective number of keys

Bearing safety factor
SF_bearing = p_allow / p

where p_allow = allowable bearing pressure for the hub material (MPa); p = actual bearing pressure (MPa)

Minimum key length and design guidance

The minimum key length required for each failure mode is derived by rearranging the shear and bearing formulae. The governing minimum is the larger of the two, and the recommended design length adds a 50% margin (L_rec = 1.5 × L_min) while also respecting the 1.5 × d rule of thumb. The DIN 6885 auto-size lookup selects the standard b × h × t1 × t2 dimensions directly from the shaft diameter, so the designer needs only to confirm the key length against the hub face width.

Status thresholds used by the tool: SF_min ≥ 2.0 → SAFE; 1.2 ≤ SF_min < 2.0 → MARGINAL; SF_min < 1.2 → FAIL.

Worked example

Check a single DIN 6885 parallel key on a 40 mm diameter steel shaft transmitting 200 N·m nominal torque (Ka = 1.0, no shock). Key: b = 12 mm, h = 8 mm, t1 = 5 mm (standard DIN 6885 row for d = 38–44 mm), L = 50 mm. Key material: C45 (τ_allow = 290 MPa, Normal fit Kt = 1.0). Hub material: S235 (p_allow = 140 MPa).

Given

  • Shaft diameter d40 mm
  • Nominal torque T200 N·m
  • Application factor Ka1.0 (no shock)
  • Key width b12 mm
  • Key height h8 mm
  • Shaft keyway depth t15 mm
  • Key length L50 mm
  • Key material τ_allow290 MPa (C45, Normal fit)
  • Hub p_allow140 MPa (S235)

Result

  • Shear stress τ16.7 MPa
  • Bearing pressure p66.7 MPa
  • SF_shear17.4
  • SF_bearing2.10
  • SF_min (governing)2.10 — SAFE
  1. Design torque: T_d = T × Ka = 200 × 1.0 = 200 N·m.
  2. Shear stress: τ = (T_d × 2000) / (d × b × L) = (200 × 2000) / (40 × 12 × 50) = 400 000 / 24 000 = 16.7 MPa.
  3. Shear safety factor: SF_shear = τ_allow / τ = 290 / 16.7 ≈ 17.4 — shear is very generous.
  4. Hub engagement height: h − t1 = 8 − 5 = 3 mm.
  5. Bearing pressure: p = (2 × T_d × 1000) / (d × (h − t1) × L) = (2 × 200 × 1000) / (40 × 3 × 50) = 400 000 / 6 000 = 66.7 MPa.
  6. Bearing safety factor: SF_bearing = p_allow / p = 140 / 66.7 ≈ 2.10 — bearing governs.
  7. Minimum safety factor: SF_min = min(17.4, 2.10) = 2.10 → SAFE (threshold ≥ 2.0).

Illustrative — verify against your actual geometry, material allowables and application factor. The tool computes both failure modes simultaneously and selects the standard key dimensions automatically from the DIN 6885 table.

Frequently asked questions

Which standard does this shaft key calculator use?

Parallel key strength is evaluated to DIN 6885 / ISO 3912 — the standards for rectangular parallel keys and keyways. Key dimensions are auto-selected from the DIN 6885 Part 1 table. Woodruff keys are analysed to DIN 6888, and spline connections follow ISO 4156 / ANSI B92.1. The governing standard and method are shown in the generated PDF report.

What is the difference between shear and bearing failure for a key?

Shear failure is sliding of the key across the shaft–hub interface plane; it depends on the key width, length and the key material's shear strength. Bearing (surface) failure is compressive crushing of the hub keyway flank; it depends on the hub engagement height (h − t1), key length and the hub material's allowable bearing pressure. Both modes are checked, and the lower safety factor governs. For soft hubs (cast iron, soft steel), bearing typically governs at short key lengths.

How does multi-key load sharing work?

DIN 6885 and Roloff-Matek apply a load-sharing factor k_s because manufacturing tolerances prevent keys from sharing the load equally. The effective number of keys is n_keys × k_s: for two keys k_s = 0.75 (effective 1.5 keys); for three keys k_s = 0.67 (effective 2.0 keys). A single key always carries its full load (k_s = 1.0). The calculator applies this correction automatically and also lets you adjust k_s manually.

When should I use a Woodruff key instead of a parallel key?

Woodruff keys (DIN 6888) are self-aligning — their circular disc shape seats automatically in the shaft keyway, making them ideal for tapered shaft ends, light machinery and instruments where assembly alignment matters. However, they cut deeply into the shaft, reducing its cross-section more than a parallel key does, and they are not suitable for high torque loads — the rule of thumb is to switch to a parallel key for torques above roughly 200 N·m.

Is the shaft keys calculator free?

You can use it during a free 30-minute preview session with no sign-up required, and a free 14-day account trial unlocks every calculator with no credit card needed. The branded PDF engineering report and saved calculations are part of a paid plan.

Related calculators

Run the Shaft Keys on your own numbers

Free 30-minute preview — no sign-up. A free 14-day account trial unlocks every tool and the branded PDF report, no credit card required.

Start free