Key Size Calculator

A machine key transmits torque between a shaft and a hub (a pulley, gear, or coupling) by sitting in matching keyways cut into both parts. Sizing a key correctly means two separate steps: first selecting the key's cross-section (width and height) based on the shaft diameter using a recognized standard, and second calculating the minimum key length needed to safely carry the actual transmitted torque without failing.

Step 1 — Standard cross-section: key width and height are not arbitrary; they follow standard proportions (this calculator uses IS 2048-style parallel key sizing) tied directly to shaft diameter, since the key must fit a keyway of a size the hub manufacturer will also expect. Picking the standard size for a given shaft diameter ensures compatibility with off-the-shelf pulleys, gears and couplings.

Step 2 — Required length, from two independent strength checks: once width and height are fixed, the key's length must be long enough to survive two different failure modes, and the longer of the two results governs:

Shear failure: L = 2T / (τ × W × D)

The shear check considers the key failing by shearing straight across its width, along the shaft's outer surface. The torque T is resisted by the shear stress τ acting over the key's shear area (width W × length L), at the shaft's radius (D/2) as the moment arm — rearranging that torque balance for length gives the formula above.

Crushing failure: L = 4T / (σc × H × D)

The crushing (bearing) check considers a different failure mode — the sides of the key being crushed by the contact pressure against the keyway walls. Only half the key's height (H/2) is in bearing contact on each side, and the allowable bearing (compressive) stress σc is normally taken as roughly twice the allowable shear stress τ for the same key material, since materials generally tolerate more compressive stress than shear stress before yielding.

Whichever of the two calculated lengths is larger is the governing case — the key must be at least that long to avoid failing in that mode. A practical design then adds a margin (this calculator applies 15%) on top of the governing theoretical length, both for a safety margin and because standard key stock is typically only available in fixed length increments.

1. Checking only shear or only crushing, not both. The two failure modes are independent and depend differently on key width versus height — skipping one check can miss the actual governing (weaker) failure mode, especially since crushing often governs for wider, shorter keys and shear can govern for narrower, taller ones.

2. Using the shaft diameter as the moment arm without dividing by 2. Torque acts at the shaft's radius, not its full diameter — using diameter directly instead of radius in the torque balance halves the calculated stress (or doubles the calculated required length), a common algebra slip when rearranging the torque equations.

3. Assuming full key height is in bearing contact for the crushing check. Only half the key height (H/2) is engaged in bearing contact on each side of a standard sunk key — using the full height H instead of H/2 in the crushing formula understates the actual bearing stress (or overstates the safe length).

4. Using a non-standard width/height without checking hub compatibility. A calculated "ideal" cross-section that doesn't match the shaft diameter's standard key size may not fit a purchased pulley, gear, or coupling's factory-cut keyway — stick to the standard size for the shaft diameter unless the mating hub is also custom-made.

5. Ignoring stress concentration at the keyway. Cutting a keyway into a shaft removes material and creates a stress concentration that reduces the shaft's own torque capacity below that of a plain round shaft of the same diameter — this calculator sizes the key itself, but shaft strength with the keyway factored in needs its own separate check.

6. Not adding a design margin over the bare calculated minimum length. The theoretical minimum length from the shear/crushing checks is a bare limit, not a design length — applying a margin (commonly 15–25%) accounts for uncertainties in actual load, minor misalignment, and rounds up to commercially available key stock lengths.