Use this engineering calculation for a transparent preliminary estimate or independent arithmetic check when geometry, materials, loads, operating conditions, and units are defined consistently.

First Teeth

Required integer input.

Second Teeth

Required integer input.

Pitch cone angle of the first straight bevel gear in a 90° intersecting-shaft pair: atan(z1/z2). The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.^[1]

First Pitch Degrees (°)

The resulting first pitch degrees returned as a number.

• Ideal speed and pitch relationships do not include slip, tooth or belt geometry limits, center distance, wrap, tension, efficiency, wear, vibration, service factors, or strength. Manufacturer selection procedures remain necessary.
• Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.

Check assumptions against drawings, measurements, current material data, and the applicable design code. Apply required load combinations and safety factors, then obtain qualified review and testing for consequential designs.

• Critical Shaft Speed

  Undamped first critical rotational speed estimated from a measured static shaft deflection under gravity: n=30√(g/δ)/π.

• Gear Module Finder

  Metric spur-gear module m=d/z from pitch-circle diameter in millimeters and whole tooth count.

• Propeller Efficiency

  Propulsive efficiency as thrust times advance speed divided by shaft power; assumes steady straight-ahead motion.