Bevel Gear Pitch Angle Calculator
For straight bevel gears on 90-degree shafts, the pitch cone angles come straight from the tooth counts: delta1 = atan(z1/z2) and delta2 = atan(z2/z1), summing to 90 degrees. Use the working bevel gear calculator for the angles plus cone distance, face width and torque.
Pitch cone angles
On perpendicular shafts the two pitch cones share the 90-degree shaft angle in proportion to the tooth counts:
tan(delta1) = z1/z2, delta2 = 90 - delta1
Equal gears are miter gears
With z1 = z2 both cones sit at 45 degrees - a miter gear pair. Unequal counts tilt the cone toward the larger gear.
Beyond the angles
The working calculator also returns cone distance, recommended face width (typically <= A/3), pitch diameters, output RPM and torque for straight bevel pairs.
Frequently asked questions
What if the shaft angle is not 90 degrees?
The general relation is tan(delta1) = sin(sigma)/(z2/z1 + cos(sigma)) for shaft angle sigma. The working calculator covers the common perpendicular case; non-90 layouts follow the same geometry with sigma in place of 90.
Why do the pitch angles matter?
They set the blank machining angles and the mounting geometry: each gear must be cut and mounted so the pitch cones share an apex. Errors show up as edge contact and noise.
Related pages
- Bevel gear calculator - working pitch cone angles, cone distance, face width and torque.
- Gear ratio calculator - ratio, output speed and torque for plain pairs.
- Gear module calculator - module / DP conversions used to size the teeth.
- Worm gear calculator - the high-ratio right-angle alternative.