How to use this calculator
- Enter tooth counts. Use pinion and driven gear tooth counts.
- Enter module. Use the large-end transverse module or equivalent pitch size.
- Set shaft angle. Use 90 degrees for common right-angle bevel gear pairs.
- Add speed and torque. Enter optional input RPM, torque and efficiency for output values.
- Read geometry. Use pitch angles, cone distance and face-width guide for layout, then do strength rating separately.
How it works
A straight bevel pair has pitch cones instead of pitch cylinders. For shaft angle
Sigma and tooth counts z1 and z2:
delta1 = atan(sin(Sigma) / (z2/z1 + cos(Sigma)))
The second pitch angle is delta2 = Sigma - delta1.
Pitch diameters are d1 = m x z1 and d2 = m x z2.
Cone distance follows from the pitch cone triangle:
R = (d1/2) / sin(delta1). The calculator uses
min(R/3, 10m) as a conservative face-width guide.
Worked example
Verified against the live calculator
A 20-tooth pinion driving a 40-tooth gear at a
90 degree shaft angle has ratio 2:1. The pinion pitch
angle is atan(20/40) = 26.565 degrees; the gear pitch angle is
63.435 degrees.
With module 2, pitch diameters are 40 mm and
80 mm. Cone distance is about 44.72 mm, so the first-pass
face width guide is 14.91 mm.
Frequently asked questions
How do I calculate bevel gear ratio?
Bevel gear ratio is driven gear teeth divided by pinion teeth, i = z2/z1. Output speed is input speed divided by that ratio, and output torque is input torque multiplied by the ratio and efficiency.
How are bevel gear pitch cone angles calculated?
For shaft angle Sigma, pinion pitch angle is delta1 = atan(sin(Sigma)/(z2/z1 + cos(Sigma))). For a standard 90 degree pair this simplifies to delta1 = atan(z1/z2), and the gear pitch angle is 90 degrees minus that.
What is cone distance?
Cone distance is the distance from the pitch cone apex to the large end pitch circle. For the pinion, R = (d1/2)/sin(delta1). It sets the scale for face width and bevel blank geometry.
How wide should a bevel gear face be?
A conservative first-pass guide is face width no more than one third of cone distance and no more than about 10 modules. Final gearing should be rated by a gear design standard or manufacturer.
Does this design spiral bevel gears?
No. This is straight bevel pitch geometry for intersecting shafts. Spiral bevel and hypoid gears need additional geometry, cutter system data and rating methods.
Does it work in inches?
Yes. Toggle units to read module-equivalent length, pitch diameters, cone distance and face width in inches. Tooth counts and angles stay the same.
Method & assumptions
- Straight bevel gear pitch geometry for intersecting shafts.
- Module is treated as the large-end transverse module.
- Face-width output is only a layout guide; it is not a tooth-strength rating.
- Backlash, profile shift, cutter system, bearing loads, tooth bending, contact stress, lubrication and mounting deflection are not included.