When two shafts meet at an angle—usually 90°—you can't use spur or helical gears. You need bevel gears: conical gears whose teeth are cut on the surface of a cone rather than a cylinder. The pitch surfaces roll on each other like two ice cream cones tip-to-tip.

The three flavors you'll actually encounter:

• Straight bevel gears — teeth cut straight along the cone's slant. Simple, cheap, and noisy. Good for low speeds (under ~1000 rpm) and where axial thrust must be minimized. Think hand drills and differential gears in cheap tools.
• Spiral bevel gears — teeth are curved and angled, so multiple teeth engage gradually. Quieter, smoother, and can handle 2–3× the load of straight bevels at high speeds. Automotive differentials use these almost exclusively.
• Hypoid gears — a spiral bevel variant where the pinion axis is offset from the gear axis (doesn't intersect). This lets you lower the driveshaft in rear-wheel-drive cars, dropping the transmission tunnel. Trade-off: high sliding action requires extreme-pressure (EP) gear oil, which is why you never put motor oil in a diff.

Real-world example: A hand-cranked eggbeater. The handle rotates a large bevel gear whose axis is horizontal. It meshes with two smaller bevel gears mounted on vertical shafts (the beater blades). One crank rotation drives the beaters at a much higher rpm, and the 90° change of axis is what lets your hand rotate horizontally while the beaters spin vertically.

The rule of thumb: Gear ratio equals the ratio of pitch cone radii (or tooth counts), just like spur gears:

ratio = N_gear / N_pinion

A 12-tooth pinion driving a 36-tooth bevel gear gives a 3:1 reduction. But unlike spur gears, bevel gears generate significant axial thrust—the teeth are trying to push the gears apart along their shafts. You must use thrust bearings (tapered rollers are the standard choice) and set the correct backlash and tooth contact pattern during assembly. This is done by shimming the pinion in and out until a mark of Prussian blue on the teeth shows contact centered on the tooth face. Get this wrong and you'll hear whining, feel vibration, and destroy the gear set in hours.

Design gotcha: Bevel gears must be mounted in matched pairs. You can't swap in a pinion from another gear set even with identical specs—they're lapped together at the factory.