Rider-matched picks
Size-matched fenders & mudguards picks for small children (ages 3-5), with fit and feature priorities curated for how small children (ages 3-5) actually ride.
Check Amazon for current pricing and availability.

Royalbaby
Front + rear fender set sized for 20" kids bikes. Confirm rim brake / tire clearance before install.

Syncros
Universal MTB front fender - zip-ties to the fork crown and lower legs of any suspension fork. Designed to be wide enough to clear a 2.6" tire and short enough not to interfere with crown-mounted accessories. Bolt-on, no tools needed.

Syncros
Fork-specific fender designed for the Fox 34 SC (Step-Cast) and other 34 mm-stanchion XC/trail forks. Bolts directly to the brake-arch holes instead of using zip ties - cleaner install and steadier under hits. Won't fit 32 mm or 36 mm forks.

Syncros
Shorter and lighter than the standard Trail Fender - keeps mud out of the goggles without the extra polypropylene tail. Universal zip-tie mount fits any suspension fork. Orange colorway is the only one consistently in stock on Amazon.
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For small children, bike size is determined by wheel diameter - not frame size. At this age, the priority is confidence and safety over performance. Your child should be able to touch the ground flat-footed when seated at the lowest saddle position. A bike that's too large is dangerous - children cannot control bikes they can't reach the ground from. Consider starting with a balance bike (no pedals) for children under 4, as this teaches balance and steering before adding pedal complexity. For pedal bikes, look for models with coaster brakes (backpedal to stop), which are easier for small hands than hand brakes. Bike weight matters enormously at this age - a bike that weighs more than 30% of the child's body weight will be hard to control. Expect to replace the bike every 1-2 years as your child grows.
Fenders are sized to two dimensions: wheel diameter (12-20" for kids, 26"/27.5"/29"/700c for adults) and tire width (commonly 23-32 mm for road, 32-45 mm for commuter/gravel, 2.0-2.4" for MTB and kids bikes). Fenders should sit roughly 8-12 mm clear of the tire on each side and overlap the tire by 5-10 mm. Three broad styles: full-wrap fenders bolt to frame and fork eyelets and cover roughly 60% of the wheel for maximum spray protection (best for daily commuters and rain bikes); clip-on / strap-on fenders use rubber straps or P-clips around the seatpost and fork legs and trade coverage for tool-free install (best for road bikes without eyelets); and minimal racing-style ass-savers protect only the rider's backside and are mostly a token gesture for unexpected showers. Kids fenders tend to be plastic, sized 12/14/16/18/20", and clip to the frame with the bike's existing brake-mount or kickstand bolts.