In CA, Class 1 and 2 are allowed wherever regular pedal bikes are allowed, except for off road trails on federal lands, or where specifically restricted.
Class 3 bikes generally are not allowed on C1 and 2 bike paths, but are on general roads and hiways. None require any special licensing or equipment, and are generally consider a 'bicycle'.
Offroad is a whole 'nother can of worms.
California Legal eBike Classifications Guide
Where can I ride my new eBike?
California adopted new laws for legal eBikes in 2015, breaking the bikes down into three classes. The classifications are primarily based on where they are allowed to operate.
AB 1096: Electric Bicycles
This is the law that defines electric bicycles as those with fully operable pedals and an electric motor of less than 750 watts. It also creates three classes of electric bicycles based on their motor speed and level of electric assist. Electric bikes subsequently fell into classes 1, 2, and 3.
Important note! CA State AB1096 established a default framework – where a local jurisdiction (city, county, etc.) had not put any form of ordinance in place for electric bikes. A local jurisdiction (city, county, etc.) may enact an ordinance to allow or restrict electric bike usage for their area that may differ from the State default.
Class 1 eBike
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Class 1 eBike, or low-speed pedal-assisted electric bicycles, is equipped with a motor that provides assistance only when the rider is pedaling and that stops providing assistance when the bicycle reaches 20 mph. These e-bikes are legal on any paved surface that a regular bike is allowed to operate.
Class 2 eBike
Class 2 eBikes, or low-speed throttle-assisted electric bicycle, are equipped with motors that can exclusively propel the bicycle, but that cannot provide assistance when the bike reaches 20 mph. These e-bikes are legal on any paved surface that a regular bike is allowed to operate.
Class 3 eBike
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Class 3 eBike, or speed pedal-assisted electric bicycle, is equipped with a motor that provides assistance only when the rider is pedaling and stops providing assistance when the bicycle reaches 28 mph. Operators of Class 3 e-bikes must be 16 or older and wear a helmet. Class 3 e-bikes are prohibited from Class I multi-use bike paths unless specifically authorized by a local ordinance.
Below is a simple visual infographic for determining what class your eBike falls into: