Can you take candles on a plane?

The rule for candles comes from the Civil Aviation Bureau's list of restricted items. On international flights its liquids list applies as well.

A candle is judged by what it is made of: wax that holds its shape, or gel that sits in a container.

The TSA lists solid and gel candles separately

Solid Candles and Gel-Type Candles are separate items on the TSA's list. Solid candles are a yes for carry-on and for checked bags. Gel-type candles are a no for carry-on and a yes for checked bags. The gel entry offers no size allowance, where the agency's Hair Gel entry reads less than or equal to 3.4oz/100 ml allowed.

In Japan the question is whether the candle keeps its shape

Candles are not printed on Japan's liquids list, which is written for international flights departing from Japan. Its opening notes give a test in place of a name: the gel is restricted, and so are articles which cannot keep their shape without the container. A later note says the screener at the Security Check Points gives the concrete judgment.

Australia clears the candle and flags the candlestick

CASA's Pack Right has a Candles entry flagged as able to be checked in and carried on, with no quantity set. Its condition says candles are not considered to be dangerous goods, then turns to what travels with them: candlesticks and various candlestick holders may be considered a security risk.

Bringing candles into Japan: animal quarantine

Japan's Animal Quarantine Service publishes criteria for products it clearly recognises as posing no risk of spreading pathogens. Those products are excluded from the scope of the Designated Items even when they are derived from materials that would otherwise fall under them. Candles are printed in the examples for its industrial products standard, straight after soap.

Extra conditions apply in the United States.

Each row comes from that authority's own page. Airlines can be stricter, and the screening officer has the final say.