It is possible to tell whether a candle is a paraffin candle in some cases, such as when wax has been left raw and without wax colorants. However, there are some times in which it isn't possible to tell what type of wax was used unless there is a label on the candle. With the many candle colors and scents on the market, it is possible to change the natural color and smell of any type of wax and render it unrecognizable.
Read the label. If the candle doesn't say what type of wax it is, it is most likely a paraffin candle. Most candles are made from paraffin because it is inexpensive, durable and takes scent and color well. If a candle is made from a more expensive specialty wax, that will be advertised prominently on the label.
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Look at the color of the candle if it has not been colored. If the candle is white with a slightly translucent appearance, it is likely paraffin wax. If it is an even, opaque white with no translucence, it has likely been colored and whether it is paraffin wax will not be apparent from the color alone. A candle that has a slightly pinkish-gray color is likely a bayberry wax candle. The color of bayberry wax is prized and those candles aren't colored artificially.
Touch the top and press down gently. If the candle is a freestanding candle that is not in a container, it should be firm. If there is any give to the wax, it is probably either beeswax or bayberry wax.
Check the color of taper candles to determine whether they are bayberry or paraffin. Taper candles that are a medium olive green with gray areas on the outside of the wax are likely made of bayberry. These are traditional Christmas candles because of the use of bayberry wax in Colonial times. This precise color with its grayish residue is hard to reproduce by simply coloring paraffin wax. If a taper candle is a different color and is hard to the touch when pressed, it is likely a paraffin candle. A taper candle that is not olive green and gray and that gives way when pressed is likely a beeswax candle.