Can I measure how many calories I'm burning while riding an exercise bike?

There isn't a lot of difference between them. Cardio is all about getting you heart rate higher so Treadmill or Bike is often down to which you personally prefer. You could also use a rowing machine to get the same cardio workout.
The biggest difference is mostly which muscle groups your using to pump up your heart rate.

You cannot go wrong with spinning your Bike at the gym. Not only are or stationary bikes better for all fitness levels, but they are also the ideal tool for finishing daily exercise targets. In fact, you can Spin Your Bike 30-45 minutes workout that can burn 300 or more calories, depending on concentration and strength.

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Recumbent bike works best for elderly people with back and hip problems because of the relaxed position and the angle that put's less pressure on those areas. Upright exercise bike works on more areas than the recumbent bikes including the lower abdominal muscles.

If you cycle for an hour around 15 miles per hour, you willburn about 1400 calories.

Stationary bikes provide a no impact workout because your feet never leave the bike pedals. This is preferable if you have back or joint problems that cannot tolerate repeated jarring of high impact exercises.

Stationary biking can burn 315 to 466 calories when done vigorously. This is a great exercise especially if you are trying to lose weight. You'll burn more calories in less time compared to other cardio exercises like high impact aerobics. You'll never burn this amount of calories while playing.