Python 2, 33 bytes

print len(open(__file__).read())# 

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Try it doubled

Explanation

This opens up the source code using open(__file__).read() and gets its length using len the # prevents any additional code from being read. When the source is doubled so is the length.

Python 2, 33 bytes

print len(open(__file__).read())# 

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Try it doubled

Python 3, 28 bytes

print(len(*open(__file__)))# 

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Try it doubled

Explanation

This opens up the source code using open(__file__) and gets its length using len the # prevents any additional code from being read. When the source is doubled so is the length.

Python 2, 33 bytes

print len(open(__file__).read())# 

Try it online!

Try it doubled

Python 2, 33 bytes

print len(open(__file__).read())# 

Try it online!

Try it doubled

Explanation

This opens up the source code using open(__file__).read() and gets its length using len the # prevents any additional code from being read. When the source is doubled so is the length.