What is the smallest number which can be represented in python?

Question

What is the smallest number which can be represented in python?

I have seen as small as 2.05623357236e-296 but can there be any smaller?

Answer 1

Check out sys.float_info

>>> import sys
>>> sys.float_info 
sys.float_info(max=1.7976931348623157e+308, max_exp=1024, max_10_exp=308, min=2.2250738585072014e-308, min_exp=-1021, min_10_exp=-307, dig=15, mant_dig=53, epsilon=2.220446049250313e-16, radix=2, rounds=1)

From the docs

min       DBL_MIN      minimum positive normalized float 
min_exp   DBL_MIN_EXP  minimum integer e such that radix**(e-1) is a normalized float

On my system it is mentioned as min=2.2250738585072014e-308

Answer 2

Check sys.float_info.min. Note that this is the minimum normalized value; the minimum denormalized value may be smaller but numerical accuracy will suffer.

With usual 64-bit floating-point numbers, the normalized min is approximately 2.2e-308. The denormalized min can be much less, down to 4.94e-324:

>>> 5e-324
4.9406564584124654e-324

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It is also worth pointing out that the decimal module's Decimal type can represent arbitrarily small numbers, limited only by available memory.