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The standard size for adults is a ¾ double bass. A large double bass such as a ⅞ or 4/4 is very rare and not commonly used.  

In general for children choose a bass one size smaller than usual violin size for age.

Approximate sizing for age:
Size of Double BassAge of Child
1/85-7 years
1/47-9 years
1/29-13 years
3/413 years to adult

Further refinements for deciding on double bass size.

Adjust the length of the spike so that the bridge is at the same level as the large knuckles (metacarpal phalangeal joint) while the arm hangs down.

Your right arm should now be able to bow comfortably with the bow at the appropriate position midway between the bridge and the fingerboard. If you are bowing above the fingerboard, try a bass one size down. If you feel more comfortable bowing very close to the bridge, try a bass one size up.

The left hand should be about level with your face when in first position. Your index finger should approximately point towards your eyebrow.

A ½ size bass is usually good for players up to around 12 years of age. (150cm)