On the safe side
Definition 1 of 1
Pro Tip 1/3Risk Avoidance
The phrase suggests actions are taken to prevent potential problems, even if they seem unlikely. 
He decided to save the document frequently to be on the safe side.
Pro Tip 2/3Not Just Fear
Using 'on the safe side' does not mean one is fearful, but rather careful and thoughtful. 
She double-checked her essay to be on the safe side before submitting.
Pro Tip 3/3Casual Expression
It's commonly used in everyday conversation rather than in formal writing or speeches. 
I might wear a jacket to the party, just to be on the safe side.