Quick answer: You need 24/7 answering if you offer emergency service, if your best jobs come in after hours, or if you are losing calls at night and on weekends. If all of your calls arrive during business hours and you never miss one, you may not need it yet. For most home service businesses, the after-hours call is the one most worth catching.

Start with where your jobs come from
Look at when your phone actually rings. If a real share of your work shows up at night, early morning, or on weekends, those calls are worth catching, and they are exactly the ones a normal office misses. If your calls are steady and only during the day, the case is weaker.
The emergency test
If you advertise emergency or same day service, you almost certainly need around the clock coverage. The customer with a real emergency will not wait for business hours, and the company that answers gets the job, often the highest value one of the week.
The calls you never see
The hardest part of this decision is that missed calls are invisible. You do not get a report of the people who called at 8pm and hung up. Pull your phone records and look at calls outside business hours. The number is usually higher than owners expect, and every one was a person who needed something.
When you probably do not need it yet
If you are small, do not offer emergency service, and genuinely catch every call during the day, you can wait. Just revisit it as you grow, because missed after-hours calls are one of the quietest ways a business leaves money on the table.

