Most social media management work is sold as a flat monthly retainer rather than pure hourly billing, since clients want predictable costs. A common approach is to estimate the real monthly hours (content creation, scheduling, community management, reporting) and multiply by your target hourly rate to set the retainer, then revisit that math every few months as scope inevitably grows, which it almost always does with social media work.
A rate only matters if it actually gets collected. Once you've picked a number, send a professional invoice that states your terms clearly, and consider a simple contract for anything beyond a quick one-off, it's the easiest way to avoid scope creep eating into that hourly number. If you want to see how your rate translates into real take-home pay after taxes and time off, try the freelance take-home pay calculator.