Rate math
Start with the salary you would need in cash, add a benefits and tax buffer (self-employment tax, health insurance, retirement matching — 25–35% is a common band), then add annual business expenses. That sum is the amount the year must collect.
Billable hours are not the hours you are awake. They are:
hours = (52 − weeks off) × hours/week × billable%
Proposals, bookkeeping, sales, and slack in the calendar are the unbillable remainder. Many independents land around 50–70% utilization. Hourly rate is total needed ÷ billable hours. Daily rate here caps a day at 8 hours so a 50-hour week does not pretend every hour invoices.
If the number shocks you, that is usually the model working. Undercutting it means you are the one funding the client's discount — with your vacation, your health plan, and your nights.