MATHEMATICAL & STATUTORY SPECIFICATION

Payroll Formulas & Statutory Methodology

Transparent equations, rounding algorithms, and federal/state labor code citations powering every calculation on WorkHoursCalculator.app.

📅 Effective & Verified: October 27, 2026 🏛️ Editorial & Statutory Compliance: Quantitative Payroll Engineering Desk 🔒 App Package ID: com.workhourscalculator.app

1. Net Shift Duration & Midnight-Crossover Equation

For each daily shift $i$ with clock-in time $T_{\text{in}}$ (in minutes from 00:00), clock-out time $T_{\text{out}}$, and unpaid bona fide meal break $B_i$ (in minutes):

RawShiftMins(i) = (T_out >= T_in) ? (T_out - T_in) : ((T_out + 1440) - T_in)
RawNetMins(i) = max(0, RawShiftMins(i) - B_i)

Adding 1440 minutes (24 hours) whenever $T_{\text{out}} < T_{\text{in}}$ ensures that overnight graveyard shifts (for example, 22:00 to 06:30) accurately evaluate to 510 raw minutes minus break time, without requiring users to enter multi-day calendar dates.

2. Timeclock Rounding Algorithms (29 CFR § 785.48(b))

Under 29 CFR § 785.48(b), employers are permitted to round employee punch times to the nearest 5 minutes, one-tenth of an hour (6 minutes), or quarter-hour (15 minutes), provided the arrangement averages out over time and does not systematically fail to compensate employees for time worked. Our engine computes both exact minutes and rounded minutes:

• Exact Mode: NetMins(i) = RawNetMins(i)
• FLSA 15-Min: NetMins(i) = round(RawNetMins(i) / 15) * 15 [1–7m rounds down; 8–14m rounds up]
• 1/10th Hr (6m): NetMins(i) = round(RawNetMins(i) / 6) * 6
• Nearest 5-Min: NetMins(i) = round(RawNetMins(i) / 5) * 5
• Decimal Hours: DecHrs(i) = NetMins(i) / 60.0

The Rounding Audit Differential displayed in the Wage Protection Bar is calculated as:

RoundingDiffHrs = (Sum(NetMins) - Sum(RawNetMins)) / 60.0
RoundingDiffPay = RoundingDiffHrs * BaseHourlyRate

3. Federal FLSA Overtime Model (29 CFR § 778.101)

Under the federal Fair Labor Standards Act (FLSA), non-exempt employees must receive overtime compensation at a rate not less than one and one-half times (1.5x) their regular rate of pay for all hours worked in excess of 40 hours in a single 7-day workweek. For bi-weekly (14-day) periods, each 7-day workweek is evaluated independently (hours cannot be averaged across two weeks):

Week 1 (Days 1–7): RegHrs_W1 = min(40.0, Sum(DecHrs_1..7)), OTHrs_W1 = max(0, Sum(DecHrs_1..7) - 40.0)
Week 2 (Days 8–14): RegHrs_W2 = min(40.0, Sum(DecHrs_8..14)), OTHrs_W2 = max(0, Sum(DecHrs_8..14) - 40.0)

4. California Daily Overtime, Double-Time & § 226.7 Meal Penalty Model

Under California Labor Code § 510, overtime is calculated on both a daily and weekly basis without pyramiding (duplicating) daily and weekly overtime hours:

5. Primary Public Data & Regulatory Citations

Editorial & Statutory Payroll Disclaimer: workhourscalculator.app is an independent educational payroll estimation tool and statutory labor law reference publication. We are not a certified public accounting (CPA) firm, law firm, or licensed payroll processor, and our calculations do not constitute formal legal or tax advice. All figures generated by our calculators are mathematical estimates based on public federal and state labor benchmarks (29 CFR Part 785 FLSA, U.S. DOL Wage and Hour Division, IRS Publication 15, and California Labor Code §§ 510 & 226.7). For complete details on our calculation equations and public statutory citations, please review our Payroll Formulas & Methodology and Full Payroll & Legal Disclaimer.