The math, line by line

How the math works.

These are the worked examples the pay engine is built and tested against. Every figure below is computed from the inputs beside it, and checked against the engine's own specification on every build of this site.

Example 1

A nurse's fortnight.

Three 12s most weeks, a night differential after 6 p.m., a weekend differential, and a half-hour lunch deducted whether it was taken or not.

What goes in

Base rate
$36.00 / hr
Overtime
over 40 hrs a week, 1.5×
Night diff
+$2.10 / hr, starts 6 p.m. or later
Weekend diff
+$1.50 / hr, Sat and Sun
Unpaid break
0:30, automatic
Pay period
bi-weekly, Sat Aug 1 – Fri Aug 14
Workweek starts
Saturday
Shifts
7, totalling 78.0 paid hrs

Rules applied

  • Week 1 (Aug 1–7) came to 46.5 paid hours, so 6.5 of them are overtime.
  • Week 2 (Aug 8–14) came to 31.5 hours and adds no overtime at all.
  • Overtime is a weekly test, so the two weeks never pool.
  • Both differentials are paid on their qualifying hours, at straight time.

What comes out

Regular 71.5 hrs × $36.00
two thousand five hundred seventy-four dollars
Overtime 6.5 hrs × $54.00 (1.5 × $36.00)
three hundred fifty-one dollars
Night diff 34.5 hrs × $2.10
seventy-two dollars 45
Weekend diff 36.0 hrs × $1.50
fifty-four dollars
Gross Gross, three thousand fifty-one dollars 45, estimate

78.0 paid hours · 71.5 straight · 6.5 at a premium

This is the whole product in one screen: a number a nurse can read aloud to payroll, with every line showing the hours and the rate it came from. The overtime lands entirely in week one, which matters as soon as you compare the two methods below.

Example 2

Two ways to figure overtime, on the same fortnight.

Same nurse, same seven shifts, same 78.0 hours. Two totals, and both of them are used by real employers.

The common method

Regular hours at the base rate, overtime hours at 1.5 × the base rate, and the differentials paid at straight time on top.

$3,051.45

The federal regular-rate method

Every hour at straight time including the differentials, then a regular rate for the week, then an overtime premium of half that rate on the overtime hours.

$3,057.27

The difference

All of it in week one, because that is where the overtime is. Roughly one hundred and fifty dollars a year for this worker, and considerably more for someone with bigger differentials.

+$5.82

Week by week, both methods
Workweek Paid hrs Common Regular rate Federal
Week 1 · Aug 1–7 46.5 $1,874.25 $37.7903 $1,880.07
Week 2 · Aug 8–14 31.5 $1,177.20 — $1,177.20
Period 78.0 $3,051.45 — $3,057.27

Week 2 is identical under both methods, because with no overtime hours the regular rate never enters the arithmetic. That is why matching your employer's check and knowing what the federal method produces are two different jobs — and why ShiftStub does both, and shows you the gap. A gap is information about which method a check was figured with. It is not a finding that anybody was underpaid.

Example 3

California daily overtime.

A nurse in California working four days: 12, 12, 14, and 8 hours.

What goes in

Base rate
$55.00 / hr
Daily OT
over 8 hrs, 1.5×
Daily double time
over 12 hrs, 2×
Weekly OT
over 40 hrs, 1.5×
Hours worked
46.0 in the week

Rules applied

  • Monday and Tuesday: 8 hours straight, then 4 hours at time and a half.
  • Wednesday: 8 straight, 4 at time and a half, then 2 at double time.
  • Thursday: 8 hours, all straight time.
  • Weekly test: 32 hours have not already been paid a premium — under 40, so it adds nothing.

What comes out

Regular 32.0 hrs × $55.00
one thousand seven hundred sixty dollars
Overtime 12.0 hrs × $82.50 (1.5 × $55.00)
nine hundred ninety dollars
Double time 2.0 hrs × $110.00 (2 × $55.00)
two hundred twenty dollars
Gross Gross, two thousand nine hundred seventy dollars, estimate

46.0 paid hours · 32.0 straight · 14.0 at a premium

Here is the trap this defeats. The week totals 46 hours, which looks like 6 hours of weekly overtime waiting to be paid. It is not: the daily rule already paid those hours, and paying them again would be counting the same hour twice. A calculator that adds the weekly rule on top of the daily one overpays, tells the worker they were shorted, and sends them to payroll with a wrong number.

Example 4

The seventh consecutive day.

A retail worker in California: six 8-hour days, then 10 hours on day seven.

What goes in

Base rate
$20.00 / hr
Days 1–6
8 hrs each
Day 7
10 hrs
Seventh-day rule
first 8 hrs 1.5×, then 2×
Hours worked
58.0 in the week

Rules applied

  • Day seven is priced by the seventh-day rule: 8 hours at time and a half, then 2 at double time.
  • That leaves 48 hours the daily rules have not touched.
  • The weekly test runs on those 48: 8 of them are over 40, at time and a half.
  • Total at time and a half: 8 from the weekly test plus 8 from day seven.

What comes out

Regular 40.0 hrs × $20.00
eight hundred dollars
Overtime 16.0 hrs × $30.00 (1.5 × $20.00)
four hundred eighty dollars
Double time 2.0 hrs × $40.00 (2 × $20.00)
eighty dollars
Gross Gross, one thousand three hundred sixty dollars, estimate

58.0 paid hours · 40.0 straight · 18.0 at a premium

Two rules, applied to two different sets of hours, and no hour paid twice. Whether the seventh-day premium survives an alternative workweek schedule is a question this site does not answer — it is one of the rules still with counsel.

Example 5

The hospital 8/80.

An eight-hour nurse on a 14-day work period: ten shifts, one of them ten hours long.

What goes in

Base rate
$36.00 / hr
Work period
14 days
Daily test
over 8 hrs, 1.5×
Period test
over 80 hrs, 1.5×
Shifts
9 × 8 hrs, 1 × 10 hrs
Hours worked
82.0 in the period

Rules applied

  • The daily test collects 2 hours — only the ten-hour day goes over 8.
  • The period test collects 2 hours — 82 minus 80.
  • The greater of the two applies. They tie, at 2 hours.
  • The hour that satisfies both tests is still one hour, and is paid once.

What comes out

Regular 80.0 hrs × $36.00
two thousand eight hundred eighty dollars
Overtime 2.0 hrs × $54.00 (1.5 × $36.00)
one hundred eight dollars
Gross Gross, two thousand nine hundred eighty-eight dollars, estimate

82.0 paid hours · 80.0 straight · 2.0 at a premium

A naive implementation adds the two tests together and pays 4 hours here instead of 2. That is a $108 error on one check, in the worker's favour, which sounds harmless until they take the number to payroll and it is wrong. Under 8/80, ShiftStub compares the tests and credits one against the other — which is exactly the language real hospital contracts use.

Example 6

A firefighter's §207(k) work period.

24 on, 48 off, on a 21-day work period. Seven 24-hour shifts.

What goes in

Base rate
$22.00 / hr
Work period
21 days
Fire threshold
159 hrs
Shifts
7 × 24 hrs
Hours worked
168.0 in the period

Rules applied

  • Fire and police may use a work period of 7 to 28 days instead of a workweek.
  • A 21-day fire period carries a 159-hour overtime threshold.
  • Overtime is the hours over the threshold: 168 minus 159.
  • There is no weekly test at all under a §207(k) period.

What comes out

Regular 159.0 hrs × $22.00
three thousand four hundred ninety-eight dollars
Overtime 9.0 hrs × $33.00 (1.5 × $22.00)
two hundred ninety-seven dollars
Gross Gross, three thousand seven hundred ninety-five dollars, estimate

168.0 paid hours · 159.0 straight · 9.0 at a premium

No other consumer hours app models this. It is why a firefighter opening a normal tracker sees a week flagged as an error, or a 24-hour shift split into two days and counted wrong. Sleep and meal-time exclusions can apply to shifts over 24 hours under some agreements; those are outside what the engine computes, and the app says so where the rule is set.

Example 7

The night the clocks change.

Twice a year an overnight shift is not as long as the wall clock says it was. Both directions are handled, and both say so on the shift.

Spring forward · Sat Mar 7 2026

7:00 p.m. → 7:30 a.m., half-hour break

The wall clock says
12.5 hrs
Really elapsed
11.5 hrs
Paid
11.0 hrs

“Clocks sprang forward during this shift (−1:00).”

Fall back · Sat Oct 31 2026

7:00 p.m. → 7:30 a.m., half-hour break

The wall clock says
12.5 hrs
Really elapsed
13.5 hrs
Paid
13.0 hrs

The extra hour is real worked time. In California it also crosses the 12-hour daily threshold, so the thirteenth hour is double time.

A shift's identity is its wall-clock times in the zone it was recorded in, but the hours come from the actual instants. Travelling to another timezone does not rewrite what you already worked, and a shift never moves days because your phone moved.

Example 8

One workweek, split across two checks.

Semi-monthly pay at $20.00/hr. The workweek runs Sun Aug 30 to Sat Sep 5 — 44 hours, 16 of them in August and 28 in September.

The August 16–31 check

Regular16.0 hrs × $20.00
$320.00
Paid $320.00

All straight time. At this point the workweek is not over, so no overtime is owed yet.

The September 1–15 check

Regular24.0 hrs × $20.00
$480.00
Overtime4.0 hrs × $30.00 (1.5 × $20.00)
$120.00
Paid $600.00

The workweek ends here, so this is where the overtime is recognised — all 4 hours of it.

The workweek totals $920.00 either way. Overtime is recognised where the workweek ends, not where the check does. This is the single most common reason a semi-monthly check looks wrong and is not — and the reason a tracker that adds up hours between two pay dates gives the wrong answer twice a month.

Example 9

A raise, mid-week.

$18.00 to $20.00, effective Thursday. 44 hours: 24 at the old rate, 20 at the new.

The federal regular-rate method

Straight time on all 44 hours is $832.00. The regular rate is $832.00 ÷ 44 = $18.9091. The overtime premium is half of that, on 4 hours.

$869.82

The rate-in-effect method

The overtime hours fell after the raise, so they are priced at 1.5 × $20.00. 24 hours at $18.00, 16 at $20.00, and 4 at $30.00.

$872.00

The difference

The common method comes out higher here. The comparison line is signed, and it points both ways.

+$2.18

This is why the comparison is never framed as “your employer underpaid you”. On the nurse's fortnight the federal method pays more; here the common one does. Which method applies can depend on what was agreed in advance. ShiftStub shows you both, and which one your stub looks like it used, so you can ask a question rather than make an accusation.

The rule underneath all of it

No hour is ever counted twice.

Nearly every example on this page is really the same rule. Two overtime rules can both have an opinion about one hour of your week: the daily one and the weekly one, the daily one and the period one, the seventh-day one and the weekly one. When they do, that hour is paid a premium once, and it leaves the pool the other rule is looking at.

Get that wrong in one direction and you underpay. Get it wrong in the other and you tell a worker they are owed money they are not owed, which is worse, because they take it to payroll and lose the argument. That is why ShiftStub's pay engine was written and tested against roughly 1,300 cases before a single screen of the app was designed, and why a full year of shifts recomputing in under 16 milliseconds matters: there is never a stale number on screen.

What this page is not

It is not legal advice, and it is not a complete account of the law. Several of these rules have conditions, exemptions and open questions — whether the seventh-day premium survives an alternative workweek schedule, exactly how the healthcare alternative-workweek bands work, how sleep time is treated on a 24-hour fire shift. Where the answer is not settled, ShiftStub does not pretend it is, and neither does this page.

If you think a check is short, the arithmetic here is a starting point for a conversation with your employer, your union, or your state labour agency. It is not a determination.