Rounding, priced
What a Rounding Rule Costs a Paycheck
Five identical days of 9:00 AM to 5:03 PM pay $807.50 counted to the minute, $812.50 under a 5-minute rule, $815.00 under a 6-minute rule, and $800.00 under a 10- or 15-minute rule. Same punches, same $20.00 rate, $15.00 spread. The arithmetic behind each number is set out below, and every figure was read back off the calculator on this site rather than worked out on paper.
Five identical days, five rules
Each of the five days runs 9:00 AM to 5:03 PM with no break. That is 8:03 of clock time. Enter those punches into the time card calculator, set the rate to $20.00, the weekly threshold to 40 and the multiplier to 1.5, then change only the rounding drop-down.
Three minutes past the hour is doing the work here. At a 5- or 6-minute setting, 8:03 rounds up and the week gains time. At 10 or 15, the same 8:03 rounds down to 8:00 and the week loses it. Nothing about the punches changed between those rows.
Why the week moves five times as much as the day
The setting is applied once per day, and the weekly total is the sum of those rounded days. So a rule that shifts one day by 3 minutes shifts a five-day week by 15 minutes — and a rule that shifts it by 8 minutes shifts the week by 40.
Row by row for the 5-minute rule
Monday 8:03 → 8:05 +2 min
Tuesday 8:03 → 8:05 +2 min
Wednesday 8:03 → 8:05 +2 min
Thursday 8:03 → 8:05 +2 min
Friday 8:03 → 8:05 +2 min
+10 min on the week → 40:15 becomes 40:25
Row by row for the 15-minute rule
Monday 8:03 → 8:00 −3 min
Tuesday 8:03 → 8:00 −3 min
Wednesday 8:03 → 8:00 −3 min
Thursday 8:03 → 8:00 −3 min
Friday 8:03 → 8:00 −3 min
−15 min on the week → 40:15 becomes 40:00
The pay follows, including the overtime line
Pay is not proportional to the hour count once the week crosses the threshold, because the minutes above 40 are paid at 1.5×. Every week in the table above sits near that line, so a small change in hours becomes a larger change in pay.
Exact to the minute — 40:15 at $20.00
Regular: 40:00 × $20.00 = $800.00
Overtime: 0:15 at 1.5× = $7.50
$807.50
Nearest 6 min — 40:30 at $20.00
Regular: 40:00 × $20.00 = $800.00
Overtime: 0:30 at 1.5× = $15.00
$815.00
Nearest 15 min — 40:00 at $20.00
Regular: 40:00 × $20.00 = $800.00
Overtime: none, the week does not pass 40:00
$800.00
The 15-minute rule does not merely take 15 minutes away. It takes away all 15 minutes of overtime and pays the remainder at the straight rate, which is why the gap to the 6-minute rule is $15.00 rather than a few dollars.
For completeness, the two rules that move 8:03 by much less also pay much less differently:
5 minutes a day is 25 minutes on the week. 6 minutes a day is 30. That is the whole difference between a $812.50 week and an $815.00 week — one minute per day, multiplied by five.
Which rules favour the worker, and which do not
The direction depends entirely on where the punches land inside the step. Move the end of the day to 5:10 PM and the picture reverses: 8:10 rounds up to 8:15 at a quarter-hour, and the week gains 25 minutes instead of losing 15.
Put the two tables side by side and the pattern is plain. The same 15-minute rule costs the worker $7.50 when the day ends at 5:03 and pays them $12.50 more when it ends at 5:10. A rounding rule is not generous or stingy in itself — it is a fixed grid, and your punches either fall on the lucky side of it or they do not.
Long weeks: the same rule still moves the number, but not always down
Once a week runs well past 40 hours the overtime line is safely crossed, so the question becomes simply whether the rule adds or removes minutes. Here is a week of Monday 8:00–4:23, Tuesday 8:00–4:37, Wednesday 8:00–5:10 with a 30-minute break, Thursday 7:30–4:02, Friday 8:00–5:38 with a 60-minute break.
The 6-minute rule shaves 2 minutes off this particular week; the 15-minute rule adds 10. Both are the same rule, behaving the same way — rounding five days independently. Four of these five days sit within 7 minutes of a 15-minute mark, which is why that rule moves all of them at once.
What a rule costs over a month
A single week makes rounding look like pocket change. Repeated across a month it does not, because the rule is applied on every day the person works. Take one shift that starts at 9:02 AM and ends at 5:20 PM — 8 hours 18 minutes of clock time — and work it 20 times. Left alone, that is 166:00 for the month. Apply a rule to each day first and the same 20 shifts come out differently.
Three rules, all of which sound like "rounding off the odd minutes", land $40.00 apart over 20 days on exactly the same punches — and the cheapest of the three is the coarsest one. Every row above is the five-day total read off the calculator multiplied by four, since the month repeats the same week four times.
Where those daily figures come from
The entry is 9:02 AM, the exit is 5:20 PM, and the worked time is 8 hours 18 minutes. Each rule moves both punches to the nearest mark on its own grid, and it matters which mark is nearer.
Nearest 7 minutes: one day, both punches
9:02 AM is 2 min from 9:00 and 5 min from 9:07 → 9:00
5:20 PM is 1 min from 5:21 and 6 min from 5:14 → 5:21
Worked: 9:00 to 5:21 = 8:21
Five days = 41:45 · twenty days = 167:00
Nearest 5 minutes: the same two punches
9:02 AM → 9:00 (2 min back)
5:20 PM → 5:20 (already on the mark)
Worked: 9:00 to 5:20 = 8:20
Five days = 41:40 · twenty days = 166:40
Nearest 15 minutes: the same two punches
9:02 AM is 2 min from 9:00 and 13 min from 9:15 → 9:00
5:20 PM is 5 min from 5:15 and 10 min from 5:30 → 5:15
Worked: 9:00 to 5:15 = 8:15
Five days = 41:15 · twenty days = 165:00
Note what happened to the exit punch. At 15 minutes it moves backwards 5 minutes, at 5 minutes it does not move at all, and at 7 minutes it moves forwards 1 minute. The same 5:20 PM stamp is worth three different amounts depending on which grid the employer chose.
The page's own rule, stated
Everything above was produced by the calculator on this site, whose rounding behaves to one written definition:
- Rounding is applied once per day, to that day's worked minutes.
- Worked minutes are measured after any unpaid break has been subtracted.
- The day is moved to the nearest multiple of the step, so a punch 3 minutes past a mark moves back to it and a punch 3 minutes short of the next mark moves forward to it.
- A punch exactly half a step out goes up. That is the page's own published example: at 15 minutes, 8:53 becomes 9:00, not 8:45.
- The weekly total is the sum of the rounded days, and decimal hours are converted from that weekly total once — not from the daily decimals added together.
- Overtime is everything strictly above the weekly threshold, and it is calculated after rounding, so the rule reaches into the overtime line as well.
The last two points are the ones that surprise people. Because rounding happens before the threshold test, a rule that removes 15 minutes from a week can remove the entire overtime portion — as it did with the five 8:03 days, where $807.50 became $800.00. And because decimal hours come from the weekly total, a week that shows 40:50 shows 40.83, not the sum of five separate decimals. The calculator's own notes cover both, and the overtime calculator takes the split on from there.
What to check before you trust a rounded total
- Find the step, not the label. "Rounded" means nothing on its own. Ask whether it is 5, 6, 10 or 15 minutes, and whether it is applied to each day or to the week.
- Check whether it is applied before or after breaks. On this calculator it is after, so a break reduces the minutes that get rounded.
- Check whether the overtime test runs on rounded or exact hours. If rounding runs first, a rule that shaves time can also shave the overtime rate off those minutes.
- Run the week at two settings and compare the gross. That is the only way to see what your own pattern of punches does under the grid, because the same rule pays more or less depending on where inside the step your punches land.
- Write down the rule you actually used. A total that cannot be re-derived from the punches and the rule is not a total anyone can defend later.