Calculation Methodology

01Time Duration

Time Duration

Wall-clock model

TimeDateLab compares the displayed local clock and calendar values. It does not perform timezone conversion and does not calculate real zoned elapsed time across DST transitions. Every duration fact is derived from total seconds.

Model: Wall-clock time
Timezone: Not applied
DST: Not applied
Truth source: Total seconds

Time-only calculation

Calculation rule

Total seconds= end seconds− start seconds+ next-day offset × 86,400

The next-day offset is either 0 days or 1 day. Same-day calculations add no day; Ends next day adds exactly 86,400 seconds.

Time-only edge cases

09:00 → 09:00: Result: 0 hours
09:00 → next day 09:00: Result: 24 hours
23:59:59 → next day 00:00:00: Result: 1 second
11:30 PM → next day 1:15 AM: Result: 1 hour 45 minutes

If the end is earlier than the start and next-day semantics are disabled, the calculator returns a recoverable error instead of a negative duration.

Date & time calculation

Calculation model

Date-time scalar= civil day index × 86,400+ seconds of dayDuration= end scalar − start scalar

Dates make the day boundary explicit, so Ends next day is not used in this mode. A reversed date-time returns an error. Timezone and DST elapsed-time semantics still do not apply.

Precision and rounding

The default visible and calculation precision is minute precision.
Include seconds enables second precision. Disabling it resets hidden start and end seconds to zero.
The exact duration remains based on total seconds. Decimal hours and decimal minutes are derived from it.
Decimal values use two-place half-up rounding. The ≈ marker appears only when the displayed decimal is not exact.

Limits

Supported clock range: 00:00:00–23:59:59.
Leap seconds are not included.
No timezone conversion or DST elapsed-time adjustment is applied.

02Work Hours

Work Hours

Single-shift model

Work Hours Calculator uses the same timezone-free Wall-clock Duration as Time-only Calculation. It accepts one start time, one end time, an explicit 0-or-1 next-day offset, and one whole-minute break deduction.

Calculation rule

Gross seconds= end seconds − start seconds+ next-day offset × 86,400Net work seconds= gross seconds − break minutes × 60

Break minutes must be a non-negative whole number and cannot exceed the gross shift.
Net work time, decimal hours, and total minutes are all derived from the same net-second fact.
Decimal hours use the same two-place half-up rule as Time Duration.
Weekly cards, multiple shifts, pay, overtime, tax, holidays, timezones, and DST are outside this model.

03Day Counter

Day Counter

Civil-date model

Civil dates use the proleptic Gregorian calendar from 0001-01-01 through 9999-12-31. The modern Gregorian leap-year rule is projected backward before 1582. Each validated date becomes an integer civil day index for subtraction.

Calendar: Proleptic Gregorian
Range: 0001-01-01–9999-12-31
Date value: Civil day index

Leap-year rule

A year is a leap year when it is divisible by 4, except when divisible by 100, unless it is also divisible by 400.

1900: Not a leap year
2000: Leap year
2100: Not a leap year

Endpoint rule

Default

[start, end)

Start date included · End date excluded

Include end date on

[start, end]

Start date included · End date included

Same date: Off: 0 days · On: 1 day
Adjacent dates: Off: 1 day · On: 2 days

Weekday and weekend breakdown

Monday–Friday are weekdays. Saturday–Sunday are weekend days. Public holidays are not subtracted, so this is not a holiday-aware business-days calendar.

Every complete 7-day span contributes 5 weekdays and 2 weekend days. Any remaining dates are classified individually.

Calculation invariant

Weekdays + weekend days = calendar days

Edge cases and limits

The same endpoint and calendar rules continue across month and year boundaries, including the 1900 and 2000 leap-year cases.
When the end date is earlier, the calculator reports an error. It does not silently swap the dates or return an absolute value.
There is no public-holiday calendar, custom workweek, or date add/subtract function.

04Shared model

Shared model and data boundary

Local calculation

Calculation happens in your browser. No calculation or business API receives calculator inputs in order to produce the result.

Deterministic model

The same validated values and the same explicit policy produce the same calculation result.

Structured errors

Invalid or ambiguous states produce visible, recoverable errors instead of silent correction.

Only when you choose Share are normalized inputs and policies encoded in the portion of the address after #. Calculated results are not encoded, and the fragment is not sent in ordinary HTTP requests.

The fragment can still appear in browser history, browser sync, the clipboard, messaging services you choose, and the recipient’s device.

Analytics boundary

TimeDateLab loads Google Analytics for page-level measurement but defines no custom product-interaction events. Calculator inputs, exact results, and Share Fragments are not sent to analytics.

Read the full Privacy policy

05Verification

Verification

Implementation confidence comes from several complementary kinds of checks.

Boundaries: Fixed examples cover leap-year boundaries, same-time and overnight cases, supported date-range edges, and reversed inputs.
Invariants: Generated inputs check relationships such as weekday and weekend conservation, stable share round trips, and safe invalid-state handling.
Independent comparison: During development, civil-date calculations are compared with an independent calendar implementation. The comparison library is development-only and is not shipped in production.
Browser and interface: Real-browser checks cover English and Chinese calculator flows, keyboard and accessibility behavior, mobile and zoom layouts, sharing, copying, error recovery, and network/privacy boundaries.

These checks improve confidence, but they do not prove that defects are impossible, provide certification, or constitute formal verification.