Core Time Math

Core Time Math is the layer below the calendar: questions answered entirely in hours, minutes, and seconds, without a date attached. How long between two clock times. What a quarter hour looks like as a decimal. Where the midpoint of a shift falls. Whether two appointment windows actually overlap, and by how much. These look like the simplest possible arithmetic, and mostly they are, but the small decisions inside them (does "9:00 to 5:00" mean an eight-hour span or a nine-hour one, does a negative result mean the day wrapped past midnight) are exactly where a plain calculator gives a silently wrong answer.

What tends to go wrong here

An overnight span is the most common failure mode: 11 PM to 2 AM is a three-hour duration, not a negative one, but only if the calculation knows to treat the end time as the next day. Decimal-hour conversion is another: 7 hours 15 minutes is 7.25 decimal hours, not 7.15, a rounding mistake that quietly compounds across a timesheet. Overlap and gap questions between more than two intervals get harder to eyeball the moment a third or fourth window is added, which is exactly when a deterministic calculation is worth more than mental math.

The convention that matters most

Every duration on this site states its counting convention plainly: whether an endpoint is included or excluded, and whether a span is treated as wrapping past midnight or constrained to a single day. Nothing here silently assumes a 24-hour wrap; it is either stated or asked for.

Where to go next

Once a duration needs to be placed on a specific calendar date rather than floating in the abstract, see Date & Calendar Math. Once it needs to respect a working schedule rather than the full 24-hour clock, see Work Hours, Timecards & Shifts.

Core Time Math tools

• Time Duration CalculatorFind the duration between two times, on the clock or as elapsed real time.
• Add / Subtract Time CalculatorMove a time forward or backward by a duration, with day rollover.
• Multi-Interval Time TotalSum several time periods, with an option to remove double-counted overlaps.
• Decimal Hours ConverterConvert between decimal hours and hours/minutes/seconds in either direction.
• Time Unit ConverterConvert fixed elapsed-time units: seconds, minutes, hours, days, and weeks.
• Time Midpoint CalculatorFind the halfway point in time between two clock times or instants.
• Time Interval Overlap CalculatorFind the time common to two or more intervals, if any.
• Time Gap Between IntervalsFind the unused time separating two intervals, or their overlap.
• Time Range SplitterDivide a time range into equal slices, or fixed-duration slices with a remainder.
• Elapsed / Remaining Time CalculatorSee live elapsed time since, or remaining time until, a target moment.