Time Unit Converter

Time is the one unit family everyone uses daily and almost nobody converts in base ten. Sixty, sixty, twenty-four, seven — none of it is decimal, which is why a plain calculator gets it wrong.

About time conversion

The factors are ancient and stubborn. Sixty seconds to a minute and sixty minutes to an hour come from Babylonian base-sixty arithmetic, which survived because sixty divides neatly by two, three, four, five and six. Twenty-four hours and seven days are separate conventions with their own histories, and none of it is decimal.

That is why adding times on an ordinary calculator fails. Forty-five minutes plus forty-five minutes is an hour and a half, not ninety of anything you can then treat as 1.90. Payroll systems avoid the problem by working in decimal hours, where seven hours thirty is 7.5 rather than 7.30 — and confusing the two is the most common timesheet error there is.

A year here is 365.25 days, which is the Julian year and the average once leap years are counted. That is deliberate: a fixed factor has to be reversible, so a year converted to days and back must give a year. Calendar arithmetic — how many days between two actual dates, which months those cross — is a different problem and the date calculators handle it properly.

For anything involving specific dates, use those rather than this. This is for converting durations: how many seconds in a week, how many hours in a working year, how many minutes a process takes.

What it works out

• Seconds, minutes, hours, days, weeks and years
• Every unit shown at once
• Durations rather than calendar dates

The formula

Converted = Value × (seconds per from-unit) ÷ (seconds per to-unit)

Everything routes through seconds. Ninety minutes is 5,400 seconds, and dividing by the 3,600 in an hour gives 1.5 hours.

The factors: 60 seconds to a minute, 3,600 to an hour, 86,400 to a day, 604,800 to a week. That last one is worth a glance — a week is well over half a million seconds, which is a useful sense of scale for anything measured in them.

A year is taken as 365.25 days, giving 31,557,600 seconds. The quarter day is the leap year averaged in, and it makes the conversion reversible: a year converts to days and back to exactly a year.

A common approximation worth knowing: a year is very nearly π times ten million seconds. It is out by half a per cent, which is close enough for an order-of-magnitude check and a pleasing coincidence.

Second

The base unit everything routes through.

365.25

Days in an average year, leap years included, so conversions reverse.

Decimal hours

What payroll uses. 7.5 rather than 7:30.

A worked example

Questions

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