The Babylonians, Your Fingers, and the Most Divisible Number Under 100
The number 60 was not chosen because the Babylonians had 60 fingers. They had ten, like everyone else. Base-60 was a cultural innovation, probably inherited from the Sumerians who preceded them in Mesopotamia, and it might have originated as a merger of two earlier counting systems: base-10 (fingers) and base-12 (finger joints �?count the three joints on each of your four non-thumb fingers with your thumb as the pointer, and you get 12 per hand). Ten times twelve is 120. Twelve times five is 60. The archaeology is uncertain, but the arithmetic is not: base-60 produced the densest concentration of divisors of any number base used by any major civilization. Divide 60 by 2, 3, 4, 5, 6, 10, 12, 15, 20, or 30 and you get an integer. A merchant, a tax collector, a priest tracking lunar months �?none of them needed fractions to divide a quantity of 60.
The sexagesimal system flowed from Babylonian accounting into Babylonian astronomy. The sky was divided into 360 degrees (6 × 60). The hour �?originally a seasonal unit that varied in length between summer and winter �?was standardized by Greek astronomers into 1/24 of a day and subdivided into 60 minutes, each of 60 seconds. The words "minute" and "second" come from the Latin pars minuta prima (first small part) and pars minuta secunda (second small part) �?the first and second subdivisions of the hour. The terminology was formalized by the 13th-century English scholar Roger Bacon and entered standard astronomical usage through the Alfonsine Tables, a set of planetary position calculations compiled in Toledo around 1270.
When mechanical clocks spread across Europe in the 14th century, clockmakers adopted the astronomers' subdivisions. The clock face with 12 hours, 60 minute marks, and a second hand (added later, in the 17th century, when escapement mechanisms became precise enough to measure single seconds) is a direct descendant of a Sumerian accounting system from 4,000 years ago. The most universal piece of modern infrastructure �?the unit that governs every HTTP timeout, every basketball shot clock, every GPS satellite's onboard clock correction, and every distributed system leader election �?traces back to a civilization that built ziggurats and wrote on clay tablets. No other unit of measurement has a lineage that clean.
The Second: From a Fraction of a Day to an Atom in a Vacuum Chamber
The second has been redefined more times than any other SI base unit. Originally: 1/86,400 of a mean solar day �?the length of time it takes the Earth to rotate once relative to the Sun, averaged over a year. This worked until the 20th century, when quartz clocks revealed that the Earth's rotation varied by milliseconds from year to year, season to season, and even day to day. A clock defined by the Earth was a clock that drifted.
In 1956, the second was redefined as 1/31,556,925.9747 of the tropical year 1900 �?a specific astronomical reference epoch. This was more stable than the day-to-day rotation, but it was not measurable in real time. You couldn't check a clock against the tropical year 1900 without performing astronomical observations and integrating over months.
In 1967, the 13th General Conference on Weights and Measures abandoned astronomy entirely and redefined the second in terms of quantum mechanics: exactly 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom. The cesium atom's single valence electron, in its ground state, can be in one of two energy levels depending on whether the electron's magnetic moment is aligned with or against the nucleus's magnetic moment. The transition between those two hyperfine levels releases or absorbs a photon of exactly 9.192631770 GHz. Count 9,192,631,770 cycles of that radiation and you have measured one second with a precision limited only by your ability to count and your cesium fountain clock's ability to isolate the atom from external magnetic fields.
The current state of the art �?cesium fountain clocks at NIST (Boulder, Colorado), PTB (Braunschweig, Germany), and NPL (Teddington, UK) �?achieves accuracy of roughly 1 part in 10¹�? equivalent to drifting by less than one second over the entire 13.8-billion-year age of the universe. Experimental optical lattice clocks using strontium or ytterbium atoms, operating at optical frequencies (~10¹�?Hz) rather than microwave frequencies (~10¹�?Hz), are approaching 1 part in 10¹�? The second will likely be redefined again before 2030, based on an optical transition rather than a microwave one. The minute �?exactly 60 of whatever the current definition of a second is �?inherits all of that precision. The formula is one multiplication. The physics behind it is the most accurate measurement humans have ever made.
Worked Examples
1 min �?60 s
1 × 60 = 60. The definition. Nine billion cesium cycles, sixty times. The basketball shot clock, the microwave timer, the "one minute remaining" in a Zoom meeting �?every one of them counts exactly 60 of the same seconds. There is no other unit conversion on Earth with zero international variation and zero measurement uncertainty. Even the meter �?defined via the speed of light �?has an uncertainty of 3 parts in 10¹�?due to the practical realization of the standard. The second is more precisely realizable than any other unit.
5 min �?300 s
5 × 60 = 300. The default TCP keep-alive timeout for many HTTP servers. If the server doesn't hear from the client in 300 seconds, it closes the connection. A client with a 299-second keep-alive is fine. A client at 301 seconds gets disconnected and has to re-establish the TCP handshake �?adding roughly one round-trip time of latency. Network engineers tune this number in seconds. Developers configure it in minutes in a YAML file without multiplying. The gap between 5 minutes and 300,000 milliseconds (a different unit error �?confusing seconds with milliseconds) has caused more cascading failures in microservice architectures than any bug except null pointer dereferences.
45 min �?2,700 s
45 × 60 = 2,700. A soccer half �?plus stoppage time, the only sport where the clock counts up instead of down and the referee alone knows when it ends. The 45-minute half is a legacy of the original 1863 Football Association rules, which specified that a match should be played until the participants agreed it was over. The 90-minute match was standardized in 1897. The clock has been counting 2,700 seconds per half ever since, except during extra time, except during stoppage, except during VAR reviews �?a unit conversion so well-established that nobody questions it, layered with enough exceptions that the actual elapsed time can be anywhere from 2,700 to 3,600 seconds and the only person who knows the exact number is wearing a black shirt and carrying a whistle.
1,440 min �?86,400 s
1,440 × 60 = 86,400. One day. One rotation of the Earth. Give or take a millisecond �?the Earth's rotation is not constant, and the length of a day varies by roughly ±1 millisecond from year to year. On a leap-second day, the day has 86,401 seconds. On the day the leap second is abolished in 2035, the day will have exactly 86,400 seconds and the difference between atomic time and Earth time will be someone else's problem �?specifically, the ITU's, circa 2135, when the divergence reaches one minute and we either add a "leap minute" or accept that noon on the clock no longer matches noon in the sky.
When 1 Minute = 61 Seconds
The Earth's rotation is slowing. Tidal friction from the Moon transfers angular momentum from the Earth's rotation to the Moon's orbit, pushing the Moon roughly 3.8 centimeters farther from Earth each year and lengthening the day by roughly 1.8 milliseconds per century. It doesn't sound like much. Across 100 years, it's 0.18 seconds per day. Across 2,000 years, the accumulated discrepancy between where the Earth actually is in its rotation and where a clock that was set to match it 2,000 years ago would predict is several hours �?the historical record of eclipses confirms that the Sun was in a noticeably different position than a constant-rate clock would calculate.
The International Earth Rotation and Reference Systems Service (IERS), based in Paris, monitors the difference between UT1 (Earth rotation time, measured by radio telescopes observing distant quasars) and TAI (International Atomic Time, the weighted average of roughly 400 atomic clocks in 80 laboratories worldwide). When the difference between UT1 and UTC (which runs at the atomic clock's pace but is periodically adjusted) approaches 0.9 seconds, the IERS declares a leap second. Since 1972, 27 have been inserted. All were positive �?23:59:60, a 61st second. None were negative �?23:59:58, skipping a second �?because the Earth's rotation, while variable, has never accelerated enough for a day to drop below 86,400 seconds since atomic clocks began measuring it. The most recent leap second was December 31, 2016. There hasn't been one since �?the Earth's rotation has been anomalously fast in the 2020s, possibly due to changes in the Earth's core-mantle coupling, and the accumulated UT1-UTC offset has been drifting the other direction. The ITU's 2022 decision to abolish the leap second by 2035 means the 27 that have been inserted may be the last.
December 31, 2016: The Second That Broke the Internet
At midnight UTC on January 1, 2017, the 27th leap second was inserted. Within minutes, Cloudflare's DNS resolver �?the edge service that translates domain names to IP addresses for roughly 10% of the internet �?experienced a partial global outage. The root cause was in the Go programming language's standard library, specifically the interaction between Go's runtime timer and the Network Time Protocol daemon's leap-second handling.
During a leap second, an NTP daemon can handle the extra second in three ways: (1) step the clock backward by one second after the leap second passes, (2) insert the leap second by stepping the clock forward at 23:59:60, or (3) slew the clock �?gradually adjust the clock rate over several hours to absorb the extra second. Option 1 �?stepping backward �?is the simplest to implement in the NTP daemon and the most catastrophic for application software. Go's time.Timer and time.Ticker types internally compute the elapsed time as the difference between two monotonic clock readings. When the system clock was stepped backward by one second, the elapsed time calculation returned a negative value. The Go runtime, seeing a negative elapsed time for an active timer, either panicked (in debug builds) or hung the timer goroutine (in production builds). DNS queries that depended on those timers timed out. Cloudflare's edge, which serves DNS for millions of domains, dropped a fraction of its queries. The incident lasted roughly 10 minutes for the affected servers.
Cloudflare was not alone. Reddit's backend, which was running a substantially similar Go service stack on a substantially similar Linux kernel configuration, experienced database connection pool exhaustion when its connection timers hung during the leap second. LinkedIn's feed generation pipeline stalled. Yelp's search indexing fell behind. Parts of the Qantas Airways reservation system reported booking timeouts. Every affected service had one thing in common: a piece of software that assumed time never goes backward, encountering a system clock that went backward by one second, in a leap second that was inserted specifically to keep UTC aligned with the Earth's rotation. The Earth's tidal friction from the Moon, transmitted through NTP, broke the Go runtime. The causal chain is long but unbroken: the Moon's gravity �?Earth's slowing rotation �?IERS leap-second bulletin �?NTP step-backward �?Go runtime negative elapsed time �?DNS timeout �?"website is down."
The same failure mode caused a Linux kernel livelock during the June 30, 2012 leap second. The kernel's high-resolution timer subsystem (hrtimer) entered a state where certain timers were re-queued indefinitely because the kernel's time-keeping code briefly reported an inconsistent clock value during the leap second adjustment. Red Hat, SUSE, and Debian all issued kernel patches within 48 hours. The 2012 leap second incident was the one that made the Linux kernel community take leap seconds seriously as a reliability problem rather than a standards-body curiosity.
The Leap Smear: Google's Quiet Coup Against Coordinated Universal Time
After the 2012 kernel livelock, Google decided it was done with leap seconds. Rather than subject its global fleet �?then roughly 2 million servers �?to a discontinuous clock jump every 18 months, Google modified its internal NTP servers to "smear" the leap second across a 24-hour window.
The technique is straightforward: starting at noon UTC on the day before the scheduled leap second, Google's NTP servers report a clock rate that is 0.0014% slow �?roughly 13.9 microseconds per second slower than true atomic time. Over the next 86,400 seconds, the accumulated drift reaches exactly one second. At midnight UTC, when the IERS inserts the leap second, Google's clocks are already one second behind TAI �?and they smoothly re-synchronize to atomic time over the following hours by running the same smear in reverse. No individual tick is longer than 1,000,014 microseconds. No timestamp ever goes backward. No application code ever sees a negative elapsed time. The tradeoff: during the smear window, Google's clocks disagree with the rest of the world's clocks by up to 500 milliseconds.
For a search query or a video stream, 500 ms of clock skew is invisible �?the user's latency to the server is larger than the smear offset. For a financial exchange matching engine that timestamps every order to the microsecond, 500 ms of clock skew is an eternity. High-frequency trading firms do not use Google's NTP. They run their own stratum-1 time servers with GPS-disciplined oscillators and apply leap seconds directly, because sub-millisecond timestamp accuracy is a regulatory requirement under MiFID II in Europe and SEC Rule 613 (the Consolidated Audit Trail) in the United States. The leap smear is a compromise between the needs of distributed systems (don't ever jump backwards) and the needs of financial regulation (every timestamp must be traceable to UTC to within 100 microseconds). The two requirements are incompatible during a leap second. The industry's solution is to let Google and Amazon smear and let the exchanges jump, and to accept that during the 24 hours surrounding a leap second, two servers in the same data center can disagree about what time it is by half a second and neither of them is wrong.
Common Minutes to Seconds
| Minutes | Seconds | Where you see this |
|---|---|---|
| 1 min | 60 s | Definition. The minute of arc (1/60 of a degree) uses the same Babylonian ratio. |
| 5 min | 300 s | Default HTTP keep-alive. Instant ramen. The shortest meeting your calendar app allows. |
| 15 min | 900 s | Parking meter interval. TED talk. Standard break between conference sessions. |
| 30 min | 1,800 s | Sitcom runtime without ads. DNS TTL minimum for load-balanced services. |
| 45 min | 2,700 s | Soccer half. Lecture period. One billing increment for a lawyer. |
| 60 min | 3,600 s | One hour. A podcast episode. The timeout before a streaming service asks "are you still watching?" |
| 90 min | 5,400 s | Full soccer match plus stoppage time. A movie. One REM sleep cycle. |
| 1,440 min | 86,400 s | One day. One rotation of the Earth. 86,401 on a leap-second day. |
| 10,080 min | 604,800 s | One week. The standard billing period for cloud resources. |
Engineering Context
In distributed systems, timeouts and retry intervals are the most common source of cascading failures �?and minute-to-second conversion sits at the root of a disproportionate number of them. A developer writes timeout: 5 in a config file. Another developer's code reads that value and treats it as seconds. A third developer's library treats it as milliseconds. The config file doesn't label the unit. The value 5 means 5 seconds to one system, 5 minutes to another, and 5 milliseconds to a third. The thread pool that was sized for 5-second timeouts saturates when all connections block for 5 minutes instead. The service goes dark. Root cause: a bare number in a config file with no unit. Every major infrastructure project �?Kubernetes, PostgreSQL, Nginx, Redis �?uses seconds for all timeout values. Every junior developer has typed a timeout in minutes without multiplying by 60 at least once. The industry's defensive response: never name a config key timeout. Name it timeout_seconds. The unit must be in the variable name. The five characters _secs have probably prevented more production outages than every static analysis tool combined. For the reverse conversion, see seconds to minutes. For the next tier up, hours to seconds and hours to minutes span the longer timeouts �?database connection pool max lifetimes, TLS certificate expiration checks, cron job intervals. At the millisecond scale �?where embedded systems and audio processing live �?seconds to milliseconds and milliseconds to seconds handle the conversion that a real-time operating system's scheduler uses to decide which task runs next. A 1 ms scheduling quantum that a developer confuses with 1 second gives each task 1,000× more CPU time than intended �?the system doesn't crash, it just runs 1,000 times slower, and the bug is diagnosed as "performance degradation" rather than "unit error" because everything still works, just unacceptably slowly. Those are the hardest bugs to find.
More: seconds to minutes · minutes to hours · hours to minutes · hours to seconds · Time Guide
Related Unit Converters
Frequently Asked Questions
Is it true the Mars Polar Lander crashed because someone confused minutes and seconds?
No. The Mars Polar Lander (1999) crashed because a Hall-effect sensor on the landing leg registered the leg's deployment during cruise as "contact with Martian surface," and the descent engines shut off at 40 meters altitude. The unit error on that mission was in thrust �?pound-force vs. newtons, the same error as Mars Climate Orbiter. The minutes-to-seconds confusion is often conflated with these missions because they all belong to the same category: two groups using different units at an interface. But the specific "minutes vs. seconds" failure has never occurred on a NASA Mars mission. It has occurred, repeatedly, in config files and timeout settings, where a 5-minute timeout becomes a 5-second timeout and the service retries before the downstream has finished processing �?a retry storm that saturates the thread pool and takes down the cluster. The root cause is identical: a bare number with no unit label. The domain is different. The lesson is the same.
Why don't we switch to decimal time? 100 seconds per minute, 100 minutes per hour?
The French tried �?during the Revolution, alongside the metric system. The French Republican Calendar (1793�?805) divided the day into 10 hours, each hour into 100 minutes, each minute into 100 seconds. The decimal second was 0.864 conventional seconds �?slightly shorter. Decimal clocks were manufactured and installed in government buildings. They lasted about 12 years before Napoleon abolished the Republican Calendar in 1805. The decimal second failed for the same reason the metric system succeeded: everyone was already using the old system, and the cost of switching every clock, every astronomical table, every navigation chart, and every mechanical timepiece in the country was immense. The metric system succeeded because it replaced a chaos of local weights and measures �?there were over 250,000 different units in pre-revolutionary France. The time system failed because there was only one system to replace, and it was already universal. The Babylonians had won 4,000 years before the French revolutionaries were born. The 60:1 ratio has outlasted every empire that has existed since it was invented. It will outlast the metric system, the internet, and probably the nation-state.
How do I avoid time-related bugs in my code?
Four rules. One: never store a timeout as a bare number. The variable name must contain the unit �?query_timeout_seconds, retry_interval_ms. Two: never assume time only goes forward. The system clock can be stepped backward by NTP, by a leap second, by a VM migration, by a user changing the time zone. Use a monotonic clock for interval measurement �?clock_gettime(CLOCK_MONOTONIC) on Linux, time.monotonic() in Python, performance.now() in JavaScript. Three: never store a future timestamp in local time. Store it in UTC. Convert to local time only for display. Four: never assume every minute has 60 seconds. On a leap-second day, one minute has 61. If your code divides elapsed seconds by 60 to display minutes and the division produces a remainder of 61, handle it. Most code doesn't. Most code gets away with it because leap seconds happen once every 18 months on average. The code that fails is the code running during that one minute �?and the failure mode is exactly one second of incorrect output, which is small enough to be dismissed as a rounding error and large enough to corrupt a financial transaction log. The four rules are not theoretical. Every one of them has a production outage associated with it. The Cloudflare incident is rule 4. The Linux hrtimer livelock is rule 2. Every config-file timeout storm is rule 1. Rule 3 has killed satellite ground station passes when the ground software assumed local time and the satellite's telemetry was timestamped in UTC and the two disagreed by the time zone offset, and the antenna was pointed at the wrong patch of sky for the first 30 seconds of the pass. The rules are simple. Following them is what separates a system that survives a leap second from a system that becomes a postmortem document.
What happens when we abolish the leap second in 2035?
The International Telecommunication Union's World Radiocommunication Conference voted in November 2022 to abolish the leap second by 2035 �?the resolution specifically states "not later than 2035." Between now and then, no new leap seconds will be scheduled. UTC will continue to diverge from UT1. By 2035, the divergence will be roughly 1 second. After 2035, UTC will be a pure atomic time scale with no connection to the Earth's rotation. The difference between UT1 and UTC will be allowed to grow �?roughly 1 minute per century, 1 hour per 6,000 years. Astronomers, who need Earth-rotation time to point telescopes, will still compute UT1-UTC (the difference will be published by IERS as a value called DUT1, broadcast in the time signals from GPS and other GNSS satellites). Civil time �?the time on your phone, your computer, your microwave �?will no longer contain leap seconds. No server will crash because of a leap second. No DNS resolver will go down. No airline reservation system will freeze. The cost is that, eventually, clock noon will no longer match solar noon. In the year 2200, solar noon in Greenwich will occur at roughly 12:01:30 UTC. A century later, 12:03. The divergence will be visible on a sundial within a human lifetime. Most people will not notice, because most people do not navigate by the Sun. The ITU's decision was practical: the cost of leap seconds �?in software failures, in engineering hours, in operational risk �?exceeds the benefit of keeping the clock aligned with the Earth. The Moon will continue to slow the Earth's rotation. The cesium atom will continue to tick at its perfectly constant rate. After 2035, the two will be allowed to drift apart, and the second �?the most precisely measured unit in science �?will finally be free of the planet it was originally defined to measure.
How accurate is the "× 60" conversion? Is there any variation?
There is no variation. One minute equals exactly 60 SI seconds, universally. The second is defined by a fundamental physical constant �?the cesium hyperfine transition frequency �?that does not change in any reference frame in which the laws of physics hold. The minute inherits that exactness by multiplication. Unlike the foot (which differed between the US and UK until 1959), the gallon (which still differs between the US and UK), the ton (which has three definitions), and the horsepower (which has four), the minute-to-second ratio has exactly one definition in every country on Earth. It is the only unit conversion with zero international ambiguity. The only edge case is the leap second �?when 1 minute = 61 seconds for one specific minute on one specific day, by international agreement, to reconcile atomic time with a planet that doesn't rotate as smoothly as an atom vibrates. The edge case is scheduled years in advance, announced in IERS Bulletin C, and ignored at your peril. It will cease to exist in 2035. After that, the minute-to-second conversion will be the only perfectly unambiguous measurement in the human-built world �?a 4,000-year-old ratio, validated by 20th-century quantum mechanics, with no exceptions.