86,400
86400 is the number of seconds in a day — 24 hours of 3600 seconds each.
- Even
- Composite
Where 86,400 fits
Why 86,400 is special
86400 is the number the day reduces to once every inherited convention has been multiplied out, and it is the single most reused constant in computer timekeeping: Unix timestamps, cache lifetimes and scheduling intervals are all commonly expressed as multiples or fractions of it. With 96 divisors it divides evenly in almost any way a system might need.
Same number, different meanings
How 86,400 is understood across different contexts — never implying one meaning because of another.
- Mathematics
86400 is the number the day reduces to once every inherited convention has been multiplied out, and it is the single most reused constant in computer timekeeping: Unix timestamps, cache lifetimes and scheduling intervals are all commonly expressed as multiples or fractions of it. With 96 divisors it divides evenly in almost any way a system might need.
- History
86,400 = 24 × 60 × 60, and each factor has a different origin. The 24-hour day descends from Egyptian practice of dividing daylight and darkness into twelve parts each; the sixtieths come from Babylonian sexagesimal arithmetic, transmitted through Greek astronomy. So the number is the product of two unrelated ancient conventions that were never designed to combine, which is why it is 86,400 rather than any round figure.
- Science
The SI second is defined by a caesium transition and not by the Earth, which rotates slightly irregularly and on average slightly slower than the definition assumes. UTC absorbs the difference by occasionally inserting a leap second, making that day 86,401 seconds long; twenty-seven have been added since 1972 and none has ever been removed. In 2022 the General Conference on Weights and Measures resolved to stop the practice by 2035, having concluded that the disruption to computer systems outweighs the benefit of keeping clocks aligned to the rotation.
- Everyday life
There are 86,400 seconds in a day, from 24 hours of 3600 seconds each. With 96 divisors it splits evenly in almost any way a schedule might require.
- Technology & computing
86,400 is the standard one-day interval in computer timekeeping, where durations are conventionally expressed in seconds — it appears throughout Unix-style timestamp arithmetic, cache lifetimes and scheduling configuration.
Not just a mathematical number
86,400is also used in ways where ordinary arithmetic doesn't apply — each listed below with what genuinely does and doesn't follow from it.
- Mathematical number
A genuine quantity — its mathematical properties (prime, square, factors, and so on) are real facts about it.
A genuine quantity that ordinary arithmetic applies to — it can be prime, even, a perfect square, added to another number meaningfully, and so on.
- Measurement
Also used as a measurement — Hours in a day.
A quantity expressed against a defined unit or standard (24 hours in a day, 60 seconds in a minute) — arithmetic is meaningful, but the specific value is a fixed convention of the measuring system, not a discovered mathematical property.
86,400 is part of
Factors & digit properties
- Divisors (96)
- 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 64, 72, 75, 80, 90, 96, 100, 108, 120, 128, 135, 144, 150, 160, 180, 192, 200, 216, 225, 240, 270, 288, 300, 320, 360, 384, 400, 432, 450, 480, 540, 576, 600, 640, 675, 720, 800, 864, 900, 960, 1080, 1152, 1200, 1350, 1440, 1600, 1728, 1800, 1920, 2160, 2400, 2700, 2880, 3200, 3456, 3600, 4320, 4800, 5400, 5760, 7200, 8640, 9600, 10800, 14400, 17280, 21600, 28800, 43200, 86400
- Prime factorisation
- 2^7 × 3^3 × 5^2
- Digit sum
- 18
- Digital root
- 9
Representations
- Decimal
- 86400
- Scientific notation
- 8.640 × 10^4
Roman numerals
Roman numerals as modelled here goes up to 3,999.
Binary
1 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0
1 × 65,536 + 0 × 32,768 + 1 × 16,384 + 0 × 8,192 + 1 × 4,096 + 0 × 2,048 + 0 × 1,024 + 0 × 512 + 1 × 256 + 1 × 128 + 0 × 64 + 0 × 32 + 0 × 16 + 0 × 8 + 0 × 4 + 0 × 2 + 0 × 1 = 86,400
Octal
2 5 0 6 0 0
2 × 32,768 + 5 × 4,096 + 0 × 512 + 6 × 64 + 0 × 8 + 0 × 1 = 86,400
Hexadecimal
1 5 1 8 0
1 × 65,536 + 5 × 4,096 + 1 × 256 + 8 × 16 + 0 × 1 = 86,400
Read as powers of two: 65,536 + 16,384 + 4,096 + 256 + 128 = 86,400.
In historical numeral systems
Egyptian
8 fingers, 6 lotuses, 4 coils of rope
8 × 10,000 + 6 × 1,000 + 4 × 100 = 86,400. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Systems that simply cannot reach this value are left out. Where a script needs a font most readers do not have, the reading is given instead of the glyphs — see number systems for each system in full.
Other mathematical patterns
- Abundant number
- Powerful number
- Harshad (Niven) number
Related numbers & connections
86,400 is 24 × 3600 — the day in seconds, built from the seconds-per-hour figure.
View 3600 →86,400 follows directly from the 24-hour day: each of those hours contributes 3600 seconds.
Mathematically related
Other connections
- is associated withHours in a day
why?
Strength 0.50, confidence "high".
- developed fromBabylonian sexagesimal (base-60) system
why?
Strength 0.50, confidence "high".
- is associated withTime unit conversions
why?
Strength 0.50, confidence "high".
- is associated withMinutes and seconds
why?
Strength 0.50, confidence "high".
History
86,400 = 24 × 60 × 60, and each factor has a different origin. The 24-hour day descends from Egyptian practice of dividing daylight and darkness into twelve parts each; the sixtieths come from Babylonian sexagesimal arithmetic, transmitted through Greek astronomy. So the number is the product of two unrelated ancient conventions that were never designed to combine, which is why it is 86,400 rather than any round figure.
DocumentedHistory
Science
The SI second is defined by a caesium transition and not by the Earth, which rotates slightly irregularly and on average slightly slower than the definition assumes. UTC absorbs the difference by occasionally inserting a leap second, making that day 86,401 seconds long; twenty-seven have been added since 1972 and none has ever been removed. In 2022 the General Conference on Weights and Measures resolved to stop the practice by 2035, having concluded that the disruption to computer systems outweighs the benefit of keeping clocks aligned to the rotation.
DocumentedSciencePeriod: 1972 onwards; leap seconds to end by 2035
Everyday life
There are 86,400 seconds in a day, from 24 hours of 3600 seconds each. With 96 divisors it splits evenly in almost any way a schedule might require.
DocumentedEveryday life
Technology & computing
86,400 is the standard one-day interval in computer timekeeping, where durations are conventionally expressed in seconds — it appears throughout Unix-style timestamp arithmetic, cache lifetimes and scheduling configuration.
DocumentedTechnology & computing
Mathematics
86,400 = 2⁷ × 3³ × 5², giving 96 divisors — so the day divides evenly into any of 96 different interval lengths, including every whole number of minutes that divides 1,440 and every whole number of hours. That is why timetables, shift rotas and polling intervals can almost always be expressed as a whole number of seconds that fits the day exactly, and it is a direct inheritance of the highly divisible bases the units came from.
DocumentedMathematics
Common questions
How many seconds are in a day?
86,400 — 24 hours of 60 minutes of 60 seconds. Not always exactly, though: the SI second is defined by a caesium transition rather than by the Earth, which rotates slightly irregularly, so UTC occasionally inserts a leap second and makes a day 86,401 seconds long. Twenty-seven have been added since 1972 and none removed; the practice is due to end by 2035.
Is 86,400 a prime number?
No, 86,400 is not prime.
What are the factors of 86,400?
The factors of 86,400 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 64, 72, 75, 80, 90, 96, 100, 108, 120, 128, 135, 144, 150, 160, 180, 192, 200, 216, 225, 240, 270, 288, 300, 320, 360, 384, 400, 432, 450, 480, 540, 576, 600, 640, 675, 720, 800, 864, 900, 960, 1080, 1152, 1200, 1350, 1440, 1600, 1728, 1800, 1920, 2160, 2400, 2700, 2880, 3200, 3456, 3600, 4320, 4800, 5400, 5760, 7200, 8640, 9600, 10800, 14400, 17280, 21600, 28800, 43200, 86400.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 5 reviewer-confirmed records, sourced and reviewed before publication.
Last reviewed: 15 July 2026