1815
1815 is the year of the Battle of Waterloo and the close of the Congress of Vienna.
- Odd
- Composite
Where 1815 fits
Why 1815 is special
1815 ended twenty-three years of near-continuous European war. Napoleon's defeat at Waterloo in June closed the Hundred Days, and the Congress of Vienna concluded weeks earlier, redrawing borders in a settlement that kept the great powers from general war for the better part of a century. The year is also remembered for the eruption of Mount Tambora, which caused the following 'year without a summer'.
Same number, different meanings
How 1815 is understood across different contexts — never implying one meaning because of another.
- Mathematics
1815 ended twenty-three years of near-continuous European war. Napoleon's defeat at Waterloo in June closed the Hundred Days, and the Congress of Vienna concluded weeks earlier, redrawing borders in a settlement that kept the great powers from general war for the better part of a century. The year is also remembered for the eruption of Mount Tambora, which caused the following 'year without a summer'.
- History
In 1815, the Battle of Waterloo ended the Napoleonic Wars, and Tambora erupted, causing a global climate shock.
- Science
Mount Tambora erupted in April 1815 in the largest volcanic event of recorded history, injecting enough sulphate aerosol into the stratosphere to lower global temperatures measurably. The following year brought crop failures and snow in June across Europe and North America — a documented case of a single geological event altering a hemisphere's weather.
1815 is part of
Factors & digit properties
- Divisors (12)
- 1, 3, 5, 11, 15, 33, 55, 121, 165, 363, 605, 1815
- Prime factorisation
- 3 × 5 × 11^2
- Digit sum
- 15
- Digital root
- 6
Representations
- Decimal
- 1815
- Scientific notation
- 1.815 × 10^3
Roman numerals
M D C C C X V
Binary
1 1 1 0 0 0 1 0 1 1 1
1 × 1,024 + 1 × 512 + 1 × 256 + 0 × 128 + 0 × 64 + 0 × 32 + 1 × 16 + 0 × 8 + 1 × 4 + 1 × 2 + 1 × 1 = 1,815
Octal
3 4 2 7
3 × 512 + 4 × 64 + 2 × 8 + 7 × 1 = 1,815
Hexadecimal
7 1 7
7 × 256 + 1 × 16 + 7 × 1 = 1,815
Read as powers of two: 1,024 + 512 + 256 + 16 + 4 + 2 + 1 = 1,815.
In historical numeral systems
Egyptian
1 lotus, 8 coils of rope, 1 hobble, 5 strokes
1 × 1,000 + 8 × 100 + 1 × 10 + 5 × 1 = 1,815. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Babylonian
3 corner wedges (sixties place), 1 corner wedge + 5 vertical wedges (units place)
30 × 60 + 15 = 1815. Places are separated by a space on the tablet, with the higher place written first.
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
- Deficient number
- Happy number
- Harshad (Niven) number
Related numbers & connections
1815 is a year in the 19th century, in the 1810s.
Napoleon's Russian campaign of 1812 destroyed his army and Waterloo in 1815 ended his rule. The retreat did more damage than the final defeat.
View 1812 →History
In 1815, the Battle of Waterloo ended the Napoleonic Wars, and Tambora erupted, causing a global climate shock.
DocumentedHistoryGeography: globalPeriod: 1815
Science
Mount Tambora erupted in April 1815 in the largest volcanic event of recorded history, injecting enough sulphate aerosol into the stratosphere to lower global temperatures measurably. The following year brought crop failures and snow in June across Europe and North America — a documented case of a single geological event altering a hemisphere's weather.
DocumentedSciencePeriod: 1815 – 1816
Common questions
Is 1815 a prime number?
No, 1815 is not prime.
What are the factors of 1815?
The factors of 1815 are 1, 3, 5, 11, 15, 33, 55, 121, 165, 363, 605, 1815.
What is 1815 in Roman numerals?
1815 in Roman numerals is MDCCCXV.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 2 reviewer-confirmed records, sourced and reviewed before publication.
Last reviewed: 15 July 2026