42,195
42,195 metres — 26 miles and 385 yards — is the official marathon distance.
- Odd
- Composite
Where 42,195 fits
Why 42,195 is special
The marathon's distance is an accident that stuck. Early modern marathons varied around 40 km; the 1908 London Olympic course was laid out at 26 miles 385 yards, and that figure was formally adopted as the standard in 1921. The often-repeated claim that the extra 385 yards was added so the finish lay before the royal box is widely told but not firmly documented.
Same number, different meanings
How 42,195 is understood across different contexts — never implying one meaning because of another.
- Mathematics
The marathon's distance is an accident that stuck. Early modern marathons varied around 40 km; the 1908 London Olympic course was laid out at 26 miles 385 yards, and that figure was formally adopted as the standard in 1921. The often-repeated claim that the extra 385 yards was added so the finish lay before the royal box is widely told but not firmly documented.
- History
Early modern marathons were run at varying distances around 40 km. The 1908 London Olympic course measured 26 miles 385 yards, and in 1921 the IAAF adopted that figure as the standard, so a course laid out once became the permanent definition. The popular explanation that the extra 385 yards positioned the finish before the royal box is often repeated but not firmly documented.
- Sport
The marathon distance of 42,195 metres was set at the 1908 London Olympics by the layout of the course. It was formally adopted as standard in 1921 and has not changed since.
42,195 is part of
Factors & digit properties
- Divisors (16)
- 1, 3, 5, 15, 29, 87, 97, 145, 291, 435, 485, 1455, 2813, 8439, 14065, 42195
- Prime factorisation
- 3 × 5 × 29 × 97
- Digit sum
- 21
- Digital root
- 3
Representations
- Decimal
- 42195
- Scientific notation
- 4.220 × 10^4
Roman numerals
Roman numerals as modelled here goes up to 3,999.
Binary
1 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1
1 × 32,768 + 0 × 16,384 + 1 × 8,192 + 0 × 4,096 + 0 × 2,048 + 1 × 1,024 + 0 × 512 + 0 × 256 + 1 × 128 + 1 × 64 + 0 × 32 + 1 × 16 + 0 × 8 + 0 × 4 + 1 × 2 + 1 × 1 = 42,195
Octal
1 2 2 3 2 3
1 × 32,768 + 2 × 4,096 + 2 × 512 + 3 × 64 + 2 × 8 + 3 × 1 = 42,195
Hexadecimal
a 4 d 3
a × 4,096 + 4 × 256 + d × 16 + 3 × 1 = 42,195
Read as powers of two: 32,768 + 8,192 + 1,024 + 128 + 64 + 16 + 2 + 1 = 42,195.
In historical numeral systems
Egyptian
4 fingers, 2 lotuses, 1 coil of rope, 9 hobbles, 5 strokes
4 × 10,000 + 2 × 1,000 + 1 × 100 + 9 × 10 + 5 × 1 = 42,195. 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
- Triangular number
- Deficient number
Related numbers & connections
The half marathon is exactly half the marathon, so it inherits a distance that was itself fixed by extending the 1908 London course to finish in front of the royal box.
View 21097 →Marathon in 490 BC gave the modern race its name, and the 42,195 m distance was fixed in 1921 from a course extended in 1908 to finish before the royal box.
View 480 →History
Early modern marathons were run at varying distances around 40 km. The 1908 London Olympic course measured 26 miles 385 yards, and in 1921 the IAAF adopted that figure as the standard, so a course laid out once became the permanent definition. The popular explanation that the extra 385 yards positioned the finish before the royal box is often repeated but not firmly documented.
DocumentedHistoryPeriod: 1908 – 1921
Sport
The marathon distance of 42,195 metres was set at the 1908 London Olympics by the layout of the course. It was formally adopted as standard in 1921 and has not changed since.
DocumentedSportGeography: United Kingdom, then internationalPeriod: 1908; standardised 1921A record-eligible marathon must be at least 42,195 metres, never less, so certified courses are measured along the shortest possible running line and then deliberately laid out slightly long. A course found short after the event invalidates every time set on it, which is why measurement certification is a separate discipline from race organisation.
DocumentedSport
Common questions
Is 42,195 a prime number?
No, 42,195 is not prime.
What are the factors of 42,195?
The factors of 42,195 are 1, 3, 5, 15, 29, 87, 97, 145, 291, 435, 485, 1455, 2813, 8439, 14065, 42195.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 3 reviewer-confirmed records, sourced and reviewed before publication.
Last reviewed: 15 July 2026