40 is the natural number following 39 and preceding 41. In English, forty is the only number whose constituent letters appear in alphabetical order.

In mathematics

Forty is an octagonal number, and as the sum of the first four pentagonal numbers, it is a pentagonal pyramidal number. It is a Harshad number.

Given 40, the Mertens function returns 0. 40 is the smallest number n with exactly 9 solutions to the equation φ(x) = n.

Forty is the number of n-queens problem solutions for n = 7.

In science

• The atomic number of zirconium
• Negative forty is the temperature at which the Fahrenheit and Celsius scales correspond; that is, -40°F = -40°C. It is referred to as either "minus forty" or "forty below".

In astronomy,

Messier object M40, a magnitude 9.0 double star in the constellation Ursa Major

The New General Catalogue object (http://www.ngcic.org/) NGC 40, a magnitude 12.4 planetary nebula in the constellation Cepheus

The Saros number (http://sunearth.gsfc.nasa.gov/eclipse/SEsaros/SEsaros1-175.html) of the solar eclipse series which began on -1653 May 28 and ended on -373 July 4. The duration of Saros series 40 was 1280.1 years, and it contained 72 solar eclipses.

The Saros number (http://sunearth.gsfc.nasa.gov/eclipse/LEsaros/LEsaros1-175.html) of the lunar eclipse series which began on -1387 February 12 and ended on -71 April 12. The duration of Saros series 40 was 1316.2 years, and it contained 74 lunar eclipses.

In other fields

Forty is:

• in Judaic, Christian and Islamic tradition: the tag Forty days and forty nights describes the period for which rain fell during Noah's flood, the period Moses spent on Mount Sinai receiving the Ten Commandments and the period Christ spent in the wilderness. In modern Western Christian practice, Lent consists of the 40 days preceding Easter
• the usual number of days in the time of mourning in Muslim cultures.
• the number of days after death for which the ghosts of the dead hang around the site of their death, according to Russian belief
• in the maxim "Life begins at forty".
• in the expression "Forty winks", meaning a short sleep.
• the number of years of marriage as the ruby wedding anniversary.
• the code for direct dial international phone calls to Romania.
• in the designation of Interstate 40, a freeway that runs from California to North Carolina.
• in the designation for U.S. Highway 40, the 800-mile highway that runs from Baltimore, Maryland, to Vandalia, Illinois, being synonymous with the National Highway.
• the year A.D. 40, 40 BC, or (for example) 1940.
• the title of a song by U2.
• in the title of the Food Network show $40 a Day.
• in the name of WD-40, a type of spray lubricant.
• in the name of the food additive FD & C Red Dye #40, commonly known as "Red 40" [1] (http://www.red40.org/)
• the 40 ounce size used for liquor, typically fairly cheap malt beer
• in the UK, the A40 and M40 are important highways. The A40 is a trunk road in England and Wales, connecting London to Fishguard. The M40 motorway is the second motorway in the British transport network to connect London to Birmingham.