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Why does US currency have a 25 cent piece instead of a 20 cent piece? Why is there a 20 dollar bill instead of a 25 dollar bill? Why aren't both denominations the same, 20 or 25 for both the dollars and cents?

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    Wikipedia article on the quarter has your answer, albeit unsourced: "A quarter, short for quarter dollar, is a U.S. coin worth 25 cents, one-fourth of a dollar. It has been produced since 1796. The choice of 1⁄4 as a denomination—as opposed to the 1⁄5 more common elsewhere—originated with the practice of dividing Spanish milled dollars into eight wedge-shaped segments. At one time "two bits" (that is, two "pieces of eight") was a common nickname for a quarter." – two sheds Jun 12 '15 at 3:16
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    Interesting question. Never even considered how odd it is! – basher Jun 12 '15 at 18:47
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    For a brief time there was a 20 cent piece en.wikipedia.org/wiki/Twenty-cent_piece_(United_States_coin) – hatchet - Reinstate Monica Jun 12 '15 at 19:00
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    In the UK, the denominations follow a very obvious pattern: 1p, 2p, 5p, 10p, 20p, 50p, £1, £2, £5 and so on. There was a survey recently (perhaps someone can find a link) where British people were asked which new coin they'd most like to have and which current coin was the last useful. The results: the least useful current coin was the 2p coin, and the most useful new coin to have would be a 25p coin! – John Gowers Jun 12 '15 at 19:13
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    In the USSR, the coins were 1k,2k,3k,5k,10k,15k,20k,50k,1r; paper money was 1r,3r,5r,10r,25r (i.e., there was a 20k coin and a 25r note). – sds Jun 12 '15 at 19:46
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This is because Americans were used to dealing in quarters at the time the denomination was chosen. During the colonial period, a common unit of currency was one eighths of a Spanish real de a ocho. Since each of these Spanish dollars were worth eight Spanish reales it was habitual to divide the eight-real coin into 12.5% wedges known as bits. Two of these were therefore equivalent to 25% of the Spanish dollar, i.e. 25 cents.

When the nascent United States adopted its own currency standard, the original one dollar was based on the aforementioned Spanish dollar. The customary unit of two bits of the Spanish dollar thus became 25 cents of the equivalent United States dollar.

In 1793, Congress adopted decimal coinage - 100 cents to the dollar - to replace the eights into which Spanish dollars were divided. Nevertheless, old habits died hard. Congress also instructed the U.S,. Mint to coin quarter dollars. Quarters made no sense decimally, but they reflected the partition of a Spanish dollar into eight reales.

- Conlin, Joseph. The American Past: A Survey of American History, Volume II: Since 1865. Cengage Learning, 2013.

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    Could you extend your answer for the 2nd OP's question? Why is then 20 dollar note? – Voitcus Jun 12 '15 at 5:36
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    I think the above answers both: people were used to a quarter of something, but there was nothing such a 25-times-of. – algiogia Jun 12 '15 at 8:20
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    @Voitcus additionally, '25' is somewhat the exception ('20' being usually preferred because it makes calculating how much exchange the clerk has to return easier, specially at a time when there were no electronic calculators). – SJuan76 Jun 12 '15 at 9:05
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    "Quarters made no sense decimal" I don't really buy the idea that quarters make less sense than fifths. I guess it's very slightly easier to make change with 20c rather than 25c but, honestly, I can't say I've ever had a problem with the speed with which American shop assistants make change. – David Richerby Jun 12 '15 at 10:21
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    As a curiosity, in Spain before Euro was a 25 pesetas coin but no 20 pesetas coin. Now with Euro we have 20c but not 25c. – Mario Levrero Jun 12 '15 at 13:07
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I originally thought it was because of best way to reduce number of coins needed before I read Semaphore's answer.

I thought it was designed this way due to efficiency: for example at all values between 0 and 1 dollar that ends in 0 or 5

5 cent = 1 coin

10 cent = 1 coin

15 cent = 2 coins

20 cent = 2 coins (1 coin if using 5/10/20)

25 cent = 1 coin (2 coins if using 5/10/20)

30 cent = 2 coins

35 cent = 2 coins (3 coins if using 5/10/20)

40 cent = 3 coins (2 coins if using 5/10/20)

45 cent = 3 coins

50 cent = 2 coins (3 coins if using 5/10/20)

55 cent = 3 coins (4 coins if using 5/10/20)

60 cent = 3 coins

65 cent = 4 coins

70 cent = 4 coins

75 cent = 3 coins (5 coins if using 5/10/20)

80 cent = 4 coins

85 cent = 4 coins (5 coins if using 5/10/20)

90 cent = 5 coins

95 cent = 5 coins (6 coins if using 5/10/20)

1 dollar = 4 coins (5 coins if using 5/10/20)

There are only 2 occasions that 5/10/20 uses less coins than 5/10/25

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    This is kind of cheating, since most systems that use a 20 coin also have a 50. – David Richerby Jun 12 '15 at 20:53
  • @PieterGeerkens It doesn't do that at all! 5/10/20/50 beats 5/10/25 for 11 different change values (three of them by a two-coin margin); 5/10/25 only wins for two (25 and 35, each by one coin). The irony is that 5/10/25/50 and 5/10/20/50 are equally good -- the US has a 50c coin but you never see them in the wild. – David Richerby Jan 20 '18 at 20:18
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I think the real answer basically boils down to attrition. Over the years, the US has minted many denominations of coins, ranging from the half cent piece up to the $50 Half-Union coin: https://en.wikipedia.org/wiki/Coins_of_the_United_States_dollar#Obsolete_coins

Most of them have fallen out of use for various reasons, mostly because having many denominations proved inconvenient and/or confusing. The US did mint a 20 cent piece for a few years, but it was unpopular because it was easily confused with a quarter: https://en.wikipedia.org/wiki/Twenty-cent_piece_(United_States_coin) The same was true of the short-lived Susan B. Anthony dollar coin https://en.wikipedia.org/wiki/Dollar_coin_(United_States)#Susan_B._Anthony_dollar_(1979%E2%80%931981;_1999) which I suspect (along with the inconvenience of having two $1 coins of very different sizes) contributed to the current unpopularity of the dollar coin. (Gold coins are obviously a special case, thanks to FDR &c.)

I'd guess that the use of cash registers also played a part, as they can easily fit only so many pockets for coins. Perhaps that also caused the virtual abandonment of the $2 bill, and is contributing to the decline I've seen in the use of the $10 bill. (My grocery store only gives out $5 bills in change, and any $10s you give them are tucked underneath the tray.)

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