Tables 1: Measurements of coins

Here collected measurements of circulating coins of 14 major currencies across the globe. Data are based mostly on websites information of the mints or the central banks as of October 2012. Coins' data sum up to an average N to 1 ratio, which is used in tests for QCs.

Index

Table 1-1: Australian dollar coins
Table 1-2: Indonesian rupiah coins
Table 1-3: Indian rupee coins
Table 1-4: Chinese yuan coins
Table 1-5: South Korean won coins
Table 1-6: Japanese yen coins
Table 1-7: Russian ruble coins
Table 1-8: Turkish lira coins
Table 1-9: Euro coins
Table 1-10: Pound sterling coins
Table 1-11: Canadian dollar coins
Table 1-12: United States dollar coins
Table 1-13: Mexican peso coins
Table 1-14: Brazilian real coins
Table 1-15: N to 1 ratios of coins

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Table 1-1

Australian dollar coins

Denom. (A$)	Mass (g)	Density (g/cm3)	N:1 ratio
			Mass	Volume
0.01 0.02 0.05	2.60 5.20 2.83	8.89 8.89 8.93	- 2.00 1.09	- 2.00 1.08
0.1 0.2 0.5	5.65 11.30 15.55	8.93 8.93 8.93	- 2.00 2.75	- 2.00 2.75
1 2	9.00 6.60	8.56 8.56	- 0.73	- 0.73

¤ The above data are cited from Royal Australian Mint.
¤ Density is calculated from the coins' chemical compositions. e.g. A 0.01-A$ coin consists of 97% copper, 2.5% zinc, and 0.5% tin, which make the density 8.89(g/cm³) as is in the table.
¤ N:1 ratio of mass is calculated as the mass of D[N] (Denomination of HN=N (N=2~9)) divided by the mass of D[1]. e.g. N:1 ratio of the mass of 1-A$'s place is 6.60/9.00=0.73 as is shown above.
¤ Volume is derived from mass divided by density. e.g. The volume of a 0.01-A$ coin is 2.60/8.89=0.293(cm³). And a 0.02-A$ coin's volume is 5.20/8.89=0.585(cm³). Then, N:1 ratio of these two volumes is 0.585/0.293=2.00.

Table 1-2

Indonesian rupiah coins

Denom. (Rp)	Mass (g)	Diameter (mm)	Thickness (mm)	N:1 ratio
				Mass	Volume
50	1.36	20.00	2.0	-	-
100 200 500	1.79 2.38 3.10	23.00 23.00 27.00	2.0 2.3 2.5	- 1.33 1.73	- 1.15 1.72
1,000	4.50	24.15	1.6	-	-

¤ The above data are cited from Bank Indonesia.
¤ N:1 ratio of volume is calculated as the volume of D[N] divided by the volume of D[1]. e.g. The volumes of 200-rupiah to 100-rupiah is (23.00²*2.3)/(23.00²*2.0)=1.15.
¤ N:1 ratios of 10-rupiah's place and 1,000-rupiah's place cannot be calculated due to the absence of D[N] or D[1].

Table 1-3

Indian rupee coins

Denom. (Rs)	Mass (g)	Diameter (mm)	Thickness (mm)	N:1 ratio
				Mass	Volume
0.5	3.79	22	?	-	-
1 2 5	4.85 5.62 6.00	25 27 23	? ? ?	- 1.16 1.24	- ? ?

¤ The above data are cited from Reserve Bank of India.
¤ N:1 ratio of volume is unknown due to lack of necessary information.

Table 1-4

Chinese yuan coins

Denom. (CN¥)	Mass (g)	Diameter (mm)	Thickness (mm)	N:1 ratio
				Mass	Volume
0.1 0.5	? ?	19.0 20.5	? ?	- ?	- ?
1	?	25.0	?	-	-

¤ The above data are cited from People's Bank of China.
¤ N:1 ratio of mass and that of volume are unknown due to lack of necessary information.

Table 1-5

South Korean won coins

Denom. (W)	Mass (g)	Density (g/cm3)	N:1 ratio
			Mass	Volume
1 5	0.729 2.950	2.70 8.31	- 4.05	- 1.31
10 50	1.220 4.160	5.70 8.61	- 3.41	- 2.25
100 500	5.420 7.700	8.93 8.93	- 1.42	- 1.42

¤ The above data are cited from Bank of Korea.

Table 1-6

Japanese yen coins

Denom. (¥)	Mass (g)	Diameter (mm)	Thickness (mm)	N:1 ratio
				Mass	Volume
1 5	1.00 3.75	20.0 22.0	1.51 1.50	- 3.75	- 1.20
10 50	4.50 4.00	23.5 21.0	1.52 1.75	- 0.89	- 0.92
100 500	4.80 7.00	22.6 26.5	1.68 1.81	- 1.46	- 1.48

¤ The above data, excluding thickness, are cited from Japan Mint.
¤ Data of thickness are the measurements of real yen coins by the author.

Table 1-7

Russian ruble coins

Denom. (P)	Mass (g)	Diameter (mm)	Thickness (mm)	N:1 ratio
				Mass	Volume
0.01 0.05	1.50 2.60	15.5 18.5	1.25 1.45	- 1.73	- 1.65
0.1 0.5	1.95 2.90	17.5 19.5	1.25 1.50	- 1.49	- 1.49
1 2 5	3.25 5.10 6.45	20.5 23.0 25.0	1.50 1.80 1.80	- 1.57 1.98	- 1.51 1.78
10 25	5.63 10.00	22.0 27.0	2.20 2.30	- -	- -

¤ The above data are cited from Bank of Russia.
¤ 10-ruble's place does not have N:1 ratios because 25-ruble denomination is not regarded as 10-ruble's place.

Table 1-8

Turkish lira coins

Denom. (L)	Mass (g)	Diameter (mm)	Thickness (mm)	N:1 ratio
				Mass	Volume
0.01 0.05	2.20 2.90	16.50 17.50	1.35 1.65	- 1.32	- 1.37
0.1 0.25 0.5	3.15 4.00 6.80	18.50 20.50 23.85	1.65 1.65 1.90	- - 2.16	- - 1.91
1	8.20	26.15	1.90	-	-

¤ The above data are cited from Turkish State Mint.

Table 1-9

Euro coins

Denom. (€)	Mass (g)	Diameter (mm)	Thickness (mm)	N:1 ratio
				Mass	Volume
0.01 0.02 0.05	2.30 3.06 3.92	16.25 18.75 21.25	1.67 1.67 1.67	- 1.33 1.70	- 1.33 1.71
0.1 0.2 0.5	4.10 5.74 7.80	19.75 22.25 24.25	1.93 2.14 2.38	- 1.40 1.90	- 1.41 1.86
1 2	7.50 8.50	23.25 25.75	2.33 2.20	- 1.13	- 1.16

¤ The above data are cited from European Central Bank.

Table 1-10

Pound sterling coins

Denom. (£)	Mass (g)	Diameter (mm)	Thickness (mm)	N:1 ratio
				Mass	Volume
0.01 0.02 0.05	3.56 7.12 3.25	20.3 25.9 18.0	1.65 2.03 1.70	- 2.00 0.91	- 2.00 0.81
0.1 0.2 0.5	6.50 5.00 8.00	24.5 21.4 27.3	1.85 1.70 1.78	- 0.77 1.23	- 0.70 1.19
1 2	9.50 12.00	22.5 28.4	3.15 2.50	- 1.26	- 1.26

¤ The above data are cited from The Royal Mint.

Table 1-11

Canadian dollar coins

Denom. (C$)	Mass (g)	Diameter (mm)	Thickness (mm)	N:1 ratio
				Mass	Volume
0.01 0.05	2.35 3.95	19.05 21.20	1.45 1.76	- 1.68	- 1.50
0.1 0.25 0.5	1.75 4.40 6.90	18.03 23.88 27.13	1.22 1.58 1.95	- - 3.94	- - 3.62
1 2	6.27 6.92	26.50 28.00	1.95 1.75	- 1.10	- 1.00

¤ The above data are cited from Royal Canadian Mint.

Table 1-12

United States dollar coins

Denom. ($)	Mass (g)	Diameter (mm)	Thickness (mm)	N:1 ratio
				Mass	Volume
0.01 0.05	2.500 5.000	19.05 21.21	1.55 1.95	- 2.00	- 1.56
0.1 0.25 0.5	2.268 5.670 11.340	17.91 24.26 30.61	1.35 1.75 2.15	- - 5.00	- - 4.65
1	8.100	26.50	2.00	-	-

¤ The above data are cited from The United States Mint.

Table 1-13

Mexican peso coins

Denom. (MX$)	Mass (g)	Density (g/cm3)	N:1 ratio
			Mass	Volume
0.05	1.580	7.72	-	-
0.1 0.2 0.5	1.755 2.258 3.103	7.72 7.72 7.72	- 1.29 1.77	- 1.29 1.77
1 2 5	3.950 5.190 7.070	8.11 8.11 8.11	- 1.31 1.79	- 1.31 1.79
10	10.329	8.53	-	-

¤ The above data are cited from Banco de Mexico.

Table 1-14

Brazilian real coins

Denom. (R$)	Mass (g)	Diameter (mm)	Thickness (mm)	N:1 ratio
				Mass	Volume
0.01 0.05	2.43 4.10	17 22	1.65 1.65	- 1.69	- 1.67
0.1 0.25 0.5	4.80 7.55 6.80	20 25 23	2.23 2.25 2.85	- - 1.42	- - 1.69
1	7.00	27	1.95	-	-

¤ The above data are cited from Banco Central do Brasil.

Table 1-15

N to 1 ratios of coins

Place	N1:1 ratio		N2:1 ratio		N:1 ratio
	Mass	Vol.	Mass	Vol.	Mass	Vol.
0.01-A$ 0.1-A$ 1-A$ 100-Rp 1-Rs 0.1-CN¥ 1-W 10-W 100-W 1-¥ 10-¥ 100-¥ 0.01-P 0.1-P 1-P 0.01-L 0.1-L 0.01-€ 0.1-€ 1-€ 0.01-£ 0.1-£ 1-£ 0.01-C$ 0.1-C$ 1-C$ 0.01-$ 0.1-$ 0.1-MX$ 1-MX$ 0.01-R$ 0.1-R$	2.00 2.00 - 1.33 1.16 ? - - - - - - 1.57 - 1.98 - - 1.33 1.40 - 2.00 0.77 - - - - - - 1.29 1.31 - -	2.00 2.00 - 1.15 ? ? - - - - - - 1.51 - 1.78 - - 1.33 1.41 - 2.00 0.70 - - - - - - 1.29 1.31 - -	1.09 2.75 - 1.73 1.24 ? - - - - - - 1.98 - 1.98 - - 1.70 1.90 - 0.91 1.23 - - - - - - 1.77 1.79 - -	1.08 2.75 - 1.72 ? ? - - - - - - 1.78 - 1.78 - - 1.71 1.86 - 0.81 1.19 - - - - - - 1.77 1.79 - -	1.48 2.35 0.73 1.52 1.20 ? 4.05 3.41 1.42 3.75 0.89 1.46 1.73 1.49 1.76 1.32 2.16 1.51 1.63 1.13 1.35 0.97 1.26 1.68 3.94 1.10 2.00 5.00 1.51 1.53 1.69 1.42	1.47 2.35 0.73 1.41 ? ? 1.31 2.25 1.42 1.20 0.92 1.48 1.65 1.49 1.64 1.37 1.91 1.51 1.62 1.16 1.27 0.92 1.26 1.50 3.62 1.00 1.56 4.65 1.51 1.53 1.67 1.69
Average	1.46	1.44	1.60	1.59	1.70	1.53
	1.45		1.60		1.61

¤ N₁<N₂. The above currencies are all N₁=2 and N₂=5.
¤ N:1 ratio where D[N₁] and D[N₂] exist is the geometric mean of N₁:1 ratio and N₂:1 ratio. e.g. The mass ratio of 100-rupiah's place is √(1.33*1.73)=1.52.
¤ All the average ratios are geometric means. e.g. Average N₁:1 ratio of mass is ¹²√(2.00*2.00*1.33*...*1.31)=1.46.

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1¤4

An Efficient Combination of the Denominations of a Currency
 Tables 1: Measurements of coins
 Tables 2: Tests in coins' places
 Tables 3: Measurements of banknotes
 Tables 4: Tests in banknotes' low places
 Tables 5: Tests in banknotes' high places
 Tables 6: Tests of C3Ds

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© 2013 Takashi Shimazaki
Updated: April 2, 2014