T32 · Draft 0.3 · Reference tables

Tables

Reference values for T32, each computed by the TypeScript implementation when the site is built.

1Alphabet

Crockford base32: the digits and 22 letters, in order, each standing for five bits. I, L, O and U are never written. On input, upper and lower case are both accepted, O is read as 0, and I or L as 1, which helps with stamps copied by hand. U is rejected.

Character	Value	Bits
0	0	00000
1	1	00001
2	2	00010
3	3	00011
4	4	00100
5	5	00101
6	6	00110
7	7	00111
8	8	01000
9	9	01001
A	10	01010
B	11	01011
C	12	01100
D	13	01101
E	14	01110
F	15	01111

Character	Value	Bits
G	16	10000
H	17	10001
J	18	10010
K	19	10011
M	20	10100
N	21	10101
P	22	10110
Q	23	10111
R	24	11000
S	25	11001
T	26	11010
V	27	11011
W	28	11100
X	29	11101
Y	30	11110
Z	31	11111

2Length and resolution

A stamp's length says how finely the time was recorded. It says nothing about how accurate the clock was. Each character adds five bits and divides the unit by 32. Five lengths also have a fixed-width binary form, named T32-n in the specification.

Length	Unit (exact)	Unit (approx.)	Bits	Binary form
1	$2^{35}$ s	≈ 1,089 years	5
2	$2^{30}$ s	≈ 34 years	10
3	$2^{25}$ s	≈ 388 days	15
4	$2^{20}$ s	≈ 12.1 days	20
5	$2^{15}$ s	≈ 9.1 hours	25
6	$2^{10}$ s	≈ 17.1 minutes	30
7	$2^{5}$ s	32 seconds	35
8	1 s	1 second	40	T32-8
9	$2^{- 5}$ s	≈ 31.3 ms	45
10	$2^{- 10}$ s	≈ 977 µs	50	T32-10
11	$2^{- 15}$ s	≈ 30.5 µs	55
12	$2^{- 20}$ s	≈ 954 ns	60	T32-12
13	$2^{- 25}$ s	≈ 29.8 ns	65
14	$2^{- 30}$ s	≈ 931 ps	70	T32-14
15	$2^{- 35}$ s	≈ 29.1 ps	75
16	$2^{- 40}$ s	≈ 0.909 ps	80	T32-16

An encoder must not write more characters than its clock can measure. The longest it may use is the length whose unit is closest to the clock's resolution.

Source resolution	Maximum length	Unit at that length
1 second	8	1 second
100 ms	9	≈ 31.3 ms
10 ms	9	≈ 31.3 ms
1 ms	10	≈ 977 µs
1 µs	12	≈ 954 ns
1 ns	14	≈ 931 ps
1 ps	16	≈ 0.909 ps

3Eras (first character)

Each era is $2^{35}$ seconds, about 1,089 years, and every stamp written in it starts with its character. Years are UTC, in the proleptic Gregorian calendar, so era G, the present one, begins in 1999: the epoch, midnight TAI, is 23:59:28 UTC on 31 December.

0123456789ABCDEFGHJKMNPQRSTVWXYZ

The eight-character range, split by its first character. The bias puts the epoch at the exact centre: instants before 2000 start with 0 to F, and instants after it with G to Z.

Era	From	Until
0	15,423 BCE	14,334 BCE
1	14,334 BCE	13,245 BCE
2	13,245 BCE	12,156 BCE
3	12,156 BCE	11,067 BCE
4	11,067 BCE	9,978 BCE
5	9,978 BCE	8,890 BCE
6	8,890 BCE	7,801 BCE
7	7,801 BCE	6,712 BCE
8	6,712 BCE	5,623 BCE
9	5,623 BCE	4,534 BCE
A	4,534 BCE	3,446 BCE
B	3,446 BCE	2,357 BCE
C	2,357 BCE	1,268 BCE
D	1,268 BCE	179 BCE
E	179 BCE	911
F	911	1999

Era	From	Until
G	1999	3088
H	3088	4177
J	4177	5266
K	5266	6355
M	6355	7444
N	7444	8532
P	8532	9621
Q	9621	10,710
R	10,710	11,799
S	11,799	12,888
T	12,888	13,976
V	13,976	15,065
W	15,065	16,154
X	16,154	17,243
Y	17,243	18,332
Z	18,332	19,421

4Two-character prefixes, 1900–2100

Each is $2^{30}$ seconds, about 34 years. Boundaries are given to the day.

Prefix	From (UTC)	Until (UTC)
FX	1897-12-03	1931-12-13
FY	1931-12-13	1965-12-22
FZ	1965-12-22	1999-12-31
G0	1999-12-31	2034-01-09
G1	2034-01-09	2068-01-19
G2	2068-01-19	2102-01-28

5Three-character prefixes, 2020–2035

Each is $2^{25}$ seconds, about 388 days. Useful as partition keys and for range queries.

Prefix	From (UTC)	Until (UTC)
G0J	2019-02-20 12:08Z	2020-03-14 20:49Z
G0K	2020-03-14 20:49Z	2021-04-07 05:30Z
G0M	2021-04-07 05:30Z	2022-04-30 14:10Z
G0N	2022-04-30 14:10Z	2023-05-23 22:51Z
G0P	2023-05-23 22:51Z	2024-06-15 07:31Z
G0Q	2024-06-15 07:31Z	2025-07-08 16:12Z
G0R	2025-07-08 16:12Z	2026-08-01 00:52Z
G0S	2026-08-01 00:52Z	2027-08-24 09:33Z
G0T	2027-08-24 09:33Z	2028-09-15 18:13Z
G0V	2028-09-15 18:13Z	2029-10-09 02:54Z
G0W	2029-10-09 02:54Z	2030-11-01 11:34Z
G0X	2030-11-01 11:34Z	2031-11-24 20:15Z
G0Y	2031-11-24 20:15Z	2032-12-17 04:55Z
G0Z	2032-12-17 04:55Z	2034-01-09 13:36Z
G10	2034-01-09 13:36Z	2035-02-01 22:16Z
G11	2035-02-01 22:16Z	2036-02-25 06:57Z

6Common durations

A duration is a signed whole number of $2^{- 40}$ s, written exactly. It is read like a stamp with a sign and a point: the characters before the point count whole seconds in base32, and each one after it is a 32nd of the one before. So +1W is 1 × 32 + 28 = 60 seconds. A decimal value that is not a whole number of units, such as a millisecond, is truncated toward zero.

Duration	Seconds	T32 duration
1 second	1	+1
1 minute	60	+1W
1 hour	3,600	+3GG
1 day (86,400 SI s)	86,400	+2MC0
1 week	604,800	+JEM0
30 days	2,592,000	+2F380
365 days	31,536,000	+Y2CW0
Julian year (365.25 d)	31,557,600	+Y31Z0
1/32 second	0.03125	+0.1
1/1024 second	0.000977	+0.00ZZZZET
1 millisecond (truncated)	0.001	+0.010RJDTB

7Notable moments

Each moment is encoded at length 8. Before 1972, TAI − UTC was fractional, so a one-second stamp starts part-way through a UTC second.

Moment	Stamp starts (UTC)	T32
Start of range	-15422-12-06T11:41:52Z	00000000
Royal Observatory foundation stone (Gregorian)	1675-08-20T00:00:00Z	FPEY6N00
Start of the 1961 UTC definition	1961-01-01T00:00:00Z	FYVAAJG1
Apollo 11 lunar landing	1969-07-20T20:17:39.425406217Z	FZ3BMMKB
Unix epoch	1969-12-31T23:59:59.999918Z	FZ3S5F48
UTC becomes TAI − 10 s	1972-01-01T00:00:00Z	FZ5NA8WA
GPS epoch	1980-01-06T00:00:00Z	FZD6FYGK
T32 epoch (2000-01-01 TAI)	1999-12-31T23:59:28Z	G0000000
Last leap second (so far)	2016-12-31T23:59:60Z	G0FZP0S4
Signed 32-bit Unix time overflows	2038-01-19T03:14:08Z	G13S5F55
End of range	+19421-01-25T12:17:30Z	ZZZZZZZZ

8Leap seconds

All 27 leap seconds inserted so far. Each has its own T32 stamp, because to T32 a leap second is an ordinary second. IERS Bulletin C 72 announced no leap second for the end of 2026, and the CGPM has made UTC continuous from 2027-05-20, so no more are expected.

TAI − UTC in seconds, from Appendix A. Until 1972 UTC ran at an adjusted rate, so the offset grew continuously; since then it has changed only by whole leap seconds, the last at the end of 2016.

#	Inserted second (UTC)	T32	TAI − UTC after
1	1972-06-30 23:59:60	FZ64A54A	11 s
2	1972-12-31 23:59:60	FZ6KFA4B	12 s
3	1973-12-31 23:59:60	FZ7HHQ0C	13 s
4	1974-12-31 23:59:60	FZ8FM3WD	14 s
5	1975-12-31 23:59:60	FZ9DPGRE	15 s
6	1976-12-31 23:59:60	FZABVJ0F	16 s
7	1977-12-31 23:59:60	FZB9XYWG	17 s
8	1978-12-31 23:59:60	FZC80BRH	18 s
9	1979-12-31 23:59:60	FZD62RMJ	19 s
10	1981-06-30 23:59:60	FZEK51RK	20 s
11	1982-06-30 23:59:60	FZFH7EMM	21 s
12	1983-06-30 23:59:60	FZGF9VGN	22 s
13	1985-06-30 23:59:60	FZJBH9MP	23 s
14	1987-12-31 23:59:60	FZMPV8CQ	24 s
15	1989-12-31 23:59:60	FZPK2PGR	25 s
16	1990-12-31 23:59:60	FZQH53CS	26 s
17	1992-06-30 23:59:60	FZRY7CGT	27 s
18	1993-06-30 23:59:60	FZSW9SCV	28 s
19	1994-06-30 23:59:60	FZTTC68W	29 s
20	1995-12-31 23:59:60	FZW7KR4X	30 s
21	1997-06-30 23:59:60	FZXMP18Y	31 s
22	1998-12-31 23:59:60	FZZ1XK4Z	32 s
23	2005-12-31 23:59:60	G05MKP10	33 s
24	2008-12-31 23:59:60	G08EXH11	34 s
25	2012-06-30 23:59:60	G0BR4KX2	35 s
26	2015-06-30 23:59:60	G0EJBTH3	36 s
27	2016-12-31 23:59:60	G0FZP0S4	37 s

9TAI − UTC, 1961–1971, and its steps

Before 1972, UTC ran at an adjusted rate, and the difference from TAI, in seconds, followed a formula:

TAI - UTC = a + (MJD - m) \times r

MJD is the Modified Julian Date of the UTC instant, and a, m and r come from the row in force on that date. Before 1961 the difference is defined as 0.

From	a (s)	m (MJD)	r (s/day)
1961-01-01	1.4228180	37300	0.0012960
1961-08-01	1.3728180	37300	0.0012960
1962-01-01	1.8458580	37665	0.0011232
1963-11-01	1.9458580	37665	0.0011232
1964-01-01	3.2401300	38761	0.0012960
1964-04-01	3.3401300	38761	0.0012960
1964-09-01	3.4401300	38761	0.0012960
1965-01-01	3.5401300	38761	0.0012960
1965-03-01	3.6401300	38761	0.0012960
1965-07-01	3.7401300	38761	0.0012960
1965-09-01	3.8401300	38761	0.0012960
1966-01-01	4.3131700	39126	0.0025920
1968-02-01	4.2131700	39126	0.0025920

Where the formula changes, TAI − UTC can jump. A rise inserts time that UTC has no ordinary label for; a fall removes labels, which converters must reject. These are every step other than the 27 leap seconds:

Boundary (UTC)	Step (s)	Effect
1961-01-01	+1.422818	Inserted
1961-08-01	−0.05	Removed: labels in the last 0.05 s of the day before never occurred
1963-11-01	+0.1	Inserted
1964-04-01	+0.1	Inserted
1964-09-01	+0.1	Inserted
1965-01-01	+0.1	Inserted
1965-03-01	+0.1	Inserted
1965-07-01	+0.1	Inserted
1965-09-01	+0.1	Inserted
1968-02-01	−0.1	Removed: labels in the last 0.1 s of the day before never occurred
1972-01-01	+0.107758	Inserted

10Test vectors

Encoding vectors, recomputed here by the TypeScript implementation. The specification also has decoder, parser, duration and error vectors.

Case	UTC	Length	Stamp
T32 epoch	1999-12-31T23:59:28Z	8	G0000000
Unix epoch (before 1972)	1970-01-01T00:00:00Z	8	FZ3S5F48
Apollo 11 landing	1969-07-20T20:17:40Z	8	FZ3BMMKB
UTC offset becomes whole seconds	1972-01-01T00:00:00Z	8	FZ5NA8WA
Before last leap second	2016-12-31T23:59:59Z	8	G0FZP0S3
Last leap second	2016-12-31T23:59:60Z	8	G0FZP0S4
After last leap second	2017-01-01T00:00:00Z	8	G0FZP0S5
Example date	2026-10-31T03:13:00Z	8	G0S7G6B1
Example + 0.5 s (ms clock)	2026-10-31T03:13:00.500Z	10	G0S7G6B1G0
Example + 0.123 s (µs clock)	2026-10-31T03:13:00.123000Z	12	G0S7G6B13XYE
Before 1972, exact (ns clock)	1966-06-15T12:00:00.123456789Z	14	FZ0EDKA4VPC2A1
Before 1961, taken as UT	1675-08-20T00:00:00Z	8	FPEY6N00