Drift calculator

Two dates and a named pair of clocks: how much model drift accumulates between them, in microseconds, in seconds, and in metres of light path.

The calculator

The three fields below are filled with a worked example computed when this page was built: the TCL epoch of 1 January 1977 [1]Official against today's date, at 56.02 µs/day. [2] With JavaScript on, changing a field recalculates the answer in place. With JavaScript off, the filled example and the table below still hold: both were computed at build time by the same code.

Model drift
1 015 754.64 µs
The same in seconds
1.015755 s
Days in the interval
18 132
That offset as light path
304 515.580 km

Over 18 132 days, from 1977-01-01 to 2026-08-24, the model puts a clock at rest on the Moon's selenoid ahead of a clock at rest on Earth's geoid by 1 015 754.64 µs (1.015755 s).

Every figure here is a model value: no lunar clock has been built, and nothing on this page is a measurement. [3]

What the arithmetic is

Drift is one multiplication: the number of days between the two dates, times the rate in microseconds per day. Both dates are read as midnight UTC, the interval may be negative if the second date is earlier, and the function doing the multiplication is the same one behind the clock on this site and behind the JSON API.[3]

The rate is not ours. 56.02 µs/day is the published secular rate of a clock at rest on the Moon's selenoid against a clock at rest on Earth's geoid[2], and NIST states the same figure in round numbers as about 56 microseconds per day [4]Official. 58.7 µs per Earth-day is the figure the 2024 policy memorandum gives for a lunar coordinate time against Terrestrial Time [5]Official. They are not two answers to one question:the two figures compare different pairs of scales.

Typical intervals

The same multiplication for five intervals ending at midnight UTC today. Month, year and decade take their length from the calendar rather than from a round number, which is why the day counts below are not 30, 365 and 3650. [3]

Accumulated model drift over five intervals ending 2026-08-24. Both columns of figures are our own arithmetic on published rates.
IntervalFromDaysAt 56.02 µs/day, selenoid clock against geoid clockAt 58.7 µs/day, TCL against TTSource
One day2026-08-23156.02 µs58.70 µs[3]
One calendar month2026-07-24311 736.62 µs1 819.70 µs[3]
One calendar year2025-08-2436520 447.30 µs21 425.50 µs[3]
Ten calendar years2016-08-243 652204 585.04 µs214 372.40 µs[3]
Since the 1977 epoch1977-01-0118 1321 015 754.64 µs1 064 348.40 µs[3]

The model is a straight line, and the Moon is not

Everything above multiplies a constant rate by elapsed days. That is the whole model, and it is deliberately thin: a straight line through a system that is not straight.[3]

The published rate carries a periodic term of about 0.108 µs/day that varies with the phase of the Moon's orbit, and our model drops it and keeps the secular part only[2]. It also ignores tidal deformation, the varying Earth-Moon distance, and the altitude, latitude and velocity of any particular site on the lunar surface[2]. Above all it ignores the fact that no lunar time scale has been realized: there is no ensemble of clocks on the Moon to compare a prediction against[1]Official.

All of that is set out with the numbers onwhat we do not model, together withwhat we round and by how much. Read it before quoting a figure from this page: the arithmetic is exact, the rate it multiplies is not.

Keep reading

Sources

  1. Resolution to establish a standard Lunar Celestial Reference System (LCRS) and Lunar Coordinate Time (TCL) — International Astronomical Union, Commission A3 — XXXII General Assembly, . Official document. Verified .
  2. A Relativistic Framework to Estimate Clock Rates on the Moon — Neil Ashby and Bijunath R. Patla, NIST — The Astronomical Journal 168:112, . Peer-reviewed. Verified .
  3. Our calculation: the lunartime.org clock model — Lunartime Editorial, . Our calculation. Verified .
  4. What Time Is It on the Moon? — National Institute of Standards and Technology, . Official document. Verified .
  5. Policy on Celestial Time Standardization — White House Office of Science and Technology Policy, . Official document. Verified .