Atomic Time Calculator

Atomic time is a family of time scales maintained by networks of cesium atomic clocks that count SI seconds with extraordinary precision. Unlike astronomical time (which is based on Earth's rotation and is therefore slightly irregular), atomic time ticks at a constant rate determined by the natural resonance frequency of cesium-133 atoms: exactly 9,192,631,770 oscillations per second.

International Atomic Time (TAI — from the French Temps Atomique International) is the primary atomic time scale. It is a continuous, uninterrupted count of SI seconds maintained by the International Bureau of Weights and Measures (BIPM) through a weighted average of more than 400 atomic clocks in over 50 national laboratories around the world. TAI has no leap seconds and never pauses or adjusts for Earth's slowing rotation.

Coordinated Universal Time (UTC) is derived from TAI by periodically inserting leap seconds to keep UTC within 0.9 seconds of UT1 (Earth rotation time). As of 2024, TAI is ahead of UTC by 37 seconds — the cumulative result of 27 leap seconds inserted since 1972, plus the initial 10-second offset established at the TAI epoch.

This calculator shows the live relationship between UTC, TAI, GPS time, and Terrestrial Time (TT), and for any selected date it computes the exact offsets between these scales along with the Julian Date, Modified Julian Date, GPS week number, and Unix timestamp.

Each atomic time scale has a fixed or leap-second-adjusted offset from UTC. Understanding these offsets is essential for space navigation, astronomical software, and precision GPS receivers.

Earth's rotation is not perfectly constant — tidal forces from the Moon and Sun gradually slow it down, with short-term variations caused by earthquakes, atmospheric pressure changes, and fluid movements in Earth's core. The result is that a day measured by Earth's rotation is slightly longer than 86,400 SI seconds on average, and this difference accumulates over time.

To prevent UTC from drifting too far from UT1 (astronomical time based on Earth's actual rotation), the International Earth Rotation and Reference Systems Service (IERS) occasionally inserts a leap second into UTC, always at midnight on 30 June or 31 December. The leap second clock reads 23:59:60 before rolling to 00:00:00 of the next day.

Since the first leap second was inserted on 30 June 1972, 27 leap seconds have been added (as of 2024). No leap seconds were added between 2017 and 2024 because Earth's rotation has been running slightly fast in recent years. The ITU and BIPM have agreed to abolish leap seconds by 2035, allowing UTC-UT1 to drift freely up to one minute before any correction is applied.

GPS time is the continuous atomic time scale maintained by the satellites of the Global Positioning System. It was initialized to equal UTC at midnight on 5-6 January 1980, at which point TAI was already 19 seconds ahead of UTC. Because GPS time does not use leap seconds, it has remained exactly 19 seconds behind TAI since then — a constant offset that never changes.

GPS receivers compute position by measuring the arrival times of signals from multiple satellites. Because these computations depend on SI-second precision, GPS time must be continuous without the one-second jumps that leap seconds introduce into UTC. When you enable GNSS timing on a GPS device, the receiver applies a known correction to convert GPS time to UTC for display purposes.

The GPS week number displayed by this calculator counts full seven-day periods since the GPS epoch (6 January 1980). The GPS week rolled over from 1023 to 0 on 22 August 1999 and again on 6 April 2019 (1024 × 2 = 2048 weeks), so GPS receivers must manage this rollover to report correct dates.

Terrestrial Time (TT) is the theoretical time scale used as the independent variable in gravitational theories of solar system dynamics. It replaced Ephemeris Time (ET) in 1984 and is defined such that TT = TAI + 32.184 seconds. The 32.184 second offset is the accumulated difference between ET and TAI at the moment TT was defined, preserving continuity with older ephemerides.

Planetarium software, orbital mechanics calculators, and asteroid tracking systems all use TT for their internal calculations. If you are computing the position of a planet for a given date, the ephemeris expects TT as input. Converting from UTC involves adding 37 + 32.184 = 69.184 seconds (as of 2024) to UTC to obtain TT. This distinction matters at the precision level of modern astrometry but is negligible for casual sky-watching.