Gravitational Time Dilation Calculator

With this gravitational time dilation calculator you can check how much time slows down by near big objects.

Gravitational rate difference5.29215e-10the high clock runs FASTER by this fraction — 45.7242 µs per day. Higher means less deep in the well, and less deep means faster

Gained per day at altitude45.7242 µs

Gained per year16.70076 ms

Weak-field check gh/c²2.20715e-9the textbook approximation, valid while the altitude is small against the radius — it is noticeably off here, because 3.171 of a radius is not small

Surface potential depth 2GM/rc²1.39226e-9how far Earth sits down its own gravity well — for Earth this is about 1.4 parts in a billion

Escape velocity as a check11,186.14 m/sthe potential depth is exactly (v_esc/c)²

Orbital speed at that altitude3,873.16 m/s

Special-relativistic rate change-8.34562e-11-7.2106 µs per day — NEGATIVE, because a moving clock runs slow. This pulls the opposite way to gravity

Net rate difference4.45759e-1038.5136 µs per day. The two effects are comparable and OPPOSITE, so neither can be neglected — this is the GPS correction, and ignoring it puts positions out by about 11.5 km after a single day

Altitude where the two cancel3,185.5 kmat r = 1.5 times the body's radius the orbital time dilation exactly offsets the gravitational speed-up, and an orbiting clock keeps surface time

This is not about the clockstime itself runs differentlyevery process runs slower deeper in the well — atomic transitions, chemistry, ageing. There is no experiment that could detect being deep in a gravity well from the inside

The formula

dτ/dt = √(1 − 2GM/rc²); Δf/f ≈ gh/c²

Higher clocks run faster

A clock deeper in a gravitational well ticks more slowly. The effect is tiny near Earth — about 1.4 parts in a billion between the surface and infinity — but it is measurable over a few metres with modern optical clocks, and it is unavoidable for satellite navigation.

GPS needs both relativities, pulling opposite ways

A navigation satellite is high, so gravity speeds its clock by about 45 µs a day. It is also moving fast, so special relativity slows it by about 7 µs a day. The two are comparable in size and opposite in sign, leaving a net gain of roughly 38 µs a day. Ignoring the correction would accumulate a position error of about ten kilometres within a single day, which is why the satellites' clocks are deliberately offset before launch.

There is an altitude where the two effects cancel exactly: an orbit at 1.5 times the body's radius. Below it the orbital motion wins and the clock runs slow; above it gravity wins and it runs fast.

Not a fact about clocks

This is not an artefact of how clocks are built. Every physical process — atomic transitions, chemical reactions, biological ageing — runs at the same slowed rate. No local experiment can reveal how deep in a gravity well you are, which is exactly what the equivalence principle demands.