Gravitational Time Dilation
Calculator

Inputs

Time dilation factor
1.000002

Results

Time dilation factor
1.000002
Time dilation (parts per million)
2.123053

Astronomy results

Time dilation factor1.000002
Time dilation (parts per million)2.123053

formula-map diagram

Time dilation factor
1.000002
Time dilation (parts per million)
2.123053

Astronomical relationship

Formula

dt_far / dt_near = 1 / √(1 − 2GM / (r c²))

= 1.0000021230539

Note

This result is a simplified model: it applies the displayed textbook formula to the values you entered, assuming ideal spherical bodies, circular orbits, blackbody radiation and perfect optics, and ignoring atmospheric seeing, relativistic corrections beyond those stated, cosmological models and measurement uncertainty. Use published ephemerides and catalogue data for real observations.

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