Free · Physics models
Static Spherical Gravitational Clock Rates
Compare two static clock intervals using the exterior Schwarzschild gravitational time factor.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
time1 = 1000.0000 sec; time2 = 999.99788 sec; time difference = 0.0021224386 sec.
τ = t∞ √[1−2GM/(rc²)]; difference = |τ₁−τ₂|.
Worked example
Enter these known values and leave the other values blank.
- Time interval with no gravity
- 1000 sec
- Mass
- 1 Earths
- Radius
- 1 R⊕
- Mass
- 1 Suns
- Radius
- 1 R☉
- Time interval
- 999.9999993039 sec
- Time interval
- 999.9978768653 sec
- Time difference
- 0.0021224386 sec
Assumptions and limitations
- Compare two static clock intervals using the exterior Schwarzschild gravitational time factor.
- The central objects are nonrotating and spherical. The radius is measured from each center and must be outside both the object’s material surface and its Schwarzschild radius.
- The two calculations use the same distant-reference interval. They describe separate ideal static gravitational scenarios; they do not combine interacting fields, orbital speed, rotation or signals exchanged between clocks.
- G is the rounded CODATA central value 6.6743×10⁻¹¹ m³/(kg·s²), and c is exact. The absolute difference carries no sign indicating which clock is faster.
- Inputs and inverse outputs share the displayed unit selectors. Clear a known field to solve for it, and lock quantities that must remain fixed. Singular inverses may have no finite result.
- Planetary unit choices use nominal captured scales: Earth mass 5.9722×10²⁴ kg, Sun mass 1.989×10³⁰ kg, Earth radius 6,371,000 m and Sun radius 695,700,000 m. These are convenient approximate scales, not precise measured mass or radius determinations.
Common questions
Is this valid inside a star?
No. The exterior Schwarzschild factor does not describe the interior metric.
Does it include orbital time dilation?
No. These clocks are static; orbital motion needs an additional relativistic treatment.
References
Enforce the explicitly stated physical domain: Exterior radius must be positive. Exterior radius must be positive.