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    Relativity

    Time Dilation Calculator

    Special-relativistic (speed) and gravitational time dilation for a clock in motion or near a mass.

    γ = 1/√(1 − v²/c²) · dτ/dt = √(1 − r_s/r)

    Inputs

    Results

    Clock rate vs distant observer
    0.9999999998
    Time lost per period (combined)
    2.1641 × 10^-5 s
    21.641 µs
    Lorentz factor γ
    1.0000000001
    Time lost from speed only
    7.2138 µs
    Time lost from gravity only
    14.427 µs
    • To compare two clocks (for example GPS orbit vs Earth's surface), compute both and subtract: GPS clocks gain about 38 µs per day relative to the ground.
    Worked solution
    1. γ = 1/√(1 − (3,874/c)²) = 1.0000000001
    2. r_s = 0.0088701 m, √(1 − r_s/r) = 0.9999999998
    3. Combined rate ≈ √(1 − r_s/r) / γ = 0.9999999998

    How it works

    Einstein's relativity predicts that moving clocks tick slower and that clocks deeper in a gravitational well tick slower too. Both effects are measured every day: GPS satellite clocks are adjusted before launch so that, in orbit, they keep time with ground clocks.

    Variables

    • γ — Lorentz factor (moving clocks run slow by 1/γ)
    • r_s — Schwarzschild radius of the mass
    • r — clock's distance from the centre

    Assumptions and limits

    • Weak-field approximation for the combined rate (product of the two factors)
    • Non-rotating spherical mass; observer at rest far away
    • Constant speed

    For education only. These models are simplified and are not suitable for spacecraft navigation or safety-critical engineering. See our scientific accuracy policy.