PHYSICS / SPECIAL RELATIVITY
Calculate the dilated coordinate-time interval from proper time and relative speed.
METHOD / WORKED EXAMPLE
Time dilation compares one clock's proper interval with the longer coordinate interval assigned by an inertial frame in which that clock moves.
WORKED DEFAULT
For 5 seconds of proper time at 0.8c, gamma is 1.6667, so the coordinate-time interval is 8.3333 seconds and the difference is 3.3333 seconds.
READ THE RESULT
The result belongs to the stated pair of inertial frames. It does not mean a moving observer sees their own clock malfunction; each local clock records its own proper time normally.
ASSUMPTIONS AND LIMITS
Proper time is measured by a single co-located clock; acceleration and gravity are outside this special-relativity model.
Use internally consistent units and retain extra precision when carrying the result into another calculation.
COMMON QUESTIONS
Proper time is measured by a single clock present at both events, so those events occur at the same location in that clock's rest frame. If your supplied interval comes from synchronized clocks at different positions, it is generally a coordinate time and should not automatically be entered as proper time.
No. This equation models special-relativistic time dilation caused by constant relative motion between inertial frames. Gravitational potential and curved spacetime require a general-relativity model with additional information. Do not combine the effects by simply adding percentages without deriving the appropriate physical scenario and reference frame.
For uniform relative motion, simultaneity is frame-dependent, so each inertial observer can consistently assign a slower rate to separated moving clocks. Comparing reunited clocks introduces acceleration or a change of inertial frame, which breaks the simple symmetry and requires a complete path analysis beyond this one-interval calculator.
RELATED TOOLS
Use boundary
Multiply the proper-time interval by the Lorentz factor for the entered inertial-frame speed. The page evaluates the displayed equation from your supplied values and presents both symbolic and substituted KaTeX working so the arithmetic can be checked.
Delta t = gamma Delta tau