How this calculator works
The proper interval is recorded by one clock at both events, such as two ticks on a passing spacecraft clock. An inertial observer sees a longer interval by a factor gamma. This relation assumes constant relative speed in flat spacetime. It does not on its own model a full accelerating twin journey or gravitational clock effects. Zero intervals are valid for forward calculations, but they cannot determine a unique speed. The difference is calculated in a form that avoids subtracting nearly equal elapsed intervals at low speeds.
Formula
Delta t = gamma Delta tau; gamma = 1/sqrt(1-v²/c²); v = c sqrt(1-(Delta tau/Delta t)²).
Worked example
At 0.6c, gamma is 1.25. Eight seconds on the moving clock correspond to ten seconds in the observer frame, a difference of two seconds.
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Frequently asked questions
Which time is proper time?
It is the time on the single clock present at both events.
Does each observer say the other clock runs slowly?
For uniform relative motion, yes. Comparing distant events requires each frame own simultaneity convention.
Does this include gravity?
No. Use the gravitational time dilation tool for stationary clocks in a spherical gravitational field.