Special-relativity time dilation
Proper time is measured by a single clock at rest with respect to both events, so the events occur at the same position in that clock’s frame. Another inertial frame measures a longer coordinate-time interval.
The time-dilation equation depends on relative speed as a fraction of the exact speed of light. It does not include gravitational time dilation or accelerated-frame effects.
How to use the time dilation calculator
- Choose the unknown: Select coordinate time, proper time, or relative speed.
- Use matching time units: Coordinate and proper time must use the same unit.
- Enter a valid speed: For time calculations, use |v/c| below 1.
- Calculate: Review the result, Lorentz factor, and speed in meters per second.
Formula and variables
Coordinate time Δt is at least as large as proper time Δτ for subluminal relative speed.
Δt = γΔτ; γ = 1/√(1 − v²/c²)- Δt — Coordinate time
- Interval measured between events at different positions in the observing frame
- Δτ — Proper time
- Interval measured where both events occur at one position
- γ — Lorentz factor
- Relativistic time ratio
- v/c — Speed fraction
- Relative speed divided by light speed
Travel at 0.8c
A moving clock measures 1 hour of proper time while traveling at 0.8c relative to an observer.
- Proper time
- 1 hour
- Speed
- 0.8c
- γ = 1/√(1 − 0.8²) = 1.6667
- Δt = 1.6667 × 1 hour
Result: Coordinate time is approximately 1.6667 hours.
The observer’s interval is longer than the proper interval recorded by the moving clock.
Understanding your results
The effect grows rapidly near c
At ordinary speeds γ is extremely close to 1.
- At zero relative speed, Δt = Δτ.
- Coordinate time cannot be shorter than proper time in this model.
- The calculator accepts no speed equal to or greater than c.
- Reference-frame definitions matter as much as the arithmetic.
Assumptions
- Frames are inertial over the modeled interval.
- Special relativity applies in flat spacetime without relevant gravity.
- Proper and coordinate time are identified for the same pair of events.
Limitations
- Does not calculate gravitational time dilation, acceleration, simultaneity, Doppler shift, or a complete travel scenario.
- Does not determine which frame is physically appropriate from a narrative description.
- Floating-point precision becomes limiting extremely close to light speed.
Common mistakes
- Entering percent of c as 80 instead of 0.8.
- Reversing proper and coordinate time.
- Mixing time units.
- Applying the formula to gravitational time dilation.
Practical use cases
Relativity coursework
Solve standard inertial-frame time-dilation problems.
Concept exploration
Compare Lorentz factors at different fractions of light speed.
Frequently asked questions
Which time is proper time?
Proper time is measured in the frame where the two events occur at the same spatial position.
Can v equal c?
No material clock or massive observer can use an inertial frame moving at c; the formula requires |v/c| below 1.
Sources and review
- Time Dilation — OpenStax University Physics Volume 3. Accessed 2026-07-14.
- CODATA Values of the Fundamental Constants — NIST. Accessed 2026-07-14.
Reviewed 2026-07-14.