Relativistic Effects Calculator
Explore time dilation and length contraction for objects moving at relativistic speeds. Enter a speed as a fraction of light speed (β), as an SI speed, or as a Lorentz factor (γ), and see how time and space behave differently at near-light velocities.
See how time and length change at near-light speeds
Pick a speed as a fraction of light speed, enter a clock time or a length, and we'll show you time dilation, length contraction, and even simple travel age differences using special relativity.
Special Relativity in a Nutshell
Einstein's special relativity, published in 1905, revolutionized our understanding of space and time. The theory rests on two postulates: (1) the laws of physics are the same in all inertial reference frames, and (2) the speed of light in a vacuum is constant for all observers, regardless of their motion.
At speeds close to the speed of light (c ≈ 299,792,458 m/s), time and space behave differently from our everyday Newtonian intuition. This calculator illustrates the simplest special relativistic effects for objects moving at constant velocity.
Time Dilation
Proper time (τ) is the time measured by a clock that stays with the moving object—it's the time experienced by the traveler. Coordinate time (t) is the time measured by an external observer in the lab frame.
γ = 1 / √(1 - v²/c²) = 1 / √(1 - β²)
t = γτ (coordinate time = gamma × proper time)
Physical interpretation: moving clocks tick more slowly relative to a given inertial frame. If a spaceship travels at high speed, astronauts aboard experience less time passing than observers on Earth.
Length Contraction
Proper length (L₀) is the length measured in the rest frame of the object. Contracted length (L) is measured by an observer who sees the object moving.
L = L₀ / γ
Physical interpretation: moving objects appear shorter along their direction of motion to an external observer. A meter stick moving at 0.9c would appear only about 44 cm long to a stationary observer.
Simple Travel and Age Differences
Consider a traveler moving to a distant point at high speed and returning. In special relativity, the traveler experiences less proper time than the stay-at-home observer. This is the essence of the famous "twin paradox."
Lab-frame travel time: t = D/v
Traveler's proper time: τ = t/γ
Age difference: Δt = t - τ = t(1 - 1/γ)
This tool uses a simple constant-velocity model for the main leg(s) of the trip, which captures the basic intuition but doesn't model detailed accelerations.
Limitations & Assumptions
- Special relativity only: No gravity, no curved spacetime (general relativity not included).
- Constant velocity segments: Accelerations are not fully modeled; we assume instantaneous velocity changes.
- No general relativistic effects: Gravitational time dilation (e.g., near massive objects) is not considered.
- Educational purposes: For real missions or precise experiments, more detailed treatments with proper acceleration phases and gravitational effects are required.
Relativistic Effects FAQ
Common questions about special relativity, time dilation, and length contraction.
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