Explore the Special Relativity: Time Dilation & Length
Push a spaceship toward the speed of light and watch its onboard clock run slow and its length shrink, exactly as γ predicts.
- Free to use
- No signup
- Nothing to install
- Runs in your browser
Illustration. Open the tool for the real thing.
See it in action
The Special Relativity: Time Dilation & Length with sample data entered and the result showing.
What is the Special Relativity: Time Dilation & Length?
Push a spaceship toward the speed of light and watch its onboard clock run slow and its length shrink, exactly as γ predicts. It runs in your browser, so a change to a setting or a drag on an object shows up at once.
GPS satellites must correct for real time dilation from their orbital speed, and particle accelerators routinely see unstable particles 'live longer' exactly as relativity predicts.
3 steps to your result
Open the tool and follow along. Nothing to install.
What you get
Time dilation: a clock moving relative to an observer ticks slower by the Lorentz factor γ = 1/√(1-v²/c²).
Length contraction: an object moving relative to an observer is measured shorter along its direction of motion by the same factor γ.
These effects are symmetric - each observer sees the other's clock run slow and rod shrink - and only become noticeable at a sizeable fraction of the speed of light.
Push the speed slider past 0.9c and watch the ship clock nearly freeze compared to the ground clock.
Set the speed to 0.6c and check γ against the formula by hand.
Try the muon-decay-distance challenge.
Used for
Pick one to see how it fits.
Physics learners
Physics students in middle school, high school and first-year university, teachers who want a quick demonstration for the projector, and anyone revising for exams.
Try it freeTeachers
For teachers: project the Special Relativity: Time Dilation & Length Contraction Lab on the board, let students predict the result, then run it together and test this: Set the speed to 0.6c and check γ against the formula by hand. For students: change one thing at a time and write down what changes.
Try it freeHow it compares
A plain look at this tool next to the usual alternative.
| This simulation | Textbook diagram | |
|---|---|---|
| Interactive | Drag, tap and change settings | Fixed picture |
| Install | Nothing to install | Not needed |
| Cost | Free to use | Depends on the book |
Questions people ask
Why don't we notice time dilation in everyday life?
Because γ is extremely close to 1 unless v is a large fraction of the speed of light - at highway speeds the effect is many orders of magnitude too small to detect.
Is length contraction just an optical illusion?
No - it is a real effect of how space and time mix between reference frames, confirmed by particle-accelerator experiments, even though nothing physically 'squeezes' the object in its own rest frame.
Is the Special Relativity: Time Dilation & Length Contraction Lab free to use?
Yes. The Special Relativity: Time Dilation & Length Contraction Lab is free, needs no signup or download and runs in your web browser. It is part of the Physics group of AZRS simulations.
Does the Special Relativity: Time Dilation & Length Contraction Lab work on a phone or tablet?
Yes. The Special Relativity: Time Dilation & Length Contraction Lab takes touch input as well as mouse input, so you can use its 3 adjustable settings with a finger. A larger screen makes the controls and graphs easier to read.
How do I use the Special Relativity: Time Dilation & Length?
1. In the Special Relativity: Time Dilation & Length Contraction Lab, use the controls to change Ship speed, Proper time interval Δt₀ (measured on the ship), Proper length L₀ (measured on the ship). The simulation reacts instantly. 2. In the Special Relativity: Time Dilation & Length Contraction Lab, press "Fire light-clock tick" to start, reset or change what is happening. 3. Start with this experiment: Push the speed slider past 0.9c and watch the ship clock nearly freeze compared to the ground clock. Drag any glowing handle, object or slider with your mouse or finger and the Special Relativity: Time Dilation & Length Contraction Lab responds in real time. 4. Change one setting at a time and watch which readout moves, then compare it with this idea: Time dilation: a clock moving relative to an observer ticks slower by the Lorentz factor γ = 1/√(1-v²/c²).
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Push a spaceship toward the speed of light and watch its onboard clock run slow and its. Free to use.
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