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Length Contraction Calculator
Calculate relativistic length contraction at any fraction of the speed of light with visual comparisons, Lorentz factor tables, and speed references.
Length Contraction Calculator
m
Contracted Length⧉
50.004400 m
L = L₀ / γ = 100.00 / 1.999824
Length Reduction⧉
49.9956%
Percentage of original length that is contracted
Lorentz Factor (γ)⧉
1.999824
γ = 1/√(1 − v²/c²) at v = 86.6000% c
Velocity⧉
259,620.3 km/s
86.6000% of the speed of light
Rest Length⧉
100.00 m
Proper length measured in the object's rest frame
Contraction Ratio⧉
0.500044
L / L₀ — fraction of original length remaining
Length Contraction Visualization
Rest (L₀ = 100.00 m)
Contracted (L = 50.0044 m)
Contraction at Various Speeds
| v/c | γ | Contracted Length | Reduction % |
|---|---|---|---|
| 10.0% | 1.0050 | 99.4987 m | 0.50% |
| 20.0% | 1.0206 | 97.9796 m | 2.02% |
| 30.0% | 1.0483 | 95.3939 m | 4.61% |
| 40.0% | 1.0911 | 91.6515 m | 8.35% |
| 50.0% | 1.1547 | 86.6025 m | 13.40% |
| 60.0% | 1.2500 | 80.0000 m | 20.00% |
| 70.0% | 1.4003 | 71.4143 m | 28.59% |
| 80.0% | 1.6667 | 60.0000 m | 40.00% |
| 90.0% | 2.2942 | 43.5890 m | 56.41% |
| 100.0% | ∞ | 0.0000 m | 100.00% |
Key Relativistic Speeds
| Speed | v/c | Lorentz γ | Contraction | Note |
|---|---|---|---|---|
| Walking | ~0.000000005 | ~1.00 | ~0% | Immeasurable |
| Jet aircraft | ~0.000001 | ~1.00 | ~0% | Negligible |
| 10% c | 0.1 | 1.005 | 0.5% | Barely detectable |
| 50% c | 0.5 | 1.155 | 13.4% | Noticeable |
| 86.6% c | 0.866 | 2.000 | 50% | Half-length |
| 99.5% c | 0.995 | 10.01 | 90% | Extreme contraction |
Planning notes, formulas, and examples
About the Length Contraction Calculator
Length contraction is one of the most counterintuitive predictions of Einstein's special relativity: an object moving at a significant fraction of the speed of light appears shorter along its direction of motion when measured by a stationary observer. The effect, also known as Lorentz-FitzGerald contraction, was first proposed independently by George FitzGerald and Hendrik Lorentz before Einstein's 1905 theory provided the full theoretical framework.
The contracted length follows the formula L = L₀/γ, where L₀ is the rest (proper) length and γ = 1/√(1 − v²/c²) is the Lorentz factor. At everyday speeds the effect is immeasurably small, but at 86.6% the speed of light the object contracts to exactly half its rest length. At 99.5% c, it would appear just one-tenth its original size.
This calculator computes the contracted length for any velocity and rest length, displays the Lorentz factor, provides visual comparison bars, and includes tables showing how contraction scales across a range of velocities from walking speed to near-light speed.
When This Page Helps
This calculator makes one of special relativity's most fascinating predictions tangible and visual. The comparison bars and speed tables build intuition about how dramatically space itself contracts at relativistic velocities, connecting abstract equations to physical reality.
How to Use the Inputs
- Choose speed input mode: fraction of the speed of light or meters per second.
- Enter the velocity of the moving object.
- Enter the rest length (proper length) of the object in meters, km, or light-years.
- Select the appropriate length unit.
- Review the contracted length, Lorentz factor, and percentage reduction.
- Use preset buttons for common relativistic scenarios.
Formula used
Lorentz contraction: L = L₀ × √(1 − v²/c²) = L₀/γ, where L₀ is the rest (proper) length, v is velocity, c is the speed of light (299,792,458 m/s), and γ = 1/√(1 − v²/c²) is the Lorentz factor.Example Calculation
Result: Contracted length ≈ 50.0 m (γ = 2.0)
At 86.6% the speed of light, γ = 2.0, so a 100-meter object contracts to exactly 50 meters as seen by a stationary observer.
Tips & Best Practices
- At v = 0.866c, γ = 2.0 exactly — a convenient reference point.
- Contraction is negligible below 10% of light speed.
- Only the dimension parallel to motion contracts; perpendicular dimensions are unchanged.
- Enter "light-years" for unit to compute interstellar distance contraction.
- Scientific notation works in all input fields (e.g. 2.998e8 m/s).
When To Use This Calculator
Calculate relativistic length contraction at any fraction of the speed of light with visual comparisons, Lorentz factor tables, and speed references. Use it when you need a repeatable calculation in the physics / astronomy category and want the setup, result, and supporting values kept together. This is especially helpful when small input changes, unit choices, or rounding decisions can change the final number.
How To Check The Result
Start by confirming that the inputs match the formula shown on the page. Then compare the main output with the worked example and any secondary values shown by the calculator. If the result will be used in another calculation, keep extra precision until the final step and record the assumptions beside the number.
Practical Notes
Treat the result as a calculation aid rather than a substitute for context. For schoolwork, include the formula and substitution steps. For planning, technical, financial, or health-related decisions, verify important numbers against primary records, current rules, or a qualified professional before acting on them.
Sources & Methodology
Last updated:
Frequently Asked Questions
A relativistic effect where objects moving at high speeds appear shorter in their direction of motion to a stationary observer. The effect is described by L = L₀/γ.
It is a real physical effect — the measured distance genuinely contracts. It is not an optical illusion but a consequence of the geometry of spacetime.
No. In your own reference frame, everything appears normal. Length contraction is only observed by someone in a different frame of reference measuring your length.
Below about 10% of the speed of light, contraction is less than 0.5%. It becomes dramatically noticeable above 50% c and extreme above 90% c.
Yes, indirectly. Muon lifetime experiments and particle accelerator measurements are consistent with Lorentz contraction. Directly measuring contracting objects is impractical at available speeds.
No. Length contraction occurs only along the direction of motion. Perpendicular dimensions are unaffected.
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