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Speed of Light & Time Dilation Calculator

Calculate relativistic Lorentz factor γ, time dilation, and length contraction at near-light speeds.

Input Parameters

Calculation Results

Time on Earth
1.67 years
Lorentz Factor (γ)
1.667×
Elapsed Time Difference
+0.67 years on Earth
Actual Velocity
239,834 km/s (80% of c)
Spatial Length Contraction
40% shorter in direction of motion
Summary: Traveling at 80% the speed of light for 1 year on the ship corresponds to 1.67 years passing on Earth (Lorentz factor γ = 1.67).
Step-by-Step Calculation Solution
1.Lorentz Factor γ = 1 / √(1 - v²/c²) = 1 / √(1 - 0.8²) = 1.667
2.Earth Time = Ship Time × γ = 1 × 1.667 = 1.67 years
3.Speed of Light c = 299,792,458 m/s (approx. 1.08 billion km/h)

Formula & How Speed of Light & Time Dilation Calculator Works

Mathematical Formula
γ = 1 / √(1 - v²/c²) | t_earth = γ × t_ship

Einstein's Special Theory of Relativity proves that as an object approaches the speed of light (c = 299,792,458 m/s), time slows down relative to a stationary observer, and physical length contracts in the direction of motion.

How to Calculate Speed of Light & Time Dilation Calculator (Step-by-Step)
  1. Enter Velocity as % of Speed of Light (c): Input your target parameter value.
  2. Enter Travel Time on Spaceship (years): Input your target parameter value.
  3. Apply Formula: Calculate using γ = 1 / √(1 - v²/c²) | t_earth = γ × t_ship.
  4. Review Results: View exact computed answers, metrics, and worked mathematical proofs.
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Frequently Asked Questions (FAQs)

What is the speed of light in vacuum?

The speed of light (c) is exactly 299,792,458 m/s (approx. 300,000 km/s or 1.08 billion km/h).

What is the Lorentz factor?

The Lorentz factor γ = 1/√(1 - v²/c²) quantifies the extent of time dilation and relativistic mass increase.

Official Regulatory & Government Data Sources

Authoritative Standards & Verified Reference Citations

Independent & Verified

Calculations and mathematical logic on this page are grounded in published statutory rules, regulatory standards, and official government data published by the following bodies:

Australian Government Data Portal (data.gov.au)Government
Commonwealth of Australia

Open government data, scientific datums, and public sector mathematical reference datasets.

data.gov.au
National Measurement Institute (NMI)Government
Australian Department of Industry, Science and Resources

Australia's national authority on physical, chemical, and biological metric measurement standards.

www.industry.gov.au/national-measurement-institute

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