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Speed of Light & Time Dilation Calculator

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

Last reviewed by the myCalculator Editorial Team

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)

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Formula & How Speed of Light & Time Dilation Calculator Works

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

Special relativity says a moving clock runs slow compared with a stationary one by the Lorentz factor γ = 1 ÷ √(1 − v²/c²). At 80% of the speed of light γ = 1 ÷ √(1 − 0.64) = 1 ÷ 0.6 = 1.67, so one year on a fast ship is 1.67 years on Earth. At 99% of light speed γ is about 7.1. The effect is negligible at everyday speeds but is real and measured: satellite clocks must be corrected for it. Nothing with mass can reach the speed of light, which is why γ would become infinite. The calculator shows the relationship for learning and for exploring science-fiction travel times.

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.

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