Speed of Light Time Dilation Calculator

Time Dilation Equation:

\[ \Delta t' = \frac{\Delta t}{\gamma}, \quad \gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} \]

Dilated Time (Δt'):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Time Dilation?

Time dilation is a phenomenon predicted by Einstein's theory of relativity where time appears to pass at different rates for observers in different inertial frames of reference, especially when relative velocities approach the speed of light.

2. How Does the Calculator Work?

The calculator uses the time dilation equation:

\[ \Delta t' = \frac{\Delta t}{\gamma}, \quad \gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} \]

Where:

\( \Delta t' \) — Dilated time (observed time)
\( \Delta t \) — Proper time (time in rest frame)
\( v \) — Relative velocity between observers
\( c \) — Speed of light in vacuum (299,792,458 m/s)
\( \gamma \) — Lorentz factor

Explanation: As an object's velocity approaches the speed of light, time appears to slow down from the perspective of a stationary observer.

3. Importance of Time Dilation

Details: Time dilation has practical implications for GPS satellite systems, particle physics experiments, and our understanding of the universe. It's a fundamental prediction of special relativity that has been experimentally verified.

4. Using the Calculator

Tips: Enter proper time in seconds, relative velocity in meters per second, and speed of light (default is 299,792,458 m/s). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: At what speed does time dilation become noticeable?
A: Significant time dilation only occurs at velocities approaching the speed of light (10% or more of c). For everyday speeds, the effect is negligible.

Q2: Has time dilation been experimentally verified?
A: Yes, through experiments with atomic clocks on airplanes and satellites, and observations of fast-moving particles.

Q3: What happens at the speed of light?
A: The equation predicts infinite time dilation at v = c, which is why nothing with mass can reach the speed of light.

Q4: Does time dilation affect aging?
A: Yes, astronauts on the ISS age slightly slower than people on Earth, though the difference is very small (microseconds per year).

Q5: What's the twin paradox?
A: A thought experiment where one twin travels at near-light speed and returns younger than the Earth-bound twin, demonstrating time dilation.