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Time Dilation Calculator

Enter the time interval and the speed of light, and the tool will calculate the relative time

Observer Velocity (Δt):

Time Interval (v):

km/s ▾

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The time dilation calculator helps measure how time passes differently for observers in different frames of reference. This difference arises due to relative motion or variations in gravitational fields, as described by Einstein's theory of relativity.

What is Time Dilation?

"Time dilation refers to the effect where a clock moving relative to an observer or situated in a stronger gravitational field ticks slower compared to a stationary clock."

This effect becomes noticeable at speeds close to the speed of light or in intense gravitational fields. A gravitational time dilation calculator can determine how time is stretched for objects moving at high velocities or located near massive bodies in space.

How to Calculate Time Dilation?

Time dilation due to relative motion can be computed using the Lorentz factor. The equation is:

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

Where:

Δt' = Time experienced in the moving frame (dilated time)
Δt = Proper time in the stationary frame
v = Relative velocity between frames
c = Speed of light ≈ 299,792 km/s

Example Calculation:

Given:

Δt = 10 years (proper time)
v = 100,000 km/s
c = 299,792 km/s

Find: Dilated time Δt'

Solution:

Convert velocity as a fraction of the speed of light:

\[ v = \frac{100,000}{299,792} \approx 0.334c \]

Substitute into the formula:

\[ \Delta t' = 10 \times \frac{1}{\sqrt{1 - (0.334)^2}} \]

Calculate inside the square root:

\[ 1 - 0.334^2 = 1 - 0.1116 = 0.8884 \]

Take the square root:

\[ \sqrt{0.8884} \approx 0.9425 \]

Finally, calculate the dilated time:

\[ \Delta t' = 10 / 0.9425 \approx 10.61 \text{ years} \]

The moving observer experiences approximately 10.61 years, slightly longer than the 10 years measured by the stationary observer. A time dilation calculator can quickly provide results for various velocities.

Some users may want results in different units. The relativistic time dilation calculator can display outputs in seconds, minutes, hours, or years.

FAQs:

Does Light Experience Time Dilation?

No. Light always travels at speed c, and the Lorentz factor becomes undefined at v = c, making time dilation for light meaningless.

What is Lorentz Invariant?

A Lorentz invariant is a quantity that remains constant under Lorentz transformations, regardless of the observer's motion. In special relativity, the spacetime interval Δs² is the key invariant:

Δs² = c²Δt² − Δx² − Δy² − Δz²

Does Gravity Affect Time?

Yes. Strong gravitational fields slow down time relative to weaker fields. This effect is described by general relativity, and gravitational time dilation calculations compare clocks in different gravitational potentials.

Citation:

From Wikipedia: Time Dilation
From phys.libretexts.org: Relative Time in Special Relativity

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