Time
Dilation

Special & General Relativity Calculator

Use this free time dilation calculator to compare elapsed time for moving observers and clocks inside strong gravitational fields. Explore special relativity and general relativity with interactive inputs, live graphs, and animated clock visualizations.

Interactive tool

Calculate time dilation from velocity or gravity

Switch between special relativity and general relativity to estimate how much time passes for a traveler compared with a distant observer.

Lorentz
$$\Delta t=\frac{\Delta t'}{\sqrt{1-\frac{v^2}{c^2}}}$$
Relative energy required
Aboard On Earth

Time elapsed on Earth

0.00 Years

Awaiting flight parameters...

Concept guide

How time dilation works

This calculator models the two most common relativity cases people want to explore: high-speed motion and strong gravity.

Special relativity and velocity

When a traveler moves close to the speed of light, their onboard clock advances more slowly than the clock of a stationary observer. The effect is governed by the Lorentz factor, which grows rapidly as velocity approaches \(c\).

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

General relativity and gravity

Gravity also changes the rate of time. A clock deeper in a gravitational well runs more slowly than a clock farther away, which is why the calculator lets you compare distance from massive objects such as neutron stars and black holes.

$$t_f=t_0\sqrt{1-\frac{r_s}{r}}$$

Usage

How to use the time dilation calculator

  1. Select Velocity (SR) to simulate motion-based time dilation or Gravity (GR) to simulate gravitational time dilation.
  2. Adjust the inputs for velocity, travel time, gravitational source, or distance from the massive object.
  3. Read the live result, clock animation, and graph to compare the traveler frame with the distant observer frame.
  4. Use the downloadable demo output if you want to share or archive an example calculation.

What the result means

The main output shows how much time elapses for the reference observer compared with the traveler or local frame. It is ideal for intuition, classroom examples, and quick relativity comparisons.

Questions

Frequently asked questions

What is time dilation?

Time dilation is the relativistic effect where two observers measure different elapsed time because of high relative velocity or because they are located in different gravitational potentials.

What is the difference between special and general relativity here?

Special relativity models time changes caused by velocity. General relativity models time changes caused by gravity, especially near massive compact objects.

Are these results exact for real missions or astronomical systems?

The calculator uses standard educational formulas and idealized assumptions. That makes it strong for learning and comparison, even though real-world trajectories can require more detailed modeling.

Can I use this calculator for classroom demonstrations?

Yes. The interface is designed for quick experiments, visual explanation, and side-by-side comparison of relativity scenarios in class, on stream, or in educational content.