Explore Star Destinations

Time Dilation Formula Calculator

Spacecraft accelerates continuously throughout the journey. Realistic for ion drives or theoretical propulsion.

Speed vs Time
This chart shows how quickly you accelerate to a fraction of the speed of light over time.
Distance vs Time
Shows distance covered (in light-years) over time.
Traveler's vs Observer's Time
Shows how time experienced by the traveler differs from time on Earth.
Energy Requirement vs Distance
Shows the (simplified) energy requirements for maintaining relativistic travel as distance increases.
Doppler Shift vs Time
Shows how the Doppler effect changes observed wavelengths over time.
Velocity vs Distance
Shows how your speed changes as you travel further from your starting point.
Lorentz Factor vs Time
Shows how the Lorentz factor (γ) grows over time as relativistic effects increase.
Proper vs Observer Distance
Shows how distance measurements differ between the traveler's frame and the observer's frame.

How to Use This Calculator

This time dilation calculator lets you enter a distance in light-years and acceleration in m/s² to see how time dilation affects your journey. It shows differences between traveler and observer times, maximum velocity, energy requirements, Doppler shift, Lorentz factor, and how distances vary between reference frames. Charts appear after you calculate.

Results

  • Traveler's Time: How much time the person on the spaceship experiences
  • Observer's Time: How much time passes on Earth during the journey
  • Maximum Velocity: The highest speed reached, as a fraction of light speed

Interactive Charts

  • Speed vs Time: How quickly you accelerate towards light speed
  • Distance vs Time: How far you've traveled over time
  • Traveler's vs Observer's Time: Compare time passage between Earth and spaceship
  • Energy Requirement vs Distance: How much energy is needed as you travel further
  • Doppler Shift vs Time: How light wavelengths change during your journey
  • Velocity vs Distance: Your speed at different distances
  • Lorentz Factor vs Time: How much time dilation increases with speed
  • Proper vs Observer Distance: How distance measurements differ between frames

What is Time Dilation?

Time dilation is an effect from Einstein's theory of special relativity. The faster you move, the slower time passes for you compared to someone standing still. At 90% of light speed, time passes about 2.3 times slower for the traveler than for someone on Earth.

What is the Time Dilation Formula?

The Time Dilation Formula is:

t' = t / √(1 - v²/c²)

Where:
t' = time measured by the observer (on Earth)
t = time experienced by the traveler
v = velocity of the traveler
c = speed of light (299,792,458 meters per second)

Frequently Asked Questions

Why Does Time Slow Down When You Go Fast?

Einstein's Theory of Relativity says space and time are connected. When you move through space at high speeds, you move through time more slowly. Scientists have confirmed this using atomic clocks on aircraft and satellites.

Is Time Dilation Real?

Yes! GPS satellites must account for time dilation because they move at approximately 14,000 km/h and orbit far from Earth's gravitational field. Without relativistic corrections, GPS would accumulate errors of about 11 kilometers per day.

What's the Twin Paradox?

Imagine twins - one stays on Earth while the other travels in a spaceship at near light speed. At first, it seems like a paradox because each twin could say they're staying still while the other moves away. So who actually ages slower?

The key is that the traveling twin has to turn around to come home. This turning around requires acceleration (speeding up, slowing down, and changing direction). This acceleration breaks the symmetry between the twins' experiences. When the traveling twin returns, they'll be younger than their Earth-bound sibling because they experienced these changes in motion that the Earth-bound twin didn't.

Scientists have actually proven this with extremely precise atomic clocks - the clock that moves and returns really does tick more slowly than the one that stays put!

Does Gravity Affect Time?

Yes! This is called gravitational time dilation. Time moves more slowly in stronger gravitational fields. Time actually passes slightly faster at the top of a tall building compared to ground level.

Explain Time Dilation Like I'm 12

Imagine you're watching a movie on a spaceship traveling near the speed of light. What feels like 1 hour to you might be 2 hours or more for your friends back on Earth! This isn't science fiction - it's a real effect that scientists have measured using super-accurate atomic clocks.

How was this built?

This was built entirely via "vibe coding" using an AI Agent while my son was in the bath - from concept, domain purchase, development and deployment! It was an experiment to demonstrate just how much the world has changed and just how much AI Agent Development offers in terms of improving efficiency.