# How do I calculate the total time dilation experienced by an accelerating ship?

My advanced human civilisation often has high-acceleration ships travelling at near lightspeed. I know that time dilation would have a significant effect on the time experienced by the crews, but I've no idea how to calculate how much when they're under constant thrust - my usual calculation of averaging speeds won't work here as time dilation isn't linear. How can I calculate the time difference and eventual speed for 1 million G acceleration for 30min real time, or how long it would take to reach 50% lightspeed at 1 million G (for example)?

• 0.5 c = 149,896,229 m/s. 1,000,000 g = 9,806,650 m/s². 149,896,229 / 9,806,650 = 15.29 seconds. Mar 31, 2020 at 20:27
• This is very answerable with some high school physics I believe even though those numbers seem a bit high, however I am very curious: how did you come up with those numbers if you don't know the result? This looks aimless to me. I think a more logical approach would be the opposite: telling us how much time you want to save and we tell you the acceleration required? Mar 31, 2020 at 20:29
• There is a number of relativistic calculators online. However, they all solve it from acceleration and distance, not from acceleration and time. If you like, you can entering different distances until the answer time matches your desired input. Mar 31, 2020 at 20:40
• IMHO, ships (and their occupants!) that can withstand one million G seems somehow less believable than FTL. Any sublight travel will take so long in cruise that a more realistic acceleration level won't change the answer enough to matter. Mar 31, 2020 at 22:58
• Try a web search for "relativistic spaceship calculation" and you should get not only some theory but some online calculators. Apr 1, 2020 at 2:16