Time dilation calculator

This page contains a time dilation calculator. To calculate the time dilation enter a percentage of the speed of light (c)
and press the button to continue. A distance/time dilation calculator is available further down the page. (Note: the results
may contain very small precision errors but these won’t usually overly affect the results -- see below for an explanation.)

Enter a number between 0.000001 and 99.99999999999999:

At your entered percentage of c time is slowed down to

percent of its usual value.

Enter percentage of c: Distance in light years:

It would take this many years to get there at your value of c:

It would take this many years to get there at your value of c:

Explanation of precision errors: As bizarre as it seems many software programs, such as the JavaScript used on this page, produce
imprecise mathematical results when faced with lots of decimal places. This is a consequence of computers storing numbers in binary
(ones and zeros), instead of the usual decimal numbers used by people. The problem even extends to Microsoft Excel -- read more
about it here: Wikipedia article. For interest, you may want to paste the time dilation formula below into Excel. It’s the standard time
dilation formula and in this case should give a result of 1, but instead gives 0.999949999. =SQRT((1-((1*1)/(100*100))))

Perhaps one of the strangest aspects of special relativity is that distances shrink in the direction of motion. This may not
seem so important at first but it leads to something quite remarkable. Common sense tells us that if a rocket travels at
90% of the speed of light then it would take about 11 years to reach a star 10 light years away, and that is indeed what
a stationary observer would see and measure. However, for the rocket not only time but distance will dilate and the star
would be reached in about only 4.4 years. Going even faster reduces the time taken by an ever increasing amount.
To see how long it would take to reach a star or galaxy when travelling at different speeds enter a percentage of the
speed of light (c) and a distance in light years to the star or galaxy in the boxes below and click Calculate. You may
want to try the examples listed below the calculation box:

Here are some examples to try:

Apart from the Sun the nearest stars to us form the
Alpha Centauri system. It consists of three stars: Alpha
Centauri A, Alpha Centauri B and the small faint red
dwarf star Alpha Centauri C, otherwise known as
Proxima Centauri. The system is found near The
Southern Cross constellation.
The distance from Earth to the Alpha Centauri group is
4.37 light years, or 41,343,000,000,000 kilometres
(25,690,000,000,000 miles). Even our nearest neighbour
is very far away…

Betelgeuse is a well-known and spectacular
star found in the constellation Orion. It’s
classed as a red supergiant and is one of the
largest stars seen with the naked eye. It’s not
only 100,000 times brighter than the Sun but
about 1000 times its diameter.
The distance from Earth to the Betelgeuse is
about 640 light years.

The centre of the Milky Way: Our galaxy, the
Milky Way, is about 100,000 light years across.
The Sun lies on the Sagittarius arm and is
about 26,000 light years from the centre,
which very likely contains a supermassive black
hole, occasionally sucking in a crushing whole
stars.
The picture shows the central parts of the Milky
Way, as observed in the near-infrared.

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The Andromeda Galaxy: The nearest major galaxy
to our own is the Andromeda Galaxy, also known as
M31. It’s over twice the diameter of the Milky Way at
about 220,000 light years.
Although our nearest major galactic neighbour it’s
still around 2,500,000 light years away.
It’s also the furthest object that most people can see
with the naked eye. On a clear night at the right time
of year it can be seen as a faint chalk-like smudge in
the constellation Andromeda.

The furthest known galaxy (as of March 2016) goes by the
name of GN-z11. It’s around 13.4 billion light years away
(13,400,000,000 light years).
An interesting point to note is that while the light we see it by
started off on its journey over 13 billion years ago that’s as
measured by our Earth-bound clocks. Because it’s light in a
vacuum it has a 100% dilation factor and so, from the
perspective of the light itself, it got here instantly and
travelled zero distance in doing so. As the English
astronomer Sir Arthur Eddington said: Not only is the
universe stranger than we imagine, it is stranger than we
can imagine.
Even travelling at 99.9999999% of the speed of light it would
still take over half a million years to get there.

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