Interstellar Travel Time Calculator: How Long to the Stars?

Interstellar travel requires enormous speeds and brings Einstein’s special relativity into play.

Classical (non-relativistic) travel time (for Earth observers):

t = d / v

For the traveler, proper time with time dilation:

τ = t / γ = t × √(1 - v²/c²)

Where the Lorentz factor γ is:

γ = 1 / √(1 - v²/c²)

As speed approaches c, γ grows rapidly. At v = 0.9c: γ ≈ 2.29. At v = 0.999c: γ ≈ 22.4. At v = 0.9999c: γ ≈ 70.7.

What this means: The traveler ages far less than people on Earth. A round trip to Proxima Centauri (4.24 light-years) at 0.99c:

• Earth time: ~8.57 years
• Traveler’s proper time: ~1.21 years

The twin paradox: If one twin takes a fast interstellar trip and returns, they will be younger than the stay-at-home twin.
It is not really a paradox. The travelling twin accelerates and turns around, which breaks the symmetry between the two frames, so there is no contradiction to resolve.

Key distances:

• Proxima Centauri: 4.243 light-years
• Alpha Centauri A/B: 4.37 light-years
• Barnard’s Star: 5.96 light-years
• Sirius: 8.61 light-years
• Tau Ceti: 11.9 light-years
• Galactic center: ~26,000 light-years

The energy problem: At v = 0.1c, a 1,000-tonne spacecraft needs about 4.5 × 10²⁰ joules of kinetic energy. That is roughly three quarters of the world’s total annual primary energy use (about 6.2 × 10²⁰ J), poured into a single vehicle, and it ignores the equal cost of slowing back down at the far end. For scale, the Sun radiates that much in about one microsecond.

The nastiness is in how fast that scales. Kinetic energy goes as γ − 1, not as v², so raising the target from 0.1c to 0.5c does not multiply the bill by 25. It multiplies it by about 31, to 1.4 × 10²² joules, which is more than twenty years of everything humanity currently generates. At 0.9c it is about 190 years’ worth. There is no engine problem to solve here first; the energy budget is the wall.

Voyager 1, the fastest thing we have ever launched on an escape trajectory, manages 17 km/s, which is 0.0057% of c and would take roughly 74,000 years to reach Proxima Centauri.