UFO Travel Calculator
This calculator works in two modes. In Interstellar mode it applies Einstein's special relativity to compute the Lorentz factor, Earth time, ship (crew) time, time dilation, and kinetic energy for a journey at any fraction of the speed of light. In Atmospheric mode it compares how fast a UFO using a real or hypothetical propulsion system would cross any of eight major city pairs versus a regular airliner. Switch modes with the selector below.
Formula
Worked example
Traveling to Proxima Centauri (4.24 ly) at 50% of light speed: gamma = 1/sqrt(1-0.5^2) = 1.155. Earth time = 4.24/0.5 = 8.48 years. Ship time = 8.48/1.155 = 7.34 years. Time dilation = 8.48 - 7.34 = 1.14 years. Kinetic energy for a 10,000 kg craft = (1.155-1) x 10,000 x (3e8)^2 = 697 petajoules.
What is the UFO Travel Calculator?
This tool has two modes. In Interstellar mode it applies Einstein's special theory of relativity to model what would happen if a craft traveled through space at a meaningful fraction of the speed of light. You enter a destination distance, a speed (as a fraction of c, the speed of light), and the craft mass. The calculator returns the Lorentz factor, the time elapsed on Earth, the time experienced by the crew, the difference between the two (time dilation), and the relativistic kinetic energy the journey would demand. In Atmospheric mode the calculator compares how long it would take a craft with various real or hypothetical propulsion systems to fly between eight major cities, versus a standard commercial jet.
Special relativity and the Lorentz factor
Special relativity, published by Albert Einstein in 1905, showed that the laws of physics are the same in all inertial reference frames and that the speed of light in a vacuum is constant for all observers. One consequence is time dilation: a clock aboard a fast-moving spacecraft ticks more slowly than a clock at rest on Earth. The Lorentz factor (gamma) quantifies this effect. At 50% of the speed of light, gamma is 1.155, meaning the crew ages about 1.155 times more slowly than people on Earth. At 99% of c, gamma rises to about 7.09, so 1 year aboard the ship corresponds to 7.09 years on Earth. The formula is gamma = 1 / sqrt(1 - v^2 / c^2), where v is the spacecraft speed and c is the speed of light. Earth coordinate time for the journey is simply t = d / v (distance divided by speed), and ship (proper) time is tau = t / gamma.
Kinetic energy and the energy challenge
Relativistic kinetic energy is KE = (gamma - 1) x m x c^2. At non-relativistic speeds this reduces to the familiar 0.5 x m x v^2, but near the speed of light it grows far faster than that. A 10,000 kg craft at 50% of c requires roughly 697 petajoules - about the output of a large nuclear power plant running for twenty years. At 99% of c the same craft needs about 27,200 petajoules. This is why engineers and physicists who think seriously about interstellar travel focus almost entirely on the energy problem: the physics of time dilation is well understood, but generating the required energy with any technology we can conceive of today is an enormous challenge.
Atmospheric UFO propulsion: from jets to mystery engines
In Atmospheric mode the calculator compares several real propulsion systems alongside a speculative "Mysterious UFO engine." A commercial turbofan reaches about 900 km/h; the Concorde-class turbojet hit 2,200 km/h; the SR-71 Blackbird's ramjet-augmented engines reached about 3,540 km/h. Hypersonic scramjet concepts target speeds around Mach 25 (30,600 km/h), and chemical rockets can sustain around Mach 30 in space. An ion thruster achieves low thrust but continuous acceleration, reaching up to 200,000 km/h in deep space over months. The hypothetical UFO engine is set at 10,000,000 km/h - about 0.0093% of the speed of light - for illustrative comparison. Even at that speed, flying from New York to London would take under two seconds.
Lorentz factor and time dilation at various speeds
| Speed (% of c) | Lorentz factor | Earth time (yr) | Ship time (yr) | KE approx. |
|---|---|---|---|---|
| 10% | 1.005 | 42.4 | 42.2 | ~22.6 PJ |
| 30% | 1.048 | 14.1 | 13.5 | ~215 PJ |
| 50% | 1.155 | 8.48 | 7.35 | ~697 PJ |
| 70% | 1.400 | 6.06 | 4.33 | ~1,800 PJ |
| 90% | 2.294 | 4.71 | 2.05 | ~5,900 PJ |
| 95% | 3.203 | 4.46 | 1.39 | ~10,100 PJ |
| 99% | 7.089 | 4.28 | 0.60 | ~27,200 PJ |
| 99.9% | 22.37 | 4.24 | 0.19 | ~95,800 PJ |
How the Lorentz factor, ship time, and kinetic energy scale with spacecraft speed (for a 10,000 kg craft traveling to Proxima Centauri, 4.24 ly).
Frequently asked questions
What does the Lorentz factor tell me?
The Lorentz factor (gamma) is the ratio of time elapsed on Earth to time elapsed on the spacecraft. A gamma of 2 means the crew ages at half the rate of people on Earth for the duration of the journey. At 99% of light speed, gamma is about 7.09, so a 1-year voyage from the crew's perspective corresponds to about 7 years on Earth.
Can anything actually travel at these speeds?
No object with mass can reach or exceed the speed of light - it would require infinite energy. Current spacecraft top out around 70 km/s (the Voyager probes and Parker Solar Probe), which is about 0.02% of the speed of light. Relativistic travel remains a theoretical exercise with today's technology, though concepts like nuclear pulse propulsion or antimatter drives are studied by researchers.
What is time dilation and why does it happen?
Time dilation arises from special relativity's requirement that the speed of light is constant for all observers. Because c cannot change, time itself must "stretch" for a moving observer so that light still covers the same distance in the same time from any frame of reference. The faster you move, the more time stretches: at 87% of c, you age at half the rate of someone at rest.
Why does kinetic energy grow so fast near the speed of light?
At non-relativistic speeds, kinetic energy is 0.5 x m x v^2. But as speed approaches c, the relativistic mass effectively increases (captured by the Lorentz factor), so each additional increment of speed requires far more energy than the last. Approaching c asymptotically requires infinite energy, which is why the speed of light is an absolute upper limit for massive objects.
How is ship time different from Earth time in practice?
If a crew departs Earth at 90% of light speed and travels to a star 4.24 light-years away, Earth observers would measure about 4.71 years passing. But the crew would experience only about 2.05 years on their clocks and bodies. They arrive younger than they would have been had they stayed on Earth. This is not a trick of perception: their biological aging, clocks, and every physical process genuinely ran slower.