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Destination Distance

Ship Speed

0.50 c
Fraction of Speed of Light
0.1c 25c 50c 75c 99.99c
Warp Factor
1.00
Star Trek Warp Scale

Destination Presets

Travel Time Results

Earth Time
--
years
Ship Time
--
years
Fuel Energy
--
Joules
Relativistic Mass
--
x rest mass

Relativistic Effects

Time Dilation

t' = t / γ = t × √(1 - v²/c²)
1.00x
Ship time passes at same rate as Earth time

Length Contraction

L' = L / γ = L × √(1 - v²/c²)
1.00x
Distance appears unchanged to ship crew

Mass Increase

m = m₀ / √(1 - v²/c²)
1.00x
Ship mass equals rest mass

Energy Required

E = mc²(1/√(1-v²/c²) - 1)
0 J
Kinetic energy needed to reach speed

Speed of Light Reference

Speed (c) 299,792,458 m/s
km/s 299,792 km/s
km/h 1,079,252,849 km/h
AU per second 0.002 AU/s
Earth to Moon 1.28 seconds
Earth to Sun 8.32 minutes
Earth to Mars (min) ~3-22 minutes
To Alpha Centauri 4.24 years

Warp Factor Reference

Warp 1 1.00c
Warp 2 8.00c
Warp 3 27.00c
Warp 4 64.00c
Warp 5 125.00c
Warp 6 216.00c
Warp 7 343.00c
Warp 8 512.00c
Warp 9 729.00c
Warp 9.9 ~3,000c
Warp 9.99 ~7,912c

How It Works - Relativity Formulas

Time Dilation (Special Relativity)

t' = t × √(1 - v²/c²)
t' = time experienced by moving observer (ship crew)
t = time experienced by stationary observer (Earth)
v = velocity of the moving object
c = speed of light (299,792,458 m/s)

As an object approaches the speed of light, time slows down for the moving observer. At 99% of c, time passes about 7 times slower aboard the ship.

Length Contraction

L' = L × √(1 - v²/c²)
L' = contracted length as measured by moving observer
L = proper length (rest length)

Objects moving at relativistic speeds appear shortened in the direction of motion. This is not an illusion - the space itself is contracted for the moving observer.

Relativistic Mass Increase

m = m₀ / √(1 - v²/c²)
m = relativistic mass
m₀ = rest mass

The effective mass of an object increases as it approaches light speed. This is why infinite energy would be required to reach exactly c.

Kinetic Energy (Relativistic)

E = m₀c²(1/√(1-v²/c²) - 1)
E = kinetic energy
m₀ = rest mass
c = speed of light

At relativistic speeds, the classical kinetic energy formula (½mv²) is no longer accurate. This relativistic formula accounts for the mass increase.

Warp Factor (Star Trek)

Warp Factor w: Speed = w³ × c (for w ≤ 9)
w = warp factor
c = speed of light

In the Star Trek universe, warp factor follows a cubic relationship with speed for factors 1-9. Above warp 9, the scale becomes exponential. Warp 1 equals light speed, Warp 9 equals 729 times light speed.