Relativistic Velocity Addition Calculator

Your details

All three velocity inputs use the same unit system.
Speed of the moving reference frame relative to a stationary observer (e.g. a spaceship).
c
Speed of the object relative to the moving frame (e.g. a projectile fired from the spaceship).
c
Whether the object moves in the same direction as the frame or against it.
Relativistic combined velocityHighly relativistic
0.846154

Speed of the object as seen by the stationary observer, using Einstein's formula

Fraction of speed of light0.846154c
Classical (Galilean) result1.1
Classical result as fraction of c1.1c
Relativistic correction0.253846
Lorentz factor (gamma)1.8764
0.846154 c
Non-relativistic<0.01Mildly relativistic0.01-0.1Moderately relativistic0.1-0.5Highly relativistic0.5-0.9Ultra-relativistic0.9+

Combined velocity is 84.6154% of c (highly relativistic regime).

  • The combined relativistic velocity is 84.6154% of the speed of light.
  • Classical mechanics would predict 110.0000% of c, but special relativity reduces this by 25.3846 percentage points, preventing any object from reaching c.
  • At this speed, the Lorentz factor gamma is 1.8764: clocks on the moving object tick 46.71% slower than a stationary clock, and lengths contract by the same proportion.

Next stepFor a complete picture of the physics at this speed, also consider time dilation and length contraction using the Lorentz factor shown above.

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