Relativistic Velocity Calculator

Easily calculate relativistic velocity with our simple online calculator. Learn the formula, meaning, and real-world examples of speed near light.

Mode

Choose between 1D collinear motion or full 3D vector components.

Input units

Pick a unit for entering velocities. Results can be shown in any unit.

Frame velocity v (S' relative to S)

If using fraction of c, enter between -1 and 1. Otherwise enter numeric speed in chosen units.

Output units

Object velocity in S' frame u'

Use positive/negative for direction along x-axis. If unit is "Fraction of c", values must be between -1 and 1.

u'_x

u'_y

u'_z

All components should be given in the same unit chosen above. The frame S' moves at velocity v along the x-axis relative to S.

Decimal places

Speed is easy to picture in daily life. Cars, trains, and planes all move fast. But when things move close to the speed of light, normal math fails. This is where relativistic velocity comes in.

We’ve built a Relativistic Velocity Calculator so you can explore this exciting concept. With it, you can see how speed, time, and energy change when objects move near light speed.

What is Relativistic Velocity?

Relativistic velocity is speed measured when motion is close to light speed. In this zone, the rules of Einstein’s special relativity apply. Time slows, mass grows, and distances shrink.

Think of it like this. A car driving at 60 mph feels normal. But if that car somehow reached half the speed of light, the math would change. Ordinary formulas break down, and relativistic formulas take over.

The Formula for Relativistic Velocity

The main formula is:

v = (u + v′) / (1 + (uv′ / c²))

Where:

v = final velocity
u = velocity of one object
v′ = velocity of another object
c = speed of light (≈ 3 × 10⁸ m/s)

This formula makes sure no object ever moves faster than light.

Relativistic Velocity and Energy

At high speeds, energy grows much faster than expected. The relativistic energy formula is:

E = γmc²

Where:

E = total energy
m = rest mass
c = speed of light
γ = Lorentz factor = 1 / √(1 − v²/c²)

This shows that as v approaches c, energy tends to infinity.

Relativistic Speed in MPH

Light moves at about 670,616,629 mph. So, if you ask, “What is relativistic speed in mph?” it simply means speeds close to this number. Even spacecraft today only reach a tiny fraction of it.

How to Use the Relativistic Velocity Calculator

Enter the speed of one object.
Enter the speed of the other object.
The calculator shows the combined relativistic velocity.

It’s that simple. You’ll get results in seconds, without messy math.

Why This Matters

Relativistic velocity is not just theory. It’s used in particle physics, space research, and GPS satellites. Without it, our tech wouldn’t stay accurate.

Think about GPS on your phone. It works only because scientists apply relativistic corrections.

Final Verdict

The Relativistic Velocity Calculator makes Einstein’s theory easy to use. You don’t need advanced math. Just enter numbers, and the tool shows the result.

It’s fun, simple, and powerful. Try it out to see the hidden side of speed.

FAQs

What is the formula for relativistic velocity?

It’s v = (u + v′) / (1 + (uv′ / c²)).

What is relativistic speed in mph?

It’s any speed close to light, which is 670,616,629 mph.

How is relativistic energy related to velocity?

Energy rises sharply as speed nears light, given by E = γmc².

Can anything move faster than light?

No. Relativity says light speed is the limit.

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