Relativistic Mechanics Calculator

Calculate time dilation, length contraction, relativistic mass, kinetic energy, and momentum from velocity as a fraction of the speed of light.

Velocity (fraction of c)

Proper Time

Proper Length

Rest Mass

Tab to move between fields

Lorentz Factor (γ)

2.29

Dilated Time

2.29 s

Contracted Length

0.44 m

≈ 5 credit cards

Relativistic Mass2.29 kg

Kinetic Energy116,474,160,483,505,620 J

Total Energy206,474,160,483,505,630 J

How to Use This Calculator

Enter Velocity (fraction of c), Proper Time, and Proper Length.
Set Rest Mass.
Review Lorentz Factor (γ), Dilated Time (s), and Contracted Length (m).
Use Relativistic Mass (kg) and Kinetic Energy (J) to inform your decision.
Use the chart to visualize the results and explore different scenarios by adjusting inputs.

How the result changes with Velocity (fraction of c)

Velocity (fraction of c)	Lorentz Factor (γ)	Dilated Time	Contracted Length
0.1	1.01	1.01 s	0.99 m
0.35	1.07	1.07 s	0.94 m
0.65	1.32	1.32 s	0.76 m
0.9	2.29	2.29 s	0.44 m

Velocity (fraction of c): Velocity as a fraction of the speed of light (0 to 1). For example, 0.9 = 90% the speed of light.
Proper Time: Time interval measured in the moving object's rest frame.
Proper Length: Length of the object measured in its rest frame.
Rest Mass: Mass of the object at rest. Electron ≈ 9.109×10⁻³¹ kg, proton ≈ 1.673×10⁻²⁷ kg.

Identify Input Parameters
4 parameters
Velocity (fraction of c) = 0.9, Proper Time = 1, Proper Length = 1, Rest Mass = 1 = 4 input(s) provided
Calculate Lorentz Factor
Lorentz Factor = g
2.29416 = 2.29416
Calculate Dilated Time
Dilated Time
2.29416 = 2.29416
Calculate Contracted Length
Contracted Length
0.43589 = 0.43589
Calculate Relativistic Mass
Relativistic Mass
2.294157338705618 = 2.294157338705618
Calculate Kinetic Energy
Kinetic Energy
116474160483505620 = 116474160483505620