What is the Lorentz factor?

γ = 1/√(1 − v²/c²). It grows without bound as v approaches c, encoding all the special-relativity effects in one number.

What is time dilation?

Moving clocks run slow. A proper time interval t₀ measured by a stationary observer becomes t = γt₀ for a moving observer. At v = 0.9c, γ ≈ 2.29, so 1 hour aboard ship becomes 2.29 hours on Earth.

What is length contraction?

Moving objects are shorter along the direction of motion. A rod of proper length L₀ has length L = L₀/γ in a frame where it moves at speed v.

What is relativistic mass?

The apparent inertial mass of a body moving at speed v: m = γm₀. This concept is somewhat dated in modern physics (we prefer to keep mass invariant and update momentum to p = γm₀v), but NESA still uses it.

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NSW · HSCModule 7

Special relativity calculator

Compute γ, time dilation, length contraction, and relativistic mass for any sub-light velocity.

Inputs

Velocity v (m/s)c = 2.998e+8 m/sProper time t₀ (s)Proper length L₀ (m)Rest mass m₀ (kg)

Result

Lorentz factor γ

1.812

β = v/c

0.8339

Time dilation t = γ t₀

1.812s

Length contraction L = L₀/γ

0.5519m

Relativistic mass m = γ m₀

1.812kg

γ = 1/√(1 − v²/c²). Moving clocks run slow; moving rods are contracted; relativistic mass is the apparent mass at speed v.

How this calculator works

The calculator computes γ = 1/√(1 − v²/c²), then applies γ to each of the three relativistic effects. For v ≪ c, γ ≈ 1 and the relativistic corrections are negligible.

Common questions

What is the Lorentz factor?: γ = 1/√(1 − v²/c²). It grows without bound as v approaches c, encoding all the special-relativity effects in one number.
What is time dilation?: Moving clocks run slow. A proper time interval t₀ measured by a stationary observer becomes t = γt₀ for a moving observer. At v = 0.9c, γ ≈ 2.29, so 1 hour aboard ship becomes 2.29 hours on Earth.
What is length contraction?: Moving objects are shorter along the direction of motion. A rod of proper length L₀ has length L = L₀/γ in a frame where it moves at speed v.
What is relativistic mass?: The apparent inertial mass of a body moving at speed v: m = γm₀. This concept is somewhat dated in modern physics (we prefer to keep mass invariant and update momentum to p = γm₀v), but NESA still uses it.