EinsteinMass

Relativistic Mass Calculator

See how mass increases as an object approaches the speed of light.

Rest mass (kg)

Velocity (fraction of c)

Relativistic mass

2.294 kg

Lorentz factor (γ): 2.294

What you entered

Rest mass: 1 kgVelocity: 0.9c

1
v/c (velocity as fraction of speed of light)
0.9= 0.9c
2
v² / c²
0.9²= 0.81
3
Lorentz factor: γ = 1 / √(1 − v²/c²)
1 / √(1 − 0.81)= 2.2942
4
Relativistic mass: m = m₀ × γ
1 × 2.2942= 2.2942 kg

Result

Relativistic mass: 2.294 kg

At 90.0% the speed of light, the Lorentz factor is 2.294, so a 1 kg rest mass appears as 2.294 kg to a stationary observer.

Relativistic mass increase with speed

Relativistic mass is the rest mass times the Lorentz factor, which rises without limit as speed approaches c.

Rest mass (kg)	Speed (fraction of c)	Lorentz factor	Relativistic mass (kg)
1	0.1	1.0050	1.0050
1	0.5	1.1547	1.1547
1	0.9	2.2942	2.2942
1	0.99	7.0888	7.0888
70	0.5	1.1547	80.8290

At 10% of light speed the increase is half a percent, which is why the effect never shows up outside particle accelerators. It then accelerates sharply: 0.99c multiplies the mass sevenfold, and the factor grows without bound as speed approaches c, which is why no massive object can reach light speed - the energy required diverges. Modern physics generally prefers to keep mass invariant and put the Lorentz factor into momentum and energy instead, so relativistic mass is best treated as a pedagogical device rather than current usage.

Why mass increases with velocity

In special relativity, an object's relativistic mass increases with velocity: m = m₀ × γ, where γ = 1/√(1 − v²/c²) is the Lorentz factor. At 90% of light speed, γ ≈ 2.29, so the object's effective mass more than doubles. At 99.9% c, γ ≈ 22.4. This is why no massive object can reach the speed of light — it would require infinite energy.

Rest mass vs relativistic mass

Modern physics prefers 'invariant mass' (rest mass m₀), which doesn't change with speed. 'Relativistic mass' is a pedagogical concept showing how inertia grows with velocity. The energy relationship E = γm₀c² is the precise formulation.

Frequently asked questions

A spaceship has rest mass 10,000 kg and travels at 0.9c — what's its relativistic mass?

Lorentz factor γ = 1/√(1 − 0.9²) = 1/√(0.19) ≈ 2.294. Relativistic mass = 10,000 × 2.294 ≈ 22,942 kg. The ship behaves as if it has more than double its rest mass, requiring enormously more energy to accelerate further.

How is relativistic mass related to E = mc²?

The full equation is E = γm₀c². At rest (γ = 1), this reduces to E = m₀c². As speed increases, γ grows, and so does total energy. Some physicists define 'relativistic mass' as γm₀ so the equation stays E = mc², but modern physics prefers keeping m as rest mass and writing E = γm₀c².

Why can't anything reach the speed of light?

As v approaches c, the Lorentz factor γ approaches infinity, meaning the energy needed to accelerate further also approaches infinity. You'd need infinite energy to push even a single electron to exactly c. This is why only massless particles (like photons) travel at light speed. The length contraction calculator shows another consequence of approaching c.