The Lorentz factor for an object at rest is exactly 1.
The Lorentz factor is defined by γ = 1/√(1 − v²/c²), where v is the object's speed relative to an inertial observer and c is the speed of light. At rest, v = 0, so the expression becomes 1/√1, which equals 1.
This value marks the boundary between relativistic formulas and their everyday low-speed limit. When speed is much smaller than c, γ is very close to 1, so relativistic corrections are difficult to notice. As speed approaches c, γ rises without bound; a massive object cannot reach light speed because doing so would require unbounded energy.
The factor appears in time dilation, length contraction, relativistic momentum and total energy. At rest, the kinetic energy is zero because E − mc² = (γ − 1)mc². However, the object's rest energy remains mc². A common mistake is to confuse γ with its reciprocal, which equals 1 at rest too but has a different physical role away from zero speed.