🚪 Barn-Pole Paradox Calculator

The Barn-Pole (Ladder) Paradox

The barn-pole paradox is a classic thought experiment in special relativity: a pole longer than a barn is carried at relativistic speed toward the barn. In the barn’s rest frame, the pole is length-contracted according to L’ = L₀/γ, where γ = 1/√(1−β²) is the Lorentz factor, so it can appear to fit entirely inside — even though in the pole’s own rest frame, it’s the barn that appears contracted and too short to contain the pole.

The apparent contradiction is resolved by the relativity of simultaneity: whether the pole “fits” depends on which frame’s definition of “at the same time” you use, and both descriptions are self-consistent within their own frame. This calculator computes the barn-frame contracted length only, to illustrate the length-contraction side of the paradox for educational exploration.