Barn-Pole Paradox Calculator

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Explore the effects of length contraction in special relativity with the classic barn-pole thought experiment.

Relativistic Parameters

Pole Rest Length (L₀)

Barn Rest Length

Velocity (fraction of c)

0c0.9c1c

Length Contraction Results

Enter parameters to calculate

About this calculator

Quick Reference

L₀Rest length (proper length)

LContracted length

vVelocity relative to observer

cSpeed of light (299,792,458 m/s)

Overview

The Barn-Pole Paradox (or Ladder Paradox) is a thought experiment in special relativity. It involves a pole moving at a high speed through a barn. Due to length contraction, the pole fits inside the barn for an observer in the barn's frame, but not for an observer in the pole's frame.

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Pro Tips

Length contraction only occurs in the direction of motion.
The Lorentz factor (γ) determines how much time dilates and lengths contract.
Simultaneity is relative—the barn doors don't close at the same time for all observers.

Fun Facts

"At 86.6% of the speed of light (0.866c), the Lorentz factor is exactly 2, meaning lengths contract by half."
"GPS satellites must account for relativity (both special and general) to maintain accuracy."
"The 'paradox' is resolved by recognizing that 'simultaneity' is not absolute."

Formula: L = L₀ / γ = L₀√(1 - v²/c²)