Barn-Pole Paradox

Written by Great Medico

Updated September 25, 2026 •2 min read

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A barn-pole paradox result can look convincing even when one unit or assumption is off. Relativistic effects stay small at everyday speeds and become strongly nonlinear as velocity approaches the speed of light. This page keeps the calculation narrow enough to trace the answer back to the values you enter.

What this calculator does

The Barn-Pole Paradox connects Speed (v), Speed ratio (β), Length of the pole (l) to the page’s lorentz factor γ. Supporting values are included only when they follow from the same relationship, so you can compare the headline with the quantities behind it.

How to use it

Enter Speed (v), Speed ratio (β), Length of the pole (l), Length of the barn (L) using the units shown beside each field. Keep all values from the same physical case, then check the headline result and any supporting values before changing one input at a time for comparison.

How the calculation works

The page forms β = v/c and γ = 1/√(1−β²). It then reports each entered proper length divided by γ as a contracted length in the selected inertial comparison. The frame selector does not change the active numeric path.

Example

With the default setup (Speed (v) = 0.8 c; Speed ratio (β) = 0.8; Length of the pole (l) = 10 m; Length of the barn (L) = 8 m), the page reports lorentz factor γ of 1.666667. This is a useful baseline: change one input and confirm the new value follows the proportionality in the formula.

How to interpret the result

Interpret the lorentz factor γ with its reference frame and proper quantity in mind. A Lorentz factor, dilated time, or contracted length does not have a frame-independent everyday interpretation; the labels define which observer the number belongs to.

Limitations and notes

This page demonstrates length contraction numerically but does not model the relativity-of-simultaneity event timing that resolves the full paradox. The Frame of reference selector does not currently change the reported calculation, so use the result as a contraction example rather than a complete spacetime analysis.