Thirty Micrometres: The Plate Separation at Which the Casimir Energy Density Equals the Cosmic Vacuum Density

The Casimir effect shows that vacuum energy differences are real and measurable, but its densities are usually quoted at nanometre-to-micrometre separations where they vastly exceed the cosmic vacuum density. This paper inverts the standard parallel-plate formula to find the separation at which the Casimir energy density equals the observed cosmic density of 5.25 x 10^-10 joules per cubic metre. The equality separation is 30.1 micrometres, verified by substitution in the accompanying script. A table from ten nanometres to one millimetre shows the density crossing the cosmic value at that row, and a sensitivity scan shows the crossing moves by less than twenty percent if the cosmic density changes by a factor of two. The calculation uses stated idealisations and reports no measurement.