Inthisarticle,westudytheexplicitexpressionsoftheconstantsintheerrorestimateofthenonconformingfiniteelementmethod.WeexplicitlyobtaintheapproximationerrorestimateandtheconsistencyerrorestimatefortheWilson'selementwithouttheregularassumption,respectively,whichimpliesthefinalfiniteelementerrorestimate.Suchexplicitapriorierrorestimatescanbeusedascomputableerrorbounds.