An accurate determination of specimen thickness is essential for quantitative analytical electron microscopy. Here we demonstrate that a position-averaged incoherent bright-field signal recorded on an absolute scale can be used to determine the thickness of on-axis crystals with a precision of ±1.6 nm. This method measures both the crystalline and the noncrystalline parts (surface amorphous layers) of the sample. However, it avoids the systematic error resulting from surface plasmon contributions to the inelastic mean-free-path thickness estimated by electron energy loss spectroscopy.