Observations from the 2012 transit of Venus are used to derive empirical formulae for long- and short-range scattered light at locations on the solar disk observed by the Hinode Extreme ultraviolet Imaging Spectrometer (EIS) and the Solar Dynamics Observatory Atmospheric Imaging Assembly (AIA) instruments. Long-range scattered light comes from the entire solar disk, while short-range scattered light is considered to come from a region within 50″ of the region of interest. The formulae were derived from the Fe xii 195.12 Å emission line observed by EIS and the AIA 193 Å channel. A study of the weaker Fe xiv 274.20 Å line during the transit and a comparison of scattering in the AIA 193 Å and 304 Å channels suggests the EIS scattering formula applies to other emission lines in the EIS wavebands. Both formulae should be valid in regions of fairly uniform emission such as coronal holes and quiet Sun, but may be less accurate for faint areas close (around 100″) to bright active regions. The formula for EIS is used to estimate the scattered light component of Fe xii λ195.12 for seven on-disk coronal holes observed between 2010 and 2018. Scattered light contributions of 56%–100% are found, suggesting that these features are dominated by scattered light, consistent with earlier work of Wendeln & Landi. Emission lines from the S x and Si x ions—formed at the same temperature as Fe xii and often used to derive the first ionization potential bias from EIS data—are also expected to be dominated by scattered light in coronal holes.