Techniques and tools for high accuracy position calculation for picture resizing in applications such as spatially-scalable video coding and decoding are described. In one aspect, resampling of a video picture is performed according to a resampling scale factor. The resampling comprises computation of a sample value at a position i, j in a resampled array. The computation includes computing a derived horizontal or vertical sub-sample position x or y in a manner that involves approximating a value in part by multiplying a 2n value by an inverse (approximate or exact) of the upsampling scale factor. The approximating can be a rounding or some other kind of approximating, such as a ceiling or floor function that approximates to a nearby integer. The sample value is interpolated using a filter.