We describe a method of morphometric characterisation of landform from DEMs. The method is implemented by first classifying every location into morphometric classes based on the mathematical shape of a locally fitted quadratic surface and its positional relationship with the analysis window. Single-scale fuzzy terrain indices of peakness, pitness, passness, ridgeness, and valleyness are then calculated based on the distance of the analysis location from the ideal cases. These can then be combined into multi-scale terrain indices to summarise terrain information across different operational scales. The algorithm has four characteristics: (1) the ideal cases of different geomorphometric features are simply and clearly defined; (2) the output is spatially continuous to reflect the inherent fuzziness of geomorphometric features; (3) the output is easily combined into a multi-scale index across a range of operational scales; and (4) the standard general morphometric parameters are quantified as the first and second order derivatives of the quadratic surface. An additional benefit of the quadratic surface is the derivation of the R2 goodness of fit statistic, which allows an assessment of both the reliability of the results and the complexity of the terrain. An application of the method using a test DEM indicates that the single- and multi-scale terrain indices perform well when characterising the different geomorphometric features.