The outputs of mathematical models are often measurements on scales which may not be properly understood by some users – this includes both lay people and specialists in other areas. This may lead to these outputs, and the underlying models, being ignored, or misunderstood, or used or interpreted in ways that misrepresent the assumptions in the model. The practical consequences of these problems range from the enormous amount of time and energy devoted to trying to educate users, to the consequences of the misinterpretation of some financial valuation models which contributed to the recent financial crash. This paper analyses some examples of these problems with short case studies of p values in statistics, financial valuation models, university league tables and sigma measures, suggests that it is often possible to redesign measurements to make them easier to interpret, and proposes some principles for doing this. In the long term, the redesign of measurements from the perspective of potential users is likely to be an important facilitator of the growth and use of knowledge. However, in the short term there are powerful inhibiting factors.