Increases in median ages, the most commonly used measure of population ageing, are rapid in today's wealthier countries, and population ageing is widely considered to be a significant challenge to the well-being of citizens there. Conventional measures of age count years since birth; however, as lives lengthen, we need to think of age also in terms of years left until death or in proportion to the expanding lifespan. Here we propose a new measure of ageing: the median age of the population standardized for expected remaining years of life. We show, using historical data and forecasts for Germany, Japan and the United States, that although these populations will be growing older, as measured by their median ages, they will probably experience periods in which they grow younger, as measured by their standardized median ages. Furthermore, we provide forecasts for these countries of the old-age dependency ratio rescaled for increases in life expectancy at birth. These ratios are forecasted to change much less than their unscaled counterparts, and also exhibit periods when the population is effectively growing younger.