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• Yield capacity describing forest site productivity was expressed through site index. • Observations from permanent plots in long-term experiments give valid reference estimates of total volume production. • Variations in volume yield levels are explained in a larger extent by basal area levels. • The yield capacity functions can be used to compare tree species' production under similar management regimes. • The functions offer far-reaching support for assessing climate change mitigation potential of boreal forests in northern Europe. Information on forest site productivity is a key component to assess the carbon sequestration potential of boreal forests. While site index (SI) is commonly used to indicate forest site productivity, expressions of SI in the form of yield capacity (potential maximum mean annual volume increment) is desirable since volume yield is central to the economic and ecological analyses of a given species and site. This paper assessed the functional relationship between SI and yield capacity on the basis of yield plot data from long-term experiments measured over several decades for Norway spruce (Picea abies), Scots pine (Pinus sylvestris), Lodgepole pine (Pinus contorta) and Larch (Larix decidua and Larix sibirica) in Sweden. Component models of total basal area and volume yield were also developed. SI was determined by existing height development functions using top height and age, whereas functions for stand-level (m2 ha−1) basal area development were constructed based on age, SI and initial stand density using difference equations and nonlinear mixed-effects models. The relation between volume yield (m3 ha−1) and top height was adjusted with total basal area production through nonlinear mixed-effects models. Species-specific parametric regression models were used to construct functional relationships between SI and yield capacity. The root mean square errors of the species-specific models ranged from 2 to 6% and 10–18% of the average values for the basal area and volume equations, respectively. For the yield capacity functions, the explained variations (R2) were within 80–96%. We compared our yield capacity functions to earlier functions of the species and significant differences were observed in both lower and higher SI classes, especially, for Scots pine and Norway spruce. The new functions give better prediction of yield capacity in current growing conditions; hence, they could later be used for comparing tree species' production under similar site and management regimes in Sweden. [ABSTRACT FROM AUTHOR]