Species richness (S) increases with area (A) as shown in the well-known power function proposed by Arrhenius: S = cA(z). We show that the exponent of the species-area curves, z, was negatively correlated with aboveground annual production (biomass) but the coefficient of the curves, c, was positively correlated with production in two communities dominated by grasses and sedges in beaver meadows in northern Minnesota. The parameters of the species-area power function were not correlated with water table depth nor with soil nutrient availabilities. We then show that the often-reported unimodal relationship between richness and productivity can be derived from the negative correlation of z and the positive correlation of c with productivity. We also show that the productivity corresponding to maximum richness declines with increasing area sampled. All other correlations of c and z with productivity yield either monotonically increasing or decreasing richness with increasing productivity. The relationships between richness and productivity depend on the area censused and the correlations of the coefficient and exponent of the species-area curve with productivity. Interpretations of diversity-productivity relationships are sensitive to plot size and require specification of the species-area relationship for the community in question.