Field experiments were conducted over 6 years at 33 sites throughout the main potato growing areas of South Australia to examine the effects of applied phosphorus (banded at planting), at rates up to 300 kg/ha, on the total yield and size distribution of tubers and to calibrate, in terms of total yield, 8 soil phosphorus extraction procedures (Colwell, Olsen, Bray 1, Bray 2, Mehlich no. 1, lactate, fluoride and total). Phosphorus application significantly (P< 0.05) increased total tuber yield at 16 sites. The mean relative yield for these responsive sites was 69.7% (range 37.4- 91.2%) compared with 97.5% (range 88.0-102.5%) for the non-responsive sites. Tuber size distributions were determined at 13 sites and, depending on site and cultivar, the yield of 80-450 g tubers for the highest yielding treatments represented from 64.2 to 93.7% of the total yield of tubers for those treatments. For each soil phosphorus extraction procedure the Mitscherlich and Smith-Dolby bent-hyperbola models and the Cate-Nelson separation were used to investigate the correlations between yield response and extractable and total phosphorus in the surface (0- 15 cm) soil samples and to calculate critical values. For loamy sand to sandy clay loam surface soils, the order of efficacy of soil tests based on the coefficients of determination (r2) calculated using the Mitscherlich and Smith-Dolby bent-hyperbola models was Bray 1 and Bray 2 > Olsen > lactate, Mehlich no. 1, fluoride and Colwell. The coefficients of determination ranged from 0.88 (Bray 1) to 0.64 (Colwell) for the Smith-Dolby bent-hyperbola model and from 0.86 (Bray 1) to 0.65 (fluoride) for the Mitscherlich model. Yield response was not correlated with total phosphorus concentration. Using the Smith-Dolby benthyperbola model the critical phosphorus values (s.e. in parentheses) were: 25.8(1.8), 40.9(2.6), l6.8(1.4), 13.9(1.0), 38.4(3.1), 24.2(2.9) and 35.1(3.0) mg/kg for the Bray 1, Bray 2, Olsen, lactate, fluoride, Mehlich no. 1 and Colwell methods, respectively. Yield deficits >20% were associated with phosphorus soil test values t 2 0 mg/kg (Bray 1 method) and P-sorption values >240 mg/kg. Rates of 48-73 kg P/ha banded at planting were required for 95% of maximum yield at the deficient sites. For acid coarse-grain sand surface soils, significant Cate-Nelson separations were obtained for the Colwell, Bray 1, Bray 2, Mehlich no. 1 and fluoride methods, the critical phosphorus values were 7.5, 7.0, 5.5, 6.5 and 8.0 mg/kg, respectively. The order of efficacy of the soil tests was Bray 2 (r2 = 0.66) >Bray 1, Colwell, Mehlich no. 1 and fluoride (all r2 = 0.55). Yield deficits >10% were associated with soil test values t 6 mg/kg (Bray 1 method). Rates of 27-59 kg P/ha banded at planting were required for 95% of maximum yield at the deficient sites. Data are presented which suggest that for similar soil types and extraction procedures critical values or critical concentration ranges may apply across a range of growing conditions, planting times and cultivars.