Strength of schedule
The NCAA Division III playoff selection committee determines strength of schedule using opponents' winning percentage and opponents' opponents' winning percentage. A team's SOS is two-thirds opponents' winning percentage (OWP) and one-third opponents' opponents' winning percentage (OOWP).Those numbers follow, calculated by PrestoSports.
We've sorted these teams by their strength of schedule. This is only part of the process used to determine who will get selected to the NCAA playoffs.
Records and winning percentage are based on all games vs. full Division III opponents.
Only games which have been played so far are counted here.
OWP: Opponents' winning percentage. OOWP: Opponents' opponents' winning percentage. SOS: two-thirds OWP and one-third OOWP.These numbers are more of a guidepost for the committee. There is no established standard for what it takes to be chosen as an at-large team, and in fact, teams in conferences with 10 members will always have their SOS trend toward .500 because of the high number of conference games. However, it is still something that is used in the selection process, which is why we note it here.
| Team | D3 record |
D3 win % |
OWP (rank) | OOWP | NCAA SOS |
| 1 Carthage | 5-5 | .500 | .6556 (1) | .5251 | 0.612 |
| 2 St. John Fisher | 6-3 | .667 | .6282 (5) | .5658 | 0.607 |
| 3 Trine | 6-4 | .600 | .6364 (4) | .5377 | 0.603 |
| 4 UW-Eau Claire | 0-10 | .000 | .6471 (3) | .5109 | 0.602 |
| 5 Alfred | 7-3 | .700 | .6190 (6) | .5530 | 0.597 |
| 6 Morrisville State | 5-4 | .556 | .6026 (12) | .5663 | 0.591 |
| 7 North Central (Ill.) | 7-3 | .700 | .6111 (8) | .5487 | 0.590 |
| 8 Cortland | 8-2 | .800 | .6047 (11) | .5594 | 0.590 |
| 9 Southwestern | 1-7 | .125 | .6491 (2) | .4649 | 0.588 |
| 10 Adrian | 7-3 | .700 | .6180 (7) | .5255 | 0.587 |
| 11 North Park | 3-7 | .300 | .6067 (10) | .5232 | 0.579 |
| 12 Sul Ross State | 1-6 | .143 | .6078 (9) | .5056 | 0.574 |
| 13 UW-La Crosse | 3-7 | .300 | .6000 (13) | .5056 | 0.569 |
| 14 Howard Payne | 1-7 | .125 | .5965 (14) | .4964 | 0.563 |
| 15 Hartwick | 3-6 | .333 | .5641 (32) | .5560 | 0.561 |
| 16 Augustana | 4-6 | .400 | .5778 (20) | .5275 | 0.561 |
| 17 Albion | 9-1 | .900 | .5667 (28) | .5489 | 0.561 |
| 18 Bethel | 5-5 | .500 | .5730 (22) | .5280 | 0.558 |
| 19 Dubuque | 8-2 | .800 | .5795 (18) | .5041 | 0.554 |
| 20 Augsburg | 5-5 | .500 | .5730 (23) | .5171 | 0.554 |
| 21 Buena Vista | 0-9 | .000 | .5802 (17) | .5013 | 0.554 |
| 22 Chicago | 6-4 | .600 | .5682 (25) | .5222 | 0.553 |
| 23 Washington U. | 6-4 | .600 | .5682 (26) | .5222 | 0.553 |
| 24 Millsaps | 2-7 | .222 | .5696 (24) | .5166 | 0.552 |
| 25 Carroll | 6-4 | .600 | .5889 (16) | .4768 | 0.552 |
| 26 Utica | 4-6 | .400 | .5465 (46) | .5546 | 0.549 |
| 27 St. Olaf | 2-8 | .200 | .5682 (27) | .5110 | 0.549 |
| 28 Union | 0-10 | .000 | .5747 (21) | .4959 | 0.548 |
| 29 Chapman | 4-5 | .444 | .5890 (15) | .4668 | 0.548 |
| 30 Brockport | 4-5 | .444 | .5385 (56) | .5653 | 0.547 |
| 31 Randolph-Macon | 4-6 | .400 | .5647 (30) | .5115 | 0.547 |
| 32 Illinois Wesleyan | 7-3 | .700 | .5506 (42) | .5357 | 0.546 |
| 33 Endicott | 5-5 | .500 | .5795 (19) | .4763 | 0.545 |
| 34 Rowan | 5-4 | .556 | .5641 (31) | .5043 | 0.544 |
| 35 St. Lawrence | 8-2 | .800 | .5465 (45) | .5388 | 0.544 |
| 36 Buffalo State | 7-3 | .700 | .5294 (64) | .5699 | 0.543 |
| 37 Hampden-Sydney | 6-4 | .600 | .5632 (33) | .5000 | 0.542 |
| 38 Case Western Reserve | 7-3 | .700 | .5556 (38) | .5149 | 0.542 |
| 39 Kalamazoo | 3-7 | .300 | .5556 (39) | .5102 | 0.540 |
| 40 Hardin-Simmons | 7-1 | .875 | .5439 (50) | .5328 | 0.540 |
| 41 Salisbury | 7-2 | .778 | .5513 (41) | .5147 | 0.539 |
| 42 St. John's | 9-1 | .900 | .5341 (60) | .5480 | 0.539 |
| 43 Ithaca | 4-6 | .400 | .5233 (76) | .5695 | 0.539 |
| 44 UW-Stout | 3-7 | .300 | .5465 (47) | .5223 | 0.538 |
| 45 Bridgewater | 3-6 | .333 | .5570 (36) | .4985 | 0.537 |
| 46 Dickinson | 3-7 | .300 | .5506 (44) | .5074 | 0.536 |
| 47 Geneva | 2-8 | .200 | .5556 (40) | .4944 | 0.535 |
| 48 Hope | 2-8 | .200 | .5444 (49) | .5162 | 0.535 |
| 49 Averett | 2-7 | .222 | .5658 (29) | .4696 | 0.534 |
| 50 Pacific | 5-4 | .556 | .5405 (52) | .5197 | 0.534 |
| 51 Texas Lutheran | 7-2 | .778 | .5397 (55) | .5216 | 0.534 |
| 52 UW-Stevens Point | 5-5 | .500 | .5294 (66) | .5412 | 0.533 |
| 53 Illinois College | 5-5 | .500 | .5618 (34) | .4743 | 0.533 |
| 54 RPI | 8-2 | .800 | .5287 (68) | .5404 | 0.533 |
| 55 Birmingham-Southern | 5-5 | .500 | .5412 (51) | .5116 | 0.531 |
| 56 Coe | 4-6 | .400 | .5455 (48) | .5012 | 0.531 |
| 57 Sewanee | 1-9 | .100 | .5402 (54) | .5112 | 0.531 |
| 58 Worcester State | 4-6 | .400 | .5506 (43) | .4892 | 0.530 |
| 59 UW-Platteville | 8-2 | .800 | .5176 (87) | .5547 | 0.530 |
| 60 MIT | 2-8 | .200 | .5568 (37) | .4697 | 0.528 |
| 61 Hanover | 2-8 | .200 | .5581 (35) | .4642 | 0.527 |
| 62 Springfield | 4-6 | .400 | .5402 (53) | .5000 | 0.527 |
| 63 Gustavus Adolphus | 7-3 | .700 | .5227 (78) | .5337 | 0.526 |
| 64 George Fox | 3-6 | .333 | .5342 (59) | .5105 | 0.526 |
| 65 Framingham State | 9-1 | .900 | .5333 (61) | .5112 | 0.526 |
| 66 Berry | 7-3 | .700 | .5294 (65) | .5189 | 0.526 |
| 67 Ursinus | 2-7 | .222 | .5309 (63) | .5112 | 0.524 |
| 68 Lakeland | 8-2 | .800 | .5281 (69) | .5165 | 0.524 |
| 69 Hendrix | 7-2 | .778 | .5256 (75) | .5195 | 0.524 |
| 70 Puget Sound | 6-3 | .667 | .5342 (58) | .5008 | 0.523 |
| 71 Franklin and Marshall | 6-4 | .600 | .5281 (70) | .5102 | 0.522 |
| 72 Hamline | 4-6 | .400 | .5227 (79) | .5175 | 0.521 |
| 73 Montclair State | 4-6 | .400 | .5294 (67) | .5023 | 0.520 |
| 74 Merchant Marine | 3-6 | .333 | .5316 (62) | .4967 | 0.520 |
| 75 Alma | 5-5 | .500 | .5169 (92) | .5243 | 0.519 |
| 76 Johns Hopkins | 10-0 | 1.000 | .5169 (89) | .5177 | 0.517 |
| 77 Heidelberg | 5-5 | .500 | .5222 (80) | .5056 | 0.517 |
| 78 St. Norbert | 10-0 | 1.000 | .5169 (90) | .5114 | 0.515 |
| 79 Concordia-Moorhead | 6-3 | .667 | .4938 (128) | .5568 | 0.515 |
| 80 Kean | 7-3 | .700 | .5176 (88) | .5085 | 0.515 |
| 81 Susquehanna | 5-5 | .500 | .5169 (93) | .5102 | 0.515 |
| 82 East Texas Baptist | 5-2 | .714 | .4898 (132) | .5641 | 0.515 |
| 83 Pacific Lutheran | 2-7 | .222 | .5270 (73) | .4894 | 0.514 |
| 84 Willamette | 2-7 | .222 | .5270 (74) | .4894 | 0.514 |
| 85 King's | 3-7 | .300 | .5222 (82) | .4961 | 0.513 |
| 86 Gettysburg | 7-3 | .700 | .5114 (100) | .5172 | 0.513 |
| 87 Rochester | 4-4 | .500 | .5070 (109) | .5255 | 0.513 |
| 88 Wilkes | 2-8 | .200 | .5222 (84) | .4950 | 0.513 |
| 89 Capital | 3-7 | .300 | .5222 (83) | .4922 | 0.512 |
| 90 Carleton | 1-9 | .100 | .5169 (95) | .5013 | 0.512 |
| 91 Albright | 9-1 | .900 | .5169 (91) | .5006 | 0.511 |
| 92 Defiance | 2-8 | .200 | .5233 (77) | .4866 | 0.511 |
| 93 Ohio Wesleyan | 5-5 | .500 | .5281 (71) | .4754 | 0.511 |
| 94 Christopher Newport | 4-6 | .400 | .5059 (111) | .5170 | 0.510 |
| 95 Wheaton (Ill.) | 10-0 | 1.000 | .4778 (151) | .5726 | 0.509 |
| 96 Hobart | 7-3 | .700 | .4943 (125) | .5384 | 0.509 |
| 97 Moravian | 8-2 | .800 | .5056 (112) | .5147 | 0.509 |
| 98 UW-Whitewater | 7-1 | .875 | .4928 (131) | .5406 | 0.509 |
| 99 Whittier | 0-9 | .000 | .5278 (72) | .4704 | 0.509 |
| 100 WPI | 7-3 | .700 | .4943 (126) | .5372 | 0.509 |
| 101 Norwich | 6-4 | .600 | .5349 (57) | .4550 | 0.508 |
| 102 McDaniel | 0-10 | .000 | .5056 (113) | .5120 | 0.508 |
| 103 Wooster | 2-8 | .200 | .5222 (85) | .4777 | 0.507 |
| 104 Central | 6-4 | .600 | .5116 (99) | .4987 | 0.507 |
| 105 Otterbein | 4-6 | .400 | .5111 (105) | .4994 | 0.507 |
| 106 Hiram | 4-6 | .400 | .5222 (81) | .4766 | 0.507 |
| 107 Bethany | 5-5 | .500 | .5111 (104) | .4978 | 0.507 |
| 108 St. Vincent | 4-6 | .400 | .5111 (106) | .4975 | 0.507 |
| 109 Carnegie Mellon | 7-3 | .700 | .5000 (115) | .5190 | 0.506 |
| 110 Bridgewater State | 7-3 | .700 | .5111 (103) | .4961 | 0.506 |
| 111 Fitchburg State | 8-2 | .800 | .5111 (102) | .4938 | 0.505 |
| 112 Marietta | 2-8 | .200 | .5111 (107) | .4922 | 0.505 |
| 113 Redlands | 4-5 | .444 | .5139 (97) | .4836 | 0.504 |
| 114 Aurora | 3-7 | .300 | .5169 (94) | .4767 | 0.503 |
| 115 Muhlenberg | 8-2 | .800 | .4944 (122) | .5159 | 0.502 |
| 116 Simpson | 4-6 | .400 | .5000 (118) | .5017 | 0.501 |
| 117 Cornell | 4-5 | .444 | .5185 (86) | .4642 | 0.500 |
| 118 Crown | 3-6 | .333 | .5139 (98) | .4733 | 0.500 |
| 119 Ripon | 7-3 | .700 | .5114 (101) | .4780 | 0.500 |
| 120 Lebanon Valley | 5-5 | .500 | .5000 (117) | .5006 | 0.500 |
| 121 Mary Hardin-Baylor | 8-1 | .889 | .4697 (166) | .5604 | 0.500 |
| 122 St. Scholastica | 8-1 | .889 | .5139 (96) | .4716 | 0.500 |
| 123 William Paterson | 1-8 | .111 | .4935 (129) | .5115 | 0.499 |
| 124 Westfield State | 2-8 | .200 | .5111 (108) | .4753 | 0.499 |
| 125 La Verne | 8-1 | .889 | .5068 (110) | .4838 | 0.499 |
| 126 Olivet | 9-1 | .900 | .4667 (168) | .5622 | 0.499 |
| 127 Widener | 6-4 | .600 | .4944 (124) | .5040 | 0.498 |
| 128 Baldwin Wallace | 7-3 | .700 | .5000 (116) | .4922 | 0.497 |
| 129 Wilmington | 1-9 | .100 | .5000 (121) | .4922 | 0.497 |
| 130 Catholic | 3-7 | .300 | .4941 (127) | .5013 | 0.496 |
| 131 UW-Oshkosh | 9-0 | 1.000 | .4675 (167) | .5530 | 0.496 |
| 132 Wabash | 10-0 | 1.000 | .5000 (114) | .4872 | 0.496 |
| 133 Linfield | 9-0 | 1.000 | .4795 (150) | .5255 | 0.495 |
| 134 Stevenson | 8-2 | .800 | .4944 (123) | .4955 | 0.495 |
| 135 Lewis and Clark | 0-9 | .000 | .4932 (130) | .4940 | 0.493 |
| 136 Washington and Jefferson | 8-2 | .800 | .4889 (134) | .5025 | 0.493 |
| 137 Lycoming | 4-6 | .400 | .4889 (135) | .5006 | 0.493 |
| 138 Mount Union | 10-0 | 1.000 | .4889 (133) | .5000 | 0.493 |
| 139 Washington and Lee | 9-0 | 1.000 | .4744 (158) | .5291 | 0.493 |
| 140 Lake Forest | 4-6 | .400 | .5000 (119) | .4776 | 0.493 |
| 141 Whitworth | 9-1 | .900 | .4750 (157) | .5260 | 0.492 |
| 142 Elmhurst | 4-6 | .400 | .4667 (171) | .5425 | 0.492 |
| 143 Guilford | 9-1 | .900 | .4824 (146) | .5103 | 0.492 |
| 144 LaGrange | 2-6 | .250 | .5000 (120) | .4722 | 0.491 |
| 145 Benedictine | 7-3 | .700 | .4831 (141) | .5034 | 0.490 |
| 146 Wartburg | 9-1 | .900 | .4719 (163) | .5258 | 0.490 |
| 147 UW-River Falls | 4-5 | .444 | .4605 (174) | .5481 | 0.490 |
| 148 Thiel | 2-8 | .200 | .4889 (136) | .4901 | 0.489 |
| 149 Wisconsin Lutheran | 5-4 | .556 | .4815 (147) | .5013 | 0.488 |
| 150 Franklin | 8-1 | .889 | .4872 (138) | .4865 | 0.487 |
| 151 FDU-Florham | 3-7 | .300 | .4831 (143) | .4938 | 0.487 |
| 152 Ohio Northern | 8-2 | .800 | .4778 (152) | .5045 | 0.487 |
| 153 Misericordia | 1-9 | .100 | .4778 (156) | .5045 | 0.487 |
| 154 Delaware Valley | 8-2 | .800 | .4778 (153) | .5028 | 0.486 |
| 155 Plymouth State | 2-8 | .200 | .4831 (145) | .4912 | 0.486 |
| 156 John Carroll | 8-2 | .800 | .4778 (154) | .5011 | 0.486 |
| 157 Juniata | 3-7 | .300 | .4719 (164) | .5125 | 0.485 |
| 158 Westminster (Pa.) | 8-2 | .800 | .4778 (155) | .4988 | 0.485 |
| 159 Massachusetts Maritime | 4-6 | .400 | .4831 (142) | .4869 | 0.484 |
| 160 Oberlin | 3-7 | .300 | .4831 (144) | .4859 | 0.484 |
| 161 Monmouth | 8-2 | .800 | .4831 (140) | .4852 | 0.484 |
| 162 Manchester | 5-4 | .556 | .4744 (159) | .4992 | 0.483 |
| 163 Millikin | 2-8 | .200 | .4494 (185) | .5484 | 0.482 |
| 164 Centre | 8-2 | .800 | .4545 (181) | .5366 | 0.482 |
| 165 Curry | 4-6 | .400 | .4886 (137) | .4681 | 0.482 |
| 166 Southern Virginia | 0-9 | .000 | .4744 (160) | .4965 | 0.482 |
| 167 Methodist | 3-6 | .333 | .4800 (149) | .4814 | 0.480 |
| 168 Westminster (Mo.) | 5-3 | .625 | .4844 (139) | .4691 | 0.479 |
| 169 Shenandoah | 4-6 | .400 | .4706 (165) | .4959 | 0.479 |
| 170 Salve Regina | 7-2 | .778 | .4810 (148) | .4747 | 0.479 |
| 171 Muskingum | 1-9 | .100 | .4667 (172) | .4956 | 0.476 |
| 172 Grove City | 0-10 | .000 | .4667 (173) | .4944 | 0.476 |
| 173 Maryville (Tenn.) | 7-2 | .778 | .4730 (161) | .4772 | 0.474 |
| 174 Minnesota-Morris | 3-6 | .333 | .4722 (162) | .4785 | 0.474 |
| 175 Wittenberg | 8-2 | .800 | .4667 (169) | .4866 | 0.473 |
| 176 Mass-Dartmouth | 4-6 | .400 | .4556 (179) | .5056 | 0.472 |
| 177 Loras | 4-6 | .400 | .4494 (183) | .5177 | 0.472 |
| 178 Austin | 4-4 | .500 | .4407 (194) | .5327 | 0.471 |
| 179 N.C. Wesleyan | 5-4 | .556 | .4667 (170) | .4729 | 0.469 |
| 180 Rhodes | 4-6 | .400 | .4419 (193) | .5187 | 0.468 |
| 181 Denison | 7-3 | .700 | .4556 (178) | .4866 | 0.466 |
| 182 Concordia (Wis.) | 3-7 | .300 | .4494 (184) | .4983 | 0.466 |
| 183 Allegheny | 0-10 | .000 | .4556 (180) | .4844 | 0.465 |
| 184 Anderson | 2-6 | .250 | .4571 (177) | .4803 | 0.465 |
| 185 Waynesburg | 3-7 | .300 | .4444 (187) | .5025 | 0.464 |
| 186 Ferrum | 2-8 | .200 | .4512 (182) | .4834 | 0.462 |
| 187 Rose-Hulman | 8-2 | .800 | .4419 (191) | .5013 | 0.462 |
| 188 TCNJ | 4-5 | .444 | .4359 (195) | .5095 | 0.460 |
| 189 Kenyon | 2-8 | .200 | .4444 (190) | .4905 | 0.460 |
| 190 Northwestern (Minn.) | 7-2 | .778 | .4444 (186) | .4888 | 0.459 |
| 191 Husson | 6-2 | .750 | .4571 (176) | .4606 | 0.458 |
| 192 Trinity (Texas) | 8-2 | .800 | .4118 (204) | .5493 | 0.458 |
| 193 Bluffton | 6-4 | .600 | .4419 (192) | .4873 | 0.457 |
| 194 Western Connecticut | 5-5 | .500 | .4270 (201) | .5170 | 0.457 |
| 195 Eureka | 4-5 | .444 | .4583 (175) | .4509 | 0.456 |
| 196 Mount St. Joseph | 7-3 | .700 | .4353 (196) | .4970 | 0.456 |
| 197 Greenville | 2-7 | .222 | .4444 (189) | .4708 | 0.453 |
| 198 Claremont-Mudd-Scripps | 7-2 | .778 | .4306 (199) | .4957 | 0.452 |
| 199 DePauw | 8-2 | .800 | .4333 (198) | .4864 | 0.451 |
| 200 Martin Luther | 2-7 | .222 | .4348 (197) | .4758 | 0.448 |
| 201 Beloit | 3-7 | .300 | .4444 (188) | .4380 | 0.442 |
| 202 Luther | 4-6 | .400 | .4045 (205) | .5132 | 0.441 |
| 203 Greensboro | 3-7 | .300 | .4198 (203) | .4777 | 0.439 |
| 204 Nichols | 1-9 | .100 | .4205 (202) | .4712 | 0.437 |
| 205 Cal Lutheran | 4-5 | .444 | .4028 (208) | .5026 | 0.436 |
| 206 Castleton | 6-3 | .667 | .4286 (200) | .4476 | 0.435 |
| 207 Huntingdon | 8-1 | .889 | .4028 (207) | .4870 | 0.431 |
| 208 Rockford | 3-7 | .300 | .4045 (206) | .4754 | 0.428 |
| 209 Pomona-Pitzer | 2-7 | .222 | .3973 (210) | .4874 | 0.427 |
| 210 Coast Guard | 5-5 | .500 | .3908 (213) | .4785 | 0.420 |
| 211 Western New England | 10-0 | 1.000 | .3750 (215) | .5051 | 0.418 |
| 212 Macalester | 4-6 | .400 | .3933 (211) | .4629 | 0.416 |
| 213 SUNY-Maritime | 5-5 | .500 | .3929 (212) | .4602 | 0.415 |
| 214 Gallaudet | 0-9 | .000 | .3974 (209) | .4411 | 0.412 |
| 215 Concordia-Chicago | 2-8 | .200 | .3721 (216) | .4868 | 0.410 |
| 216 Anna Maria | 1-9 | .100 | .3837 (214) | .4392 | 0.402 |
| 217 Knox | 3-7 | .300 | .3295 (219) | .4552 | 0.371 |
| 218 Lawrence | 1-9 | .100 | .3412 (217) | .4291 | 0.370 |
| 219 Grinnell | 2-8 | .200 | .3333 (218) | .4318 | 0.366 |
| 220 Belhaven | 0-0 | .000 | .0000 (220) | .0000 | 0.000 |
| 221 Alfred State | 0-0 | .000 | .0000 (221) | .0000 | 0.000 |
| 222 Alvernia | 0-0 | .000 | .0000 (222) | .0000 | 0.000 |
| 223 Amherst | 0-0 | .000 | .0000 (223) | .0000 | 0.000 |
| 224 Bates | 0-0 | .000 | .0000 (224) | .0000 | 0.000 |
| 225 Bowdoin | 0-0 | .000 | .0000 (225) | .0000 | 0.000 |
| 226 Brevard | 0-0 | .000 | .0000 (226) | .0000 | 0.000 |
| 227 Colby | 0-0 | .000 | .0000 (227) | .0000 | 0.000 |
| 228 Dean | 0-0 | .000 | .0000 (228) | .0000 | 0.000 |
| 229 Eastern | 0-0 | .000 | .0000 (229) | .0000 | 0.000 |
| 230 Hamilton | 0-0 | .000 | .0000 (230) | .0000 | 0.000 |
| 231 Hilbert | 0-0 | .000 | .0000 (231) | .0000 | 0.000 |
| 232 Keystone | 0-0 | .000 | .0000 (232) | .0000 | 0.000 |
| 233 Lyon | 0-0 | .000 | .0000 (233) | .0000 | 0.000 |
| 234 McMurry | 0-0 | .000 | .0000 (234) | .0000 | 0.000 |
| 235 Middlebury | 0-0 | .000 | .0000 (235) | .0000 | 0.000 |
| 236 Nebraska Wesleyan | 0-0 | .000 | .0000 (236) | .0000 | 0.000 |
| 237 Trinity (Conn.) | 0-0 | .000 | .0000 (237) | .0000 | 0.000 |
| 238 Tufts | 0-0 | .000 | .0000 (238) | .0000 | 0.000 |
| 239 University of New England | 0-0 | .000 | .0000 (239) | .0000 | 0.000 |
| 240 Wesleyan | 0-0 | .000 | .0000 (240) | .0000 | 0.000 |
| 241 Williams | 0-0 | .000 | .0000 (241) | .0000 | 0.000 |
Note: Because the NESCAC does not permit teams to participate in the football playoffs, we do not include their games in these calculations.