Between the 2010 and 2015 seasons, Cam Newton had the most rushing yards by a quarterback, with 3,207 yards.

most rushing yards by qb 2010 to 2015
NewtonWilsonVickKaepernickRodgersSmithGriffinFitzpatrickLuckCutlerTebowTannehillFreemanDaltonBortlesTaylorLockerPonderSmithPryorRyanStafford3.2k2.4k2.2k1.8k1.6k1.6k1.5k1.4k1.1k1.0k989901785766729704644639638627610536
NAMEGPRUSH YDSATTRUSH AVGRUSH YDS/GRUSH TDREC YDSRECTRGREC AVGREC YDS/GREC TD
Cam NewtonCam Newton783,2075995.441.143331133.00.40
Russell WilsonRussell Wilson642,4304115.938.012171117.00.30
Michael VickMichael Vick572,1553206.737.813-2000.00
Colin KaepernickColin Kaepernick571,8323066.032.1110000.00
Aaron RodgersAaron Rodgers871,6053095.218.412-111-1.00.00
Alex SmithAlex Smith831,5543105.018.76-411-4.00.00
Robert Griffin IIIRobert Griffin III371,4802446.140.080000.00
Ryan FitzpatrickRyan Fitzpatrick841,3602974.616.280110.00.00
Andrew LuckAndrew Luck551,1012225.020.0120000.00
Jay CutlerJay Cutler811,0302094.912.750000.00
Tim TebowTim Tebow359891975.028.3120010.00
Ryan TannehillRyan Tannehill649011775.114.155222.50.10
Josh FreemanJosh Freeman527851754.515.14-400-0.10
Andy DaltonAndy Dalton777662622.99.914181218.00.21
Blake BortlesBlake Bortles307291086.824.320000.00
Tyrod TaylorTyrod Taylor287041315.425.1510225.00.40
Jake LockerJake Locker30644956.821.550000.00
Christian PonderChristian Ponder386391265.116.87-1511-15.0-0.40
Geno SmithGeno Smith316381334.820.67131213.00.40
Terrelle PryorTerrelle Pryor15627936.741.83221122.01.50
Matt RyanMatt Ryan966101993.16.430000.00
Matthew StaffordMatthew Stafford835361852.96.510-322-1.50.00
Matt CasselMatt Cassel545221274.19.72-411-4.0-0.10
Ben RoethlisbergerBen Roethlisberger844931663.05.93-4000.00
Colt McCoyColt McCoy354201183.612.028224.00.20
StatMuse has season-level data for rushing yards going back to the 1932 season.

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