The optimal dimensions of thin coil systems of three and four square coils for producing uniform magnetic fields are calculated. We find that for three square coils, of sidedand separationsbetween the outer coils, the most uniform field distribution occurs withs/d=0.821 116 and withI′/I=0.512 797.I′/Iis the ratio of the currents in the center coil to that of the outer coils. With four square coils, the best uniformity is obtained whena/d=0.128 106 andb/d=0.505 492, whereais the distance from the center to the inner coils andbis the distance from the center to the outer coils. The ratio of the current in the inner pair of coils to that in the outer pair must beI′/I=0.423 514. We compare the uniformity of the field produced by these coil systems with each other and with Rubens’ five‐coil system, both on and off axis. It is shown that the optimal four‐coil design is superior to the three‐ and five‐coil systems. The sensitivity of the uniformity to the precision of construction is discussed. Dimensions of regions around the center of the coil systems, uniform to 1 part in 106to 1 part in 102, are given.