Insertable planar gradient coils offer the potential for significant performance increases in magnetic resonance imaging through higher gradient strength and shorter rise times. Using variational methods to minimize inductance, and thereby to optimize switching speeds, we have analyzed and constructed a biplanar y‐gradient coil for insertion into a solenoidal magnet system where z is the magnet axis. We have also analyzed biplanar x‐gradient and z‐gradient coil designs using the same methods. These biplanar coils offer an advantage over a cylindrical coil of comparable diameter in that they achieve high gradient strengths with relatively short rise times while maintaining patient access. Although the requirement that the currents for the x gradient lie in the same plane as for the y and z gradients increases the stored energy by a factor of 3 with respect to the other two gradients, this stored energy is still smaller by a factor of 2 than that of a comparably constrained x‐gradient cylindrical coil. The biplanar coil design offers improved linearity over its single planar coil alternative. The particular designs we have investigated are generally limited to small‐volume imaging.