A planimeter includes a movable housing in which are mounted orthogonally aimed x- and y-position sensors. Each position sensor comprises a piezoelectric ultrasound transmitter and receiver for sending ultrasound to a reflector disposed on a drawing and sensing resultant echoes. Circuitry in the housing computes from the sensor outputs the housing's position for each of a sequence of locations on a drawing at which a user positions the housing, and from those it computes scaled distances between those positions as well as quantities that can be derived from those distances. The transmitter's and receiver's respective positions with respect to positioning crosshairs are such as to suppress the results of orientation errors. The planimeter's handle is angled at 45.degree. to the directions in which the sensors are aimed so that it lends itself to both right- and left-handed operation.