The Planimeter

Pick a shape and press Trace — or drag the orange tracer around the figure yourself.

wheel roll ΔW 0.000 in

arm L 2.50 in

measured area 0.000 in²

true area — in²

rel. error —

A real polar (Amsler) planimeter, not a picture of one. A pole is pinned off the figure; a pole-arm reaches an elbow; a tracer-arm of length L carries a measuring wheel whose axis lies along the arm — so it rolls only on motion perpendicular to the arm. Trace any closed curve and the net wheel roll ΔW obeys Green's theorem: Area = L·ΔW. The reading is verified against the shoelace formula & closed forms — two different methods that must agree.

Figure

Tracer-arm length L 2.50 in

Figure size 1.30 in

Pole angle 155°

Pole distance 4.20 in

Show wheel-axis & roll component

Skin

Trace drives the tracer auto-magically around the boundary; watch the linkage articulate, the wheel spin, and the area climb to the true value. Or drag the orange tracer by hand: close the loop and the running area is what the wheel read. The wheel turns one way on the way out, the other on the way back — only the net roll survives, and that net roll times L is the enclosed area.