Polar Function Explorer

Enter any r = f(θ), or pick a preset — lemniscates (r² = f(θ)), roses, spirals, conics & more. Drag the dot, scrub the Cartesian wave, or press play.

✦ AI Assistant — describe a curve in plain language

r =

θ 0

sweep

drag the dot · polar (r, θ)

drag to scrub · r vs θ

3.00

plotted at

max |r|

r is positive — point plots straight along θ.

θ	r	plotted at	sign

Single HTML file · no external libraries · works offline.
Syntax: use theta as the variable · functions: sin cos tan sec csc cot sqrt abs exp ln log · constant pi · ^ for powers · explicit * for multiply.
Lemniscates: r² = f(θ) is entered as r = sqrt(f(theta)). The curve is undefined (gap) where f(θ) < 0, but the full two-loop figure appears within a single 2π sweep because the positive branch plots into both lobes via r>0 and the 180°-opposite angles.
Sweep: lemniscates / roses / cardioids need 2π; spirals 4π–6π; butterfly 12π. The preset automatically sets the correct range.