Geometry
Circles
Circumference and the areas of circles, sectors and annuli.
Geometry
Area of a circle
S = πr²→GeometryCircumference
L = 2πr→GeometryCircle arc length
l = 2πr × φ / 360°→GeometryCircle sector area
S = πr² × φ / 360°→GeometryAnnulus area
S = π(R² − r²)→GeometryAll circle properties from radius
d=2r; L=2πr; S=πr²→GeometryInscribed angle from central angle
α = φ/2→GeometryTangent–chord angle
α = φ/2→GeometryAngle inside circle from arcs
α = (φ₁+φ₂)/2→GeometryAngle outside circle from arcs
α = (φ₁−φ₂)/2→GeometryChord from radius and center distance
c = 2√(r²−d²)→GeometryTangent length from a point
t = √(OP²−r²)→GeometryTangent–secant theorem
t = √(ab)→GeometryIntersecting chords theorem
m = pq/n→GeometryPoint-to-center distance from tangent
OP = √(t²+r²)→GeometryEqual tangents from one point
PA = PB→GeometryAngle between two tangents
α = 180°−φ→GeometryTangent and secant from one point
PT = √(PA·PB)→GeometryTwo secants from one point
PA = PC·PD/PB→GeometryCentral angle from arc measure
α = φ→GeometryRelative position of two circles
Relative position of two circles: calculated from the entered values→GeometryExternal tangency of two circles
d = R+r→GeometryInternal tangency of two circles
d = |R−r|→GeometryCommon chord of two circles
c = 2√(R²−a²)→GeometryOverlap area of two circles
Overlap area of two circles: calculated from the entered values→GeometryEllipse area
S = πab→GeometryEllipse perimeter by Ramanujan approximation
P≈π[3(a+b)−√((3a+b)(a+3b))]→GeometryEllipse eccentricity
e = √(1−b²/a²)→GeometryAll ellipse properties from semi-axes
All ellipse properties from semi-axes: calculated from the entered values→