Circle and Sphere Formulas, Definitions, Example Calculation
Circle Formulas
Circle Diameter (D)
The diameter of a circle is the distance across the circle through its center, or twice the radius.
Formula: D = 2r
Example Calculation: If radius (r) = 5 units
D = 2 * 5 = 10 units
Circle Calculator
Circle Area (A)
The area of a circle is the total space enclosed by the circle's circumference.
Formula: A = πr2
Example Calculation: If radius (r) = 5 units
A = π * 52 = 25π square units
Circumference of a Circle (C)
The circumference of a circle is the distance around the circle's boundary.
Formula: C = 2πr
Example Calculation: If radius (r) = 7 units
C = 2π * 7 = 14π units
Arc Length (L)
The arc length of a circle is the distance along the portion of the circle's circumference.
Formula: L = (C / 360) * θ
Example Calculation: If circumference (C) = 10 units and central angle (θ) = 45 degrees
L = (10 / 360) * 45 = 1.25 units
Sector Area (A)
The sector area of a circle is the region enclosed by an arc and two radii.
Formula: A = (C / 360) * πr2
Example Calculation: If circumference (C) = 10 units and radius (r) = 3 units
A = (10 / 360) * π * 32 = 0.2618π square units
Sphere Formulas
Sphere Calculator
Surface Area of a Sphere (A)
The surface area of a sphere is the total area covered by the sphere's surface.
Formula: A = 4πr2
Example Calculation: If radius (r) = 3 units
A = 4π * 32 = 36π square units
Volume of a Sphere (V)
The volume of a sphere is the amount of space enclosed by the sphere's surface.
Formula: V = (4/3)πr3
Example Calculation: If radius (r) = 4 units
V = (4/3)π * 43 = (4/3)π * 64 = 256π cubic units
Surface Area of Hemisphere (A)
The surface area of a hemisphere is the total area of its curved surface.
Formula: A = 2πr2
Example Calculation: If radius (r) = 3 units
A = 2π * 32 = 18π square units
Volume of Hemisphere (V)
The volume of a hemisphere is half the volume of a sphere with the same radius.
Formula: V = (2/3)πr3
Example Calculation: If radius (r) = 4 units
V = (2/3)π * 43 = (2/3)π * 64 = 128π cubic units
Segment Volume (V)
The volume of a spherical segment is the volume of a sphere cut by a plane.
Formula: V = (1/6)πh(3a2 + h2)
Example Calculation: If height (h) = 6 units and radius of the base (a) = 5 units
V = (1/6)π * 6 * (3 * 52 + 62) = 210π cubic units