Circle Calculator (Advanced) Formula

Understand the math behind the circle calculator (advanced). Each variable explained with a worked example.

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Formulas Used

Area

area = pi * pow(r, 2)

Circumference

circumference = 2 * pi * r

Diameter

diameter = 2 * r

Sector Area

sector_area = pi * pow(r, 2) * angle_deg / 360

Arc Length

arc_length = 2 * pi * r * angle_deg / 360

Variables

VariableDescriptionDefault
rRadius5
angle_degSector Angle (degrees)(deg)90

How It Works

Circle Calculations

Formulas

  • Area = pi × r²
  • Circumference = 2 × pi × r
  • Sector Area = pi × r² × (angle / 360)
  • Arc Length = 2 × pi × r × (angle / 360)

    • A sector is a "pie slice" of the circle defined by a central angle.

    Worked Example

    A circle with radius 5, find area and a 90-degree sector.

    r = 5angle_deg = 90
    1. 01Area = pi × 25 ≈ 78.5398
    2. 02Circumference = 2 × pi × 5 ≈ 31.4159
    3. 03Sector area = 78.5398 × 90/360 ≈ 19.6350
    4. 04Arc length = 31.4159 × 90/360 ≈ 7.8540

    Frequently Asked Questions

    What is a sector?

    A sector is the region between two radii and an arc. Think of it as a "pie slice" of the circle.

    How do I find the area if I know the diameter?

    Divide the diameter by 2 to get the radius, then use A = pi × r². Alternatively, A = pi × d²/4.

    What is the relationship between arc length and sector area?

    Both are proportional to the central angle. Sector area = (1/2) × r × arc length.

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