Circle Formula.xls

Formulae for circle, arc, segment and sector: Area and dimensions.

Here are the formulae for the area and dimensions of a circle, arc, segment, and sector:

1. Circle:

• Area (A): A = π * r^2
• Circumference (C): C = 2 * π * r

Where: r = radius of the circle

2. Arc:

• Length (L): L = θ * r
• Area (A): A = (θ * r^2) / 2

Where: r = radius of the circle θ = angle of the arc in radians

3. Segment:

• Area (A_segment): A_segment = A_sector - A_triangle

Where: A_sector = (θ * r^2) / 2 (area of the sector) A_triangle = (1/2) * c * h (area of the triangle formed by the chord and the two radii) θ = angle of the arc in radians c = chord length of the segment h = height of the segment

4. Sector:

• Area (A): A = (θ * r^2) / 2
• Perimeter (P): P = r + r + L (two radii and the arc length)

Where: r = radius of the circle θ = angle of the arc in radians L = θ * r (arc length)

These formulae can be used to calculate the area and dimensions of circles, arcs, segments, and sectors. Note that for arc length and sector area calculations, the angle must be in radians. To convert from degrees to radians, use the following formula:

radians = (degrees * π) / 180