Circles — Area and Circumference
Grade 4The core circle formulas
Circumference = 2πr = πd
Area = πr²
r is the radius, d is the diameter. If you are given the diameter, halve it to get the radius before using the area formula.
Circumference involves the radius once (linear), area involves it squared. Mixing them up is the most common circle mistake — check your units (cm vs cm²) to catch it.
Arc length and sector area
An arc is a fraction of the circumference. A sector is the pie-slice area. Both use the angle as a fraction of 360°:
Arc length = (θ/360) × 2πr
Sector area = (θ/360) × πr²
where θ is the angle of the sector in degrees.
Worked example
EXAMPLE
A sector has radius 6 cm and angle 120°. Find the arc length and area. Give answers in terms of π.
Arc length = (120/360) × 2π × 6 = (1/3) × 12π = 4π cm. Area = (120/360) × π × 6² = (1/3) × 36π = 12π cm²; arc length = 4π cm.
