Use this calculator to easily calculate the area of a sector, given its radius and central angle in any metric: mm, cm, meters, km, inches, feet, yards, miles, etc. Enter radius and angle, and the tool calculates the sector’s area through ½ × r² × θ.
Pizza Slice Example
Think of a large pizza cut into slices. If the pizza has a radius of 14 inches and each slice makes a 60° angle, the area of that slice is A = ½ × r² × θ (in radians). Substituting, A = 0.5 × 14² × (60 × π/180) = 102.1 in². The calculator gives this instantly, showing how much cheese and toppings each slice really holds.
Why Sector Areas Are Important
Sectors appear in many real applications, from circular gardens to pie charts. Knowing the sector’s area helps in calculating land use, design coverage, or even interpreting data visuals. The sector calculator simplifies these problems by letting you input radius and angle directly, avoiding mistakes with fractional π values.
Formula Breakdown
The sector formula is A = ½ × r² × θ, where θ is the central angle in radians. If θ is given in degrees, it must be converted by multiplying with π/180. For example, with r = 5 m and θ = 90°, A = 0.5 × 25 × (π/2) = 19.63 m². The calculator applies this conversion automatically for convenience.
Practical Design Use
Landscape designers often create circular flower beds divided into sectors. Suppose a bed has a radius of 4 m and a sector angle of 120°. The area is A = 0.5 × 16 × (120 × π/180) = 16.76 m². The calculator provides this instantly, helping designers allocate different plant groups accurately.
Learning Geometry Concepts
Students learn that a circle is made up of 360° of sectors. The calculator demonstrates this by showing how smaller angles give smaller areas. For example, with r = 10 cm, a 30° sector is 26.18 cm², while a 180° sector is 157.08 cm². Seeing this progression reinforces the relationship between angle and area.
Comparing Sectors and Circles
The sector is just a fraction of the circle’s total area. For example, a circle with radius 12 ft has total area 452.39 ft². A 90° sector has one-fourth of that, or 113.1 ft². The calculator makes these comparisons easy, showing how changing the angle directly changes the fraction of the circle being measured.
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