Sector Area Calculator
Find the area and arc length of a circle sector.
A sector is a 'pie slice' of a circle.
How the Math Works
The Sector Area Calculator uses two fundamental formulas to analyze circular sectors. The area formula, (angle/360) π r², works by determining what fraction of the full circle the sector represents (angle divided by 360 degrees) and then multiplying that fraction by the total area of the circle (π r²). Similarly, the arc length formula, (angle/360) 2πr, calculates the portion of the circumference that forms the sector's curved edge by applying the same fractional approach to the full circumference (2πr). Both formulas elegantly scale the complete circle measurements proportionally to the sector's angle.
Practical Applications
To use this calculator practically, simply enter the sector's angle in degrees and the circle's radius. For example, if you need to find the area of a pizza slice that's 45 degrees from a 12-inch diameter pizza, you'd input 45 for the angle and 6 for the radius. The calculator instantly returns both the slice's area and the length of its crust edge. This saves time compared to manual calculations, especially when working with multiple sectors or complex problems involving circle geometry in academic or professional settings.
Day-to-Day Use
This calculator proves useful in everyday scenarios like determining how much pizza or cake each person gets when cutting rounds into proportional slices, planning circular garden beds or round patios, or calculating material needs for circular decorations and crafts. Whether you're a homeowner planning a circular flower bed, a student tackling geometry homework, or someone designing a round table setting, quickly finding sector areas and arc lengths helps ensure accurate measurements and efficient use of resources in countless practical situations.
Worked example
r 5, 60° → area 13.1, arc 5.24.
FAQ
Full circle?
At 360° you get the whole circle's area and circumference.