Compute sector area, arc length, segment area, and chord length — consistent with ProMathTools conversion-style pages.
Angle in degrees (0-360)
The circle sector and segment calculator computes the area and arc length of sectors, and the area and chord length of segments. A sector is the region bounded by two radii and an arc, while a segment is the region between a chord and its arc.
Sector Area = (θ/360) × πr² = (θ × r²) / 2 (in radians)\nArc Length = r × θ (in radians)\nSegment Area = Sector Area - Triangle Area\nChord Length = 2r × sin(θ/2)
Radius of the circle
Central angle in degrees or radians
Sector Area = (60/360) × π × 5² = (1/6) × 25π ≈ 13.09 Arc Length = 5 × (60° × π/180) = 5π/3 ≈ 5.24
Sector Area = (90/360) × π × 10² = 25π ≈ 78.54 Triangle Area = (10² × sin(90°)) / 2 = 50 Segment Area = 78.54 - 50 = 28.54
A circle sector is the region between two radii and the arc that connects them, while a circle segment is the region between a chord and the arc that connects the endpoints of the chord. The calculator can calculate area, arc length, and chord length for both circle sectors and segments. To use the calculator, simply select the type of calculation you want to perform and enter the required values. The calculator will then provide the results instantly.
To calculate the area of a circle sector, you need to know the radius of the circle and the central angle of the sector. The calculator can calculate the area of a circle sector using the formula A = (θ/360) * πr^2, where A is the area, θ is the central angle in degrees, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle. Simply enter the values into the calculator and it will provide the result.
The formula for calculating the arc length of a circle sector is L = (θ/360) * 2πr, where L is the arc length, θ is the central angle in degrees, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle. The calculator can calculate the arc length of a circle sector using this formula. To use the calculator, simply enter the radius and central angle, and the calculator will provide the arc length.
Yes, the calculator can calculate the chord length of a circle segment. To do this, you need to know the radius of the circle and the central angle of the segment. The calculator uses the formula c = 2r * sin(θ/2), where c is the chord length, r is the radius of the circle, and θ is the central angle in degrees. Simply enter the values into the calculator and it will provide the chord length of the circle segment.
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