Circle Segment Calculator

Radius of the circle.
Central angle subtended by the segment in degrees.
Math Updated 16 Jun 2026

Circle Segment Calculator is a mathematics calculator that helps you calculate circle properties such as area, perimeter, and radius. The formula used is: Segment area = Sector area − Triangle area; Sector area = (θ/360)×π×r²; Triangle area = ½×r²×sin(θ); Chord = 2r·sin(θ/2); Arc = r×θ_rad. Ensure all inputs share the same unit system (e.g. all metres or all feet) unless the formula converts between units.

Formula

Segment area = Sector area − Triangle area; Sector area = (θ/360)×π×r²; Triangle area = ½×r²×sin(θ); Chord = 2r·sin(θ/2); Arc = r×θ_rad
  • Circle Segment Calculator gives you a fast estimate using your inputs and updates instantly when you change any value.
  • Formula: Segment area = Sector area − Triangle area; Sector area = (θ/360)×π×r²; Triangle area = ½×r²×sin(θ); Chord = 2r·sin(θ/2); Arc = r×θ_rad
  • Input definitions: • Radius (cm): the numeric radius (cm) used in the calculation • Central Angle (degrees): the numeric central angle (degrees) used in the calculation
  • Manual method: write down each input, apply the formula step by step, then compare your manual result with the calculator output.
  • Ensure all inputs share the same unit system (e.g. all metres or all feet) unless the formula converts between units.
  • Results are mathematically exact given the formula and your inputs. Rounding to decimal places may introduce small display differences.
  • Check that all inputs are in the valid range for the formula. Some operations (e.g. square root, division) require non-negative or non-zero values.
  • Practical tip: test a low, medium, and high scenario to understand sensitivity before making decisions.

Example Calculation

Inputs
  • Radius (cm): 10
  • Central Angle (degrees): 90

Suppose you enter: Radius (cm) = 10, Central Angle (degrees) = 90. The calculator applies the formula (Segment area = Sector area − Triangle area; Sector area = (θ/360)×π×r²; Triangle area = ½×r²×sin(θ); Chord = 2r·sin(θ/2); Arc = r×θ_rad) and shows all output values below. Change any input field to immediately see how the result changes.

Frequently asked questions

What is the Circle Segment?
The Circle Segment Calculator is a mathematics calculator that helps you calculate circle properties such as area, perimeter, and radius. Ensure all inputs share the same unit system (e.g. all metres or all feet) unless the formula converts between units.
When should I use this calculator?
Use this calculator whenever you need a quick, accurate result for circle properties such as area, perimeter, and radius without working through the arithmetic manually.
What units should I enter?
Ensure all inputs share the same unit system (e.g. all metres or all feet) unless the formula converts between units.
How accurate are the results?
Results are mathematically exact given the formula and your inputs. Rounding to decimal places may introduce small display differences.
How do I interpret the result?
Check that all inputs are in the valid range for the formula. Some operations (e.g. square root, division) require non-negative or non-zero values.
How can I verify the calculation manually?
Use the displayed formula and work through the numbers step by step. If your manual result differs slightly, check rounding and unit conversions first.
Can I use this for planning and budgeting?
Yes. Run best-case, expected, and worst-case inputs to compare outcomes and make safer planning decisions.

Related calculators

Circle Sector Calculator Circle Sector Calculator is a mathematics calculator that helps you calculate circle properties such as area, perimeter, and radius. The formula used is: Arc length = r×θ; Area = r²θ/2; Chord = 2r·sin(θ/2); Perimeter = arc + 2r (where θ is in radians). Ensure all inputs share the same unit system (e.g. all metres or all feet) unless the formula converts between units. Circle Area and Circumference Circle Area and Circumference is a mathematics calculator that helps you calculate the area of a geometric shape from its dimensions. The formula used is: Area = π×r²; Circumference = 2π×r; Diameter = 2r. Ensure all inputs share the same unit system (e.g. all metres or all feet) unless the formula converts between units. Chord Length Calculator Chord Length Calculator is a mathematics calculator that helps you calculate chord length values from your input data. The formula used is: Chord = 2r·sin(θ/2); Sagitta = r − r·cos(θ/2); Arc = r×θ_rad; Distance from center = r·cos(θ/2). Ensure all inputs share the same unit system (e.g. all metres or all feet) unless the formula converts between units.