Circle Calculator

Circle is evaluated from Known Value, Value and Arc/Sector Angle. The calculation reports Radius, Diameter and Circumference.

Results

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About the Circle Calculator

Circle is treated here as a quantitative relation between Known Value, Value and Arc/Sector Angle and Radius, Diameter, Circumference and Area.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
C = 2pir | A = pir^2
Arc = (θ/360) x 2pir
Sector = (θ/360) x pir^2

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

C = 2pir | A = pir^2
Arc = (θ/360) x 2pir
Sector = (θ/360) x pir^2

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Olympic Running Track Inner Lane

Inputs

input_type: radius value: 36.5 angle_deg: 180
Radius: 36.5 units. Diameter: 73 units. Circumference: 229.336264 units. Area: 4,185.386813 sq units. Arc Length: 114.668132 units. Sector Area: 2,092.693406 sq units

With Known Value = radius, Value = 36.5 and Arc/Sector Angle = 180 as the stated inputs, the result is Radius = 36.5 units, Diameter = 73 units and Circumference = 229.336264 units. Each value corresponds to the declared output fields.

Example 2: Pizza Slice Area

Inputs

input_type: diameter value: 16 angle_deg: 45
Radius: 8 units. Diameter: 16 units. Circumference: 50.265482 units. Area: 201.06193 sq units. Arc Length: 6.283185 units. Sector Area: 25.132741 sq units

With Known Value = diameter, Value = 16 and Arc/Sector Angle = 45 as the stated inputs, the result is Radius = 8 units, Diameter = 16 units and Circumference = 50.265482 units. Each value corresponds to the declared output fields.

Example 3: Circular Irrigation Coverage

Inputs

input_type: radius value: 200 angle_deg: 360
Radius: 200 units. Diameter: 400 units. Circumference: 1,256.637061 units. Area: 125,663.706144 sq units. Arc Length: 1,256.637061 units. Sector Area: 125,663.706144 sq units

With Known Value = radius, Value = 200 and Arc/Sector Angle = 360 as the stated inputs, the result is Radius = 200 units, Diameter = 400 units and Circumference = 1,256.637061 units. Each value corresponds to the declared output fields.

Example 4: Gear Arc Length — Mechanical

Inputs

input_type: radius value: 6 angle_deg: 120
Radius: 6 units. Diameter: 12 units. Circumference: 37.699112 units. Area: 113.097336 sq units. Arc Length: 12.566371 units. Sector Area: 37.699112 sq units

With Known Value = radius, Value = 6 and Arc/Sector Angle = 120 as the stated inputs, the result is Radius = 6 units, Diameter = 12 units and Circumference = 37.699112 units. Each value corresponds to the declared output fields.

Common Use Cases

  • Find circumference of a circular track
  • Calculate area of a circular room or pool
  • Determine arc length of a circular path
  • Find sector area of a pie chart segment