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Inscribed Angle, Intercepted Arc and Central Angle
Yes. The intercepted arc lies opposite the inscribed vertex. The central sweep is twice the inscribed angle, and its radian value times radius gives arc length. Major arcs are allowed within the stated open bounds.
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
Example in initial displayed units: Inscribed angle θᵢ 45, Radius 2 gives Central angle θ꜀ 90, Arc length 3.141593.
θc = 2θi; intercepted arc length = rθc (radians)
Worked example
Enter these known values and leave the other values blank.
- Inscribed angle θᵢ
- 45 deg
- Radius
- 2 m
- Central angle θ꜀
- 90 deg
- Arc length
- 3.1416 m
Assumptions and limitations
- The inscribed and central angles subtend the same intercepted arc, opposite the circle point carrying the inscribed vertex. This arc can be major or minor. The inscribed angle is strictly between 0° and 180°, and the central sweep is strictly between 0° and 360°.
- Use compatible units and enough independent values. Clear unknowns before solving backward. Original reference drawings are schematic and do not scale to entered values.
Common questions
Do inscribed and central angles need the same intercepted arc?
Yes. The intercepted arc lies opposite the inscribed vertex. The central sweep is twice the inscribed angle, and its radian value times radius gives arc length. Major arcs are allowed within the stated open bounds.
References
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.