Área Setor Circular (radianos)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
A = r²θ/2
About this calculator
The circular sector area calculator in radians allows you to quickly compute the area of a slice of a circle using the radius and the central angle in radians. The formula used is A = (r² * θ) / 2, where r is the radius and θ is the angle in radians. This tool is useful for students, engineers, and professionals working with geometry or projects involving circular sectors.
To use the calculator, enter the radius and the angle in radians. The result is the sector area. Remember that the angle must be in radians; if you have the angle in degrees, convert by multiplying by π/180. The calculator can also be used for inverse problems, such as finding the radius from the area and angle.
Circular sectors appear in practical situations like calculating the area of pizza slices, gear sectors, fans, or parts of circles in architecture and design projects. They are also common in physics problems, such as moment of inertia of sectors. The accuracy of the calculation depends on the precision of the input values.
Be careful when using the calculator: ensure the angle is in radians. A common mistake is entering degrees without conversion, leading to incorrect area. Also, make sure the radius and angle are positive. For angles greater than 2π radians, the sector exceeds a full circle, but the formula still works.
Frequently asked questions
How do I convert degrees to radians?
Multiply the angle in degrees by π/180. For example, 90° = 90 * π/180 = π/2 radians.
Does the formula work for angles greater than 360°?
Yes, the formula A = r²θ/2 works for any angle in radians, even above 2π. The result will be the corresponding sector area.
What is the difference between a circular sector and a circular segment?
A circular sector is the region bounded by two radii and the arc. A circular segment is the region between the chord and the arc, excluding the triangle formed by the radii.
Can I use this calculator to find the radius if I know the area and angle?
Yes, rearrange the formula: r = √(2A/θ). Enter the area and angle in radians to get the radius.
What if the angle is given in degrees?
Convert to radians before using the calculator. Use the conversion: radians = degrees * π/180.