yCalculator

Circle Calculator

Last updated: April 2026

Enter any one value

Type into one field and the others are solved from that measurement.

Circle properties

Radius5 cm
Diameter10 cm
Circumference31.4159 cm
Area78.5398 cm²
thetaarcchordrd = 2r, C = 2pi r, A = pi r^2
Arc, sector and chord calculations

Arc length

7.854 cm

Sector area

19.635 cm²

Chord length

7.0711 cm

Segment area

7.135 cm²

Step-by-step working
  1. Known radius: r = 5
  2. d = 2r = 2 x 5 = 10
  3. C = 2pi r = 2 x pi x 5 = 31.4159
  4. A = pi r^2 = pi x 25 = 78.5398
  5. theta = 90 degrees = 1.5708 radians
  6. Arc length L = r x theta = 5 x 1.5708 = 7.854
  7. Sector area = 1/2 x r^2 x theta = 1/2 x 25 x 1.5708 = 19.635
  8. Chord length = 2r x sin(theta/2) = 2 x 5 x sin(0.7854) = 7.0711
  9. Segment area = 1/2 x r^2(theta - sin theta) = 7.135

Pi precision note

pi used: 3.14159265358979... Results are rounded to 4 decimal places.

Circle formulas and derivations

A circle can be solved from one measurement because radius, diameter, circumference, and area are all linked by pi.

What is pi?

Pi is the constant ratio between a circle's circumference and its diameter. It begins 3.14159 and continues forever without repeating.

Arc length and sector area explained

A central angle selects part of a circle. The same fraction of 360 degrees applies to circumference for arc length and to total circle area for sector area.

What does this mean?

This calculator is designed to help you understand the likely number before you make a decision or start an application.

Your result should be checked against official UK guidance, especially if your circumstances include dependants, exemptions, prior leave, or a complex immigration history.

Treat the figure as a planning tool rather than legal advice. Where the answer affects an application deadline or major payment, speak to an authorised adviser.

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