Question 1

How do I calculate the area of a circle?

Accepted Answer

Use A = π × r². Square the radius and multiply by π ≈ 3.14159. Example: r = 5 cm gives A = π × 25 = 78.54 cm². If you know the diameter, A = π × d² ÷ 4.

Question 2

How do I calculate the circumference of a circle?

Accepted Answer

Use C = 2 × π × r or, equivalently, C = π × d. A circle with a 10 cm diameter has a circumference of π × 10 = 31.42 cm.

Question 3

How do I find the diameter from the circumference?

Accepted Answer

Divide the circumference by π: d = C ÷ π. A tree trunk with a girth of 157 cm therefore has a diameter of about 157 ÷ 3.14159 = 49.97 cm, roughly 50 cm. The radius is r = C ÷ (2 × π).

Question 4

How do I find the radius from the area?

Accepted Answer

Divide the area by π and take the square root: r = √(A ÷ π). For A = 1 m² that gives r = 0.5642 m, i.e. a diameter of 1.128 m.

Question 5

What is the difference between radius and diameter?

Accepted Answer

The radius r runs from the centre to the edge, the diameter d straight through the centre from edge to edge. The diameter is therefore always twice the radius: d = 2 × r.

Question 6

How do I calculate the area of an annulus (ring)?

Accepted Answer

Subtract the area of the hole from the area of the large circle: A = π × (R² − r²). Example: R = 10 cm, r = 6 cm gives π × (100 − 36) = 201.06 cm².

Question 7

How do I calculate a circle sector?

Accepted Answer

A sector is the share α ÷ 360° of the circle. Arc length b = 2 × π × r × α ÷ 360°, area A = π × r² × α ÷ 360°. A 60° slice of a circle with r = 10 cm has a 10.47 cm arc and an area of 52.36 cm².

Question 8

What is the difference between a sector and a segment?

Accepted Answer

A sector is bounded by two radii and the arc – like a slice of cake with its tip at the centre. A segment is bounded by a chord and the arc – like an arch. Its area is the sector's area minus the triangle formed by the two radii and the chord.

Question 9

How do I find the radius of an arc from chord and height?

Accepted Answer

Use r = s² ÷ (8 × h) + h ÷ 2. An arch with a 12 cm span (chord s) and a 2 cm rise (height h) has a radius of 144 ÷ 16 + 1 = 10 cm.

Question 10

Is it enough to calculate with π = 3.14?

Accepted Answer

For most everyday tasks, yes: 3.14 is only 0.05% off the exact value. For a circle with a 1 m radius that is 16 cm² too little area. 22/7 is 0.04% too high; 355/113 is accurate to six decimal places.

Question 11

How do I convert degrees to radians?

Accepted Answer

Multiply by π ÷ 180°: 90° = π/2 ≈ 1.5708, 180° = π, 360° = 2π. In radians the arc length becomes particularly simple: b = r × α.

Guide: Circle Calculator

Circle Formulas: Circle, Annulus, Sector and Segment Explained

Area of a Circle: A = πr² with Examples (and Why Two Small Pizzas Are Less)

Circumference of a Circle – and the Diameter from the Circumference

The Number π: What It Means and How Precise You Need to Be

Circle Sector, Arc Length and Radians Explained Simply

You might also find useful

Area Calculator

Volume Calculator

Online Calculator

Rule of Three Calculator