Question 1

How do radius, diameter, circumference and area relate?

Accepted Answer

Diameter is twice the radius. Circumference is 2πr, or πd. Area is πr². Knowing any one gives the other three: from circumference, r = C ÷ 2π; from area, r = √(A ÷ π). The calculator solves in every direction, which matters because in practice you often can measure only one of them.

Question 2

Why is π irrational, and how many digits do I need?

Accepted Answer

π is the ratio of any circle's circumference to its diameter, and it cannot be expressed as a fraction of whole numbers — proved in 1761. For practical work, 3.14159 is accurate to about one part in a million. NASA uses 15 decimal places for interplanetary navigation; 40 places would compute the circumference of the observable universe to within an atom's width.

Question 3

Why does area use radius squared rather than diameter?

Accepted Answer

Because area scales with the square of any linear dimension. Doubling the radius quadruples the area, which is why a 16-inch pizza has substantially more than twice the food of a 12-inch one — 78 square inches more, about 78% extra. The same relationship makes large pipes carry disproportionately more flow than their diameter suggests.

Question 4

What is the difference between an arc, a sector and a segment?

Accepted Answer

An arc is part of the circumference — a curved line. A sector is the pie-slice bounded by two radii and an arc. A segment is the region cut off by a straight chord, the shape left when you slice the top off a circle. Their formulas differ, and picking the wrong one is a frequent error in coursework.

Question 5

How do I find arc length and sector area?

Accepted Answer

Both are fractions of the whole circle set by the angle. Arc length is (θ ÷ 360) × 2πr in degrees, or simply rθ in radians. Sector area is (θ ÷ 360) × πr², or ½r²θ in radians. The radian forms are markedly simpler, which is one of the practical reasons radians are preferred in higher mathematics.

Question 6

How do I measure the radius of something I cannot reach the centre of?

Accepted Answer

Measure a chord and the perpendicular height from its midpoint to the arc — the sagitta. Then r = (h ÷ 2) + (c² ÷ 8h). This is how you find the radius of an existing curved wall, a pipe fragment or a wheel rim without needing access to the centre, and it is a genuinely useful workshop technique.

Radius of a Circle Calculator

Everyday Uses

Any circle measurement

Comparing sizes

Arcs and sectors

Workshop measuring

Turning wheel revolutions into distance

Tree diameter from a tape measure

Frequently Asked Questions

How do radius, diameter, circumference and area relate?

Why is π irrational, and how many digits do I need?

Why does area use radius squared rather than diameter?

What is the difference between an arc, a sector and a segment?

How do I find arc length and sector area?

How do I measure the radius of something I cannot reach the centre of?

Related Calculators

Everyday Uses

Any circle measurement

Comparing sizes

Arcs and sectors

Workshop measuring

Turning wheel revolutions into distance

Tree diameter from a tape measure

Frequently Asked Questions

How do radius, diameter, circumference and area relate?

Why is π irrational, and how many digits do I need?

Why does area use radius squared rather than diameter?

What is the difference between an arc, a sector and a segment?

How do I find arc length and sector area?

How do I measure the radius of something I cannot reach the centre of?