Circles: Radius, Diameter, Circumference

G5Circles

Radius, diameter and the edge all round.

A circle's parts have special names — and one key relationship: d = 2r.

The parts of a circle.

diameter = 2 × radius

Centre → edge = radius · edge → edge through the centre = diameter · all round the edge = circumference.

Learn the Parts

1Radius.

Centre to the edge. Every radius of a circle is the same length.

2Diameter.

Edge to edge THROUGH the centre — twice the radius: d = 2r.

d = 2r

3Circumference.

The distance all the way round the edge — the circle's perimeter.

all round ⭕

💡 Key Idead = 2r works both ways: radius = diameter ÷ 2. A circle with diameter 12 cm has radius 6 cm.

Worked Example

Fill the gaps.

radius 5 cm → diameter?

2 × 5 = 10

10 cm

diameter 18 cm → radius?

18 ÷ 2 = 9

9 cm

Which is longer — a radius or a diameter?

diameter, always

Watch Out! Common Mistakes

A ‘diameter’ missing the centre.

Careful! A line edge-to-edge that misses the centre is a chord, and it’s shorter than the diameter. The diameter must pass through the centre.

Doubling when you should halve.

d = 18 → r = 36 ✕

Wrong way! The radius is the smaller one: 18 ÷ 2 = 9.

Calling the circumference ‘area’.

Wrong! Circumference is the distance around (a length); area is the surface inside. Same distinction as perimeter vs area.

⬇ Cheat Sheet

CIRCLES

Radius: centre → edge.
Diameter: edge → edge through the centre; d = 2r.
Circumference: the distance all round.
Radius = diameter ÷ 2.

Examples: r 5 → d 10 · d 18 → r 9

📄 Free printable: Download the Circles cheat sheet (PDF) — keep it by your child's desk.

Quick summary

Radius runs from the centre to the edge; all radii are equal.
Diameter runs edge to edge through the centre: d = 2r.
Circumference is the distance around the circle.
Radius = diameter ÷ 2 — know it both ways.

Frequently asked questions

What is the difference between radius and diameter?

The radius goes from the centre to the edge; the diameter goes right across through the centre. The diameter is always exactly twice the radius.

What is the circumference?

The distance all the way around the circle — its perimeter. (Calculating it with π comes at secondary school; KS2 needs the name and idea.)

What circle facts does Year 6 need?

Naming radius, diameter and circumference, and using diameter = 2 × radius in both directions.

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G4 Regular and Irregular Polygons

Circles