▶ Practice this concept

🧱 See It

Picture a bicycle wheel rolling one full turn. The distance it travels along the ground in that single rotation is exactly the distance around the outside edge of the wheel — that distance is called the circumference.

Every circle has two key measurements for its size: the diameter (a straight line across the circle, passing right through the center) and the radius (a straight line from the center out to the edge — exactly half the diameter).

✏️ Draw It

diameter = 8 cm radius = 4 cm

The radius (4 cm) is just the right half of the diameter line (8 cm) — diameter is always 2 × radius, no matter how big or small the circle is.

🔢 Write It

Circumference = 3.14 × diameter

(also written C = πd)

Circumference = 2 × 3.14 × radius

3.14 (the number written as π) is not a rounded guess for one circle — it's the same fixed ratio between circumference and diameter for every circle that has ever existed, tiny or huge.

💡 Worked Examples

Example 1 — Circle with diameter: 10 cm

  1. Formula: C = 3.14 × diameter
  2. Plug in: C = 3.14 × 10
  3. Multiply: C = 31.4
  4. Answer: C = 31.4 cm

Example 2 — Circle with radius: 7 cm

  1. Only the radius is given — find the diameter first: diameter = 2 × 7 = 14 cm
  2. Formula: C = 3.14 × diameter
  3. Plug in: C = 3.14 × 14
  4. Multiply: C = 43.96
  5. Answer: C = 43.96 cm

🧠 Quick Reference

Circumference = pi (3.14) times the diameter. No diameter given? Double the radius first.

Quick reminder: diameter = 2 × radius

👪 For Parents & Tutors

BC Curriculum (Level 2 / Grade 7, Geometry & Measurement): "Circumference and area of circles."

Big Idea: "The constant ratio between the circumference and diameter of circles can be used to describe, measure, and compare spatial relationships."

Watch for: confusing radius and diameter — plugging the radius straight into C = 3.14 × diameter without doubling it first, or the reverse, halving a diameter that didn't need it. Have him write down both the radius and the diameter explicitly before choosing a formula, rather than assuming which one a question gave him.

Comes up again: this trap resurfaces immediately in the sibling Area of Circles page, and again in this level's Volume of Cylinders and Circle Graphs pages.