Formula sheet
Circumference of circle
πd = 2πr is given on the exam formula sheet. You must still choose the right value of π (22/7 or 3.142), use the radius with 2πr and the diameter with πd, and not confuse it with the area formula.
What the symbols mean
- d Diameter, the distance straight across the circle through the centre (length unit).
- r Radius, the distance from the centre to the edge, so d = 2r (length unit).
- π Pi ≈ 3.142 or 22/7; the fixed ratio of circumference to diameter.
Given in the exam, or memorise?
πd = 2πr is given on the exam formula sheet. You must still choose the right value of π (22/7 or 3.142), use the radius with 2πr and the diameter with πd, and not confuse it with the area formula.
Why it works
π is defined as the ratio of a circle's circumference to its diameter.
- For every circle, circumference ÷ diameter is the same constant, π.
- So circumference = π × diameter = πd.
- Since d = 2r, this is also 2πr.
Worked example 1
A circular plate has radius 7 cm. Find its circumference.
(Use π = 22/7)
- Circumference = 2πr
- = 2 × 22/7 × 7
- = 2 × 22 = 44
Worked example 2
The circumference of a circle is 66 cm. Find its diameter.
(Use π = 22/7)
- Circumference = πd
- 66 = 22/7 × d
- d = 66 × 7 ÷ 22
- d = 462 ÷ 22 = 21
Where students go wrong
- Putting the diameter into 2πr, or the radius into πd, which doubles or halves the answer.
- Using this circumference formula when the question actually asks for area (πr²).
- Choosing π = 22/7 when the radius is not a multiple of 7, 3.142 is often cleaner then.
- Forgetting the answer is a length (cm), not an area.
Use it with
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
Which do I use, πd or 2πr?
They give the same answer because d = 2r. Use πd when the question gives the diameter, and 2πr when it gives the radius, that saves you a conversion step.
If you are handed a radius but use πd, remember to double it to d first, or you will halve the true circumference.
Should I use 22/7 or 3.142 for π?
Follow what the question states. If it names a value, use exactly that.
If it does not, pick whichever is neater: 22/7 works cleanly when the radius or diameter is a multiple of 7; otherwise 3.142 is usually easier. Both are accepted on the formula sheet, so the choice is about clean arithmetic.
What is the difference between circumference and area?
Circumference is the distance around the circle, measured in cm, using πd or 2πr. Area is the space inside, measured in cm², using πr².
A quick check: a length answer has single units (cm), an area answer has square units (cm²). Reading the units in the question tells you which formula is wanted.