Maths for electricians · Topic 3 of 6

Areas, circles and π

About 3 minutes · Diagrams, worked examples and a mini test

Cable sizes are areas: 2.5 mm² is the cross-sectional area of the copper. Floor areas decide how many socket circuits you need. So area comes up all the time.

Rectangles and triangles

• Rectangle: area = length × width. A 4 m × 5 m room is 20 m².
• Triangle: area = ½ × base × height. A gable wall 6 m wide and 4 m high is 12 m².

Circles and π

π (pi) is the number of times a circle's diameter fits round its edge: about 3.142. Use the π key on your calculator.

• Area = π × r², or π × d² ÷ 4 if you know the diameter.
• Circumference (distance round) = π × d.

Worked example: a 2.5 mm² conductor

A solid 2.5 mm² conductor is about 1.78 mm across. Its area is π × 1.78² ÷ 4 = π × 3.17 ÷ 4 = 2.49 mm², which rounds to 2.5 mm².

Going the other way, the diameter is d = √(4 × A ÷ π). For 6 mm²: √(24 ÷ π) = 2.76 mm.

Converting area units

Because area is two lengths multiplied, the conversion is squared too: 1 m = 1,000 mm, so 1 m² = 1,000 × 1,000 = 1,000,000 mm².

Exam tip: check whether a question gives the radius or the diameter. Using the diameter in πr² makes the answer four times too big.

Try it: Conduit fill calculator