Sheet № 153 · Foundation + Higher · AQA · Edexcel · OCR
Arc Length Formula –
Arc length is a key topic in GCSE Maths that appears on both Foundation and Higher papers across AQA, Edexcel, and OCR. An arc is a portion of the circumference of a circle, and finding its length requires combining the circumference formula with the fraction of the circle represented by the angle. This guide walks you through the formula
§Key definitions
Question:
A sector has a radius of 8 cm and an angle of 90°. Find the arc length. Give your answer to 1 decimal place.
Answer:
Arc length = 12.6 cm (1 d.p.)
Q1 (Foundation):
Find the arc length of a sector with radius 5 cm and angle 72°. Give your answer to 1 d.p.
Q2 (Foundation):
A sector has a radius of 14 cm and an angle of 180°. Find the arc length in terms of π.
Q3 (Higher):
A sector has an arc length of 20 cm and a radius of 9 cm. Find the angle at the centre to 1 d.p.
§Formulas to memorise
Arc length = (θ / 360) × 2πr
Circumference = 2πr
Identify the radius — (r) and the angle at the centre (θ) from the question or diagram.
Write the formula: — Arc length = (θ / 360) × 2πr.
Substitute — the values of θ and r into the formula.
Calculate — the answer, giving it to the degree of accuracy requested (usually 1 decimal place or in terms of π).
Worked example
A sector has a radius of 8 cm and an angle of 90°. Find the arc length. Give your answer to 1 decimal place. [DIAGRAM: circle | variant=sector | angle=90 | radiusLabel=8 cm]
Working:
⚠ Common mistakes
- ✗Using diameter instead of radius. The formula uses radius. If the question gives the diameter, halve it first before substituting.
- ✗Forgetting to multiply by 2. The circumference formula is 2πr, not πr. Missing the 2 halves your answer.
- ✗Rounding too early. Keep full calculator values until the final step, then round to the required accuracy.
✦ Exam tips
- →If the answer is requested "in terms of π", leave π in your final answer and simplify the numerical part.
- →Always check whether the question gives a radius or a diameter — this is one of the most common sources of lost marks.
- →Arc length questions can be combined with sector area questions. Make sure you use the correct formula for each part.
- →Show your substitution step clearly — this earns a method mark even if your final answer is wrong.