Arc length
Click to explore updated revision resources for GCSE Maths: Arc lengths of a circle, with step-by-step slideshows, quizzes, practice exam questions, and more!
A chord separates the circumference of a circle into two sections - the major arc and the minor arc.
It also separates the circle into two segments - the major segment and the minor segment.
The formula to calculate the arc length is: \(\text{Arc length} = \frac{\text{angle}}{360^\circ} \times \pi \text{d}\)
Example
Calculate the arc length to 2 decimal places.
First calculate what fraction of a full turn the angle is.
90° is one quarter of a full turn (360°).
The arc length is \(\frac{1}{4}\) of the full circumference.
Remember the circumference of a circle = \(\pi d\) and the diameter = \(2 \times \text{radius}\).
The arc length is \(\frac{1}{4} \times \pi \times 8 = 2 \pi\). Rounded to 3 significant figures the arc length is 6.28cm.
Question
Calculate the minor arc length to one decimal place.
\(\text{Arc length} = \frac{144^\circ}{360^\circ} \times \pi \times 7 = 8.8~\text{cm}\)
Question
Calculate the major arc length to one decimal place.
The major sector has an angle of \(360^\circ - 110^\circ = 250^\circ\).
\(\text{Arc length} = \frac{250^\circ}{360^\circ} \times \pi \times 12 = 26.2~\text{cm}\)
More guides on this topic
- NEW: Angles
- NEW: Angles in parallel lines
- NEW: Polygons
- NEW: Line and rotational symmetry
- NEW: Constructing triangles
- NEW: Ruler and compass constructions
- NEW: Loci
- NEW: Bearings
- NEW: Perimeter
- NEW: Area
- NEW: Volume of a prism
- NEW: Surface area of a prism
- NEW: Pyramids, cones and spheres
- NEW: Nets, plans and elevations
- NEW: Circumference and arc length
- NEW: Area of circles and sectors
- NEW: Higher – Circle Theorems – Calculating angles using circles
- NEW: Higher – Using the alternate segment theorem, tangents and chords
- NEW: Reflection
- NEW: Rotation
- NEW: Translation
- NEW: Enlargement
- NEW: Higher − Negative enlargements
- NEW: Higher – Combined transformations and invariant points
- NEW: Congruent and similar shapes
- NEW: Higher – Similarity in 2D and 3D shapes
- NEW: Pythagoras' theorem
- NEW: Solving 2D and 3D problems using Pythagoras' theorem
- NEW: Right-angled trigonometry
- NEW: Exact trigonometric values
- NEW: Higher – Sine rule
- NEW: Higher – Cosine rule
- NEW: Higher – 2D and 3D trigonometry problems
- NEW: Vectors
- NEW: Higher – Geometric problems using vectors
- Angles, lines and polygons - AQA
- Loci and constructions - AQA
- 2-dimensional shapes - AQA
- 3-dimensional shapes - AQA
- Circle theorems - Higher - AQA
- Transformations - AQA
- Pythagoras' theorem - AQA
- Units of measure - AQA
- Trigonometry - AQA
- Vectors - AQA
