Curriculum fit: GCSE Maths Geometry and measures (Foundation and Higher). US: Grade 7 and Geometry (Geometric Measurement and Dimension).
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What Is It?
The radius of a circle is the distance from the centre to the edge. The diameter is twice the radius, and the circumference is the distance around the circle. Area is the space inside.
Both the circumference and the area depend on π, which is about 3.14. You can leave answers in terms of π for an exact result.
Key Formulas and Ideas
- Circumference C = 2πr = πd.
- Area A = πr².
- Diameter d = 2r.
- Semicircle: half the area, and half the circumference plus the diameter for the perimeter.
Worked Examples
Circumference and Area
Find the circumference and area of a circle with radius 5 cm.
- C = 2πr = 2 × π × 5 = 10π ≈ 31.4.
- A = πr² = π × 25 = 25π ≈ 78.5.
✓ Answer C ≈ 31.4 cm, A ≈ 78.5 cm²
From the Diameter
A circle has diameter 10 cm. Find its area.
- Radius = 10 ÷ 2 = 5.
- A = π × 5² = 25π ≈ 78.5.
✓ Answer 78.5 cm²
Semicircle
Find the area of a semicircle with radius 4 cm.
- Area of a full circle = π × 16 = 16π.
- Half of it: 8π ≈ 25.1.
✓ Answer 25.1 cm²
Common Mistakes to Avoid
- Using the diameter instead of the radius in πr².
- Mixing up the circumference and area formulas.
- Forgetting to square the radius.
- Giving area in cm instead of cm².
Practice Questions
Frequently Asked Questions
Why are the area units squared?
Area measures surface, so the units are length times length, for example cm².
Should I use 3.14 or the π button?
Use the π button unless the question tells you to use 3.14, since it is more accurate.
Keep Going With These Guides
Circle Theorems Explained: Rules, Examples and Reasons
Learn the main circle theorems and use them to find angles with a reason for every step. GCSE Higher and high school Geometry, with worked examples.
GCSEA-LevelHigh SchoolVolume and Surface Area of 3D Shapes: Formulas and Examples
Find the volume and surface area of cuboids, prisms, cylinders, cones and spheres, with worked examples and a quick formula list.
GCSEHigh SchoolArea of 2D Shapes: Rectangle, Triangle, Trapezium and More
Calculate the perimeter and area of rectangles, triangles, parallelograms, trapeziums (trapezoids) and compound shapes, with worked examples.
KS3GCSEMiddle SchoolHigh SchoolSources and Review
- DfE: GCSE mathematics subject content and assessment objectives
- Common Core State Standards: Mathematics (high school)
Reviewed by StudyMorrow editorial review on 5 Nov 2026.