Key takeaway: Radius and diameter are the two basic lengths of a circle: the radius reaches from the center to the edge, and the diameter, through the center, is exactly twice as long.
Grade 77.G.B.4Geometry and Measurement
Definition of Radius and Diameter
The radius and diameter are the two basic measurements of a circle. The radius runs from the center to the edge. The diameter runs from one edge to the opposite edge and must pass through the center, so it spans the full width.
Every radius of one circle has the same length, and every diameter has the same length too. Two radii laid end to end in a straight line make one diameter. Knowing one measurement gives you the other at once, which is why circle formulas can use either.
Formula and notation
The letters \(r\) and \(d\) name the lengths, and they are linked by
\[d = 2r \qquad \text{and} \qquad r = \frac{d}{2}\]
Always read a problem carefully: a circle labeled “14 ft across” gives \(d = 14\), so \(r = 7\).
Key facts
- The diameter is the longest chord of a circle.
- Halving a diameter always gives the radius.
- Words like “across” and “wide” usually signal the diameter, not the radius.
- Mixing up radius and diameter is the top cause of wrong circle answers.
Radius and Diameter example
A round trampoline in Maya’s backyard measures 14 feet across. A pizza at the corner shop has a radius of 6.5 inches. Find the radius of the trampoline and the diameter of the pizza.
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“Across” means diameter, so \(d = 14\) feet for the trampoline.
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Radius: \(r = \frac{14}{2} = 7\) feet.
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Pizza diameter: \(d = 2 \times 6.5 = 13\) inches.
The trampoline has radius 7 feet, and the pizza has diameter 13 inches.
Common mistake
Watch out
A bike tire is labeled 26 inches across. Jonah writes \(r = 26 \times 2 = 52\) inches for its radius.
Why it is wrong
A label “26 inches across” is a diameter, and the radius is half of it, not double. Correct: \(r = 26 : 2 = 13\) inches. A radius can never be longer than the diameter of the same circle, which is a quick way to catch this slip.
Related terms and lessons
Browse the glossary: A–Z list · Grade 7 vocabulary · Geometry and Measurement