The area of a circle is the amount of flat space inside the circle, measured in square units. It equals pi times the radius squared: A = π r2. A circle with radius 5 cm has area 25π, about 78.5 square centimeters. If you know the diameter, halve it first to get the radius.
Slice the circle into thin wedges and lay them head to tail. The shape approaches a rectangle that is π r long and r tall, so its area is π r2.
Formal definition and notation
For a circle of radius r, the area of the region it encloses (the disk) is A = π r2. Equivalent forms: A = π d24 in terms of the diameter d, and A = C24π in terms of the circumferenceC. The formula follows from cutting the disk into thin wedges and rearranging them into a shape that approaches a rectangle with sidesπ r and r.
Circumference is the distance around, 2π r, in plain units. Area is the space inside, π r2, in square units. For r = 2: C = 4π, A = 4π, same number but different units.
Quick check: 3 questions
Question 1 of 3
What is the area of a circle with radius 9 cm?
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Answer: B.A = π × 92 = 81π. 18π doubles instead of squaring (that is the circumference), 324π uses the diameter 18 as the radius, and 9π forgets to square.
Question 2 of 3
A pizza has a 14-inch diameter. Using π ≈ 227, what is its area?
Show answer and explanation
Answer: C.r = 7, so A = 227 × 49 = 154. 616 uses 14 as the radius, 44 is the circumference, and 308 forgets that the area uses r2, not 2r2.
Question 3 of 3
If a circle’s radius triples, its area becomes:
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Answer: D.π(3r)2 = 9π r2, so 9 times. 3 times would be true for the circumference, 6 confuses squaring with doubling, and 27 is cubing, which is how volume scales.
Area of a Circle: frequently asked questions
How do you find the area of a circle with the diameter?
Divide the diameter by 2 to get the radius, then use A = π r2. For a diameter of 12 in, r = 6 and A = 36π ≈ 113.1in2. You can also use A = π d24 directly: π × 1444 = 36π. Both give the same answer.
Why is the area of a circle pi r squared?
Cut the circle into many thin wedges, like pizza slices, and arrange them in a row, alternating point up and point down. The result is close to a rectangle whose height is the radius r and whose length is half the circumference, π r. Rectangle area is length times height: π r × r = π r2. More slices make it closer to exact.
How do you find the area of a circle from the circumference?
First find the radius from C = 2π r, then use A = π r2. If C = 20π cm, then r = 10 cm and A = 100π ≈ 314.2cm2. A shortcut formula is A = C24π, which gives the same result in one step. Check the units at the end: the circumference is a length, but the area must be in square units.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 7.G.B.4, CCSS HSG-GMD.A.1
Cite this entry
Effortless Math Team. “Area of a Circle.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/area-of-a-circle/
Flashcard
TermArea of a Circlespace inside a circle
DefinitionA = π r2, in square units. Radius 4 cm gives 16π ≈ 50.3cm2. Halve a diameter first.
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